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Citation: Bartulovi´c, D.; Steiner, S.;
Fakleš, D.; Mavrin Jeliˇci´c, M.
Correlations among Fatigue
Indicators, Subjective Perception of
Fatigue, and Workload Settings in
Flight Operations. Aerospace 2023,10,
856. https://doi.org/10.3390/
aerospace10100856
Academic Editor: Julius Keller
Received: 8 August 2023
Revised: 21 September 2023
Accepted: 24 September 2023
Published: 29 September 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
aerospace
Article
Correlations among Fatigue Indicators, Subjective Perception of
Fatigue, and Workload Settings in Flight Operations
Dajana Bartulovi´c 1, * , Sanja Steiner 2, Dario Fakleš 3and Martina Mavrin Jeliˇci´c 1
1Faculty of Transport and Traffic Sciences, University of Zagreb, 10000 Zagreb, Croatia
2Croatian Academy of Sciences and Arts, Traffic Institute, 10000 Zagreb, Croatia
3Croatia Airlines, 10010 Zagreb, Croatia
*Correspondence: dbartulovic@fpz.unizg.hr
Abstract:
Conducting flight operations at the pace of air traffic relies on shift work, overtime work,
work at night, work in different and numerous time zones, and unbalanced flight crew schedules.
Such working hours and workload settings can cause disturbances of the circadian rhythm and
sleep disorders among flight crew members; this can result in fatigue and can have an impact on
the safety of flight operations. Fatigue impacts many cognitive abilities such as vigilance, memory,
spatial orientation, learning, problem solving, and decision making. In aviation, fatigue has been
identified as a hazard to the safety of flight operations. This paper describes objectivation methods
for data collecting processes regarding flight crew fatigue, using an electronic system of standardized
chronometric cognitive tests and subjective self-assessment surveys on the subjective perception of
fatigue. The data collected were analyzed using statistical methods to identify and quantify elements
that affect the appearance of fatigue. Finally, causal modeling methods were used to determine
correlations among the measured flight crew fatigue indicators, the subjective perception of fatigue,
and the defined workload settings. The results of this research reveal which elements strongly impact
flight crew fatigue. The detected correlations can help define improved measures for the mitigation
of fatigue risk in future flight operations.
Keywords:
correlations; fatigue indicators; subjective perception; workload settings; flight operations
1. Introduction
The growth in worldwide air traffic, including international long-haul flights, national
short-haul flights, night flights, and cargo flights, imposes a 24-h work schedule. Performing
flight operations at the pace of today’s air traffic relies on shift work, overtime work, work
at night, and work in different and numerous time zones, i.e., varied and unbalanced flight
crew schedules. These working hours and workload settings can cause disturbances of
the circadian rhythm and sleep disorders among flight crew members; this can result in
fatigue and can have an impact on the safety of flight operations [
1
,
2
]. Fatigue impacts
many cognitive abilities such as vigilance, memory, spatial orientation, learning, problem
solving, and decision making. In aviation, fatigue has been identified as a hazard to the
safety of flight operations. Due to this, fatigue risk has been widely analyzed and assessed.
Due to the severity of fatigue risk, it is necessary to implement risk mitigation measures.
Aside from the provisions of the Flight Time Limitations (FTL) regulations [
3
,
4
], a vital role
in fatigue risk mitigation is played by the Fatigue Risk Management System (FRMS), which
uses various quantification and objectivation methods to measure fatigue [5,6].
The Fatigue Risk Management System (FRMS), as defined by the International Civil
Aviation Organization (ICAO), represents a data-driven method of constant monitoring,
data collecting, analyzing, and mitigating fatigue-related safety risks in flight operations
using scientific methods, previous knowledge, and operational experience [5,7].
The data and information collected regarding crew vigilance and readiness are con-
stantly analyzed by FRMS methods and tools and used to control fatigue-related safety
Aerospace 2023,10, 856. https://doi.org/10.3390/aerospace10100856 https://www.mdpi.com/journal/aerospace
Aerospace 2023,10, 856 2 of 42
risks in flight operations. FRMS can be established as a standalone system or as a part of a
Safety Management System (SMS) [5,8].
The FRMS aims to ensure that the flight crew and cabin crew members are sufficiently
vigilant and rested to work at a satisfactory level of performance. The principles and
processes of the Safety Management System (SMS) are applied to manage the specific risks
associated with a crew member’s level of fatigue [
8
]. In the same manner as SMS, the FRMS
aims to achieve a balance between safety, productivity, and cost [
5
]. It seeks to proactively
identify opportunities to improve operational processes and reduce risks, as well as to
recognize shortcomings after adverse events. The structure of the FRMS is modelled on
the SMS basic framework [
8
]. Its basic activities are safety risk management and safety
assurance. These basic activities are governed by FRMS policy and supported by FRMS
promotion processes [5].
SMS and FRMS rely on the concept of an effective reporting culture, where staff are
trained and are constantly encouraged to report hazards whenever they are recognized in
the work environment [9].
The goals of the FRMS are to “manage, monitor and mitigate the effects of fatigue
to improve flight crew members’ alertness and reduce performance errors”, as well as to
balance safety and productivity [10].
As part of the FRMS, the most commonly used methods for the objectivation of flight
crew fatigue include subjective fatigue scales, psychomotor vigilance tests, actigraphy,
predictive models, and sleep diaries [
9
,
11
]. The subjective objectivation of fatigue is also
commonly applied in fatigue reports, which can be used as data-collection tools. Predictive
models can be found in modern crew management software; they can warn crew planners
about fatigue risk (usually with warning messages and color schemes, from green, meaning
no risk, to red, indicating a high fatigue risk). Other objectivation methods have been used
in fatigue studies for specific cases when required by an airline (e.g., for certain types of
flight operations) [9,11].
The first part of this study describes a method to measure the fatigue level of pro-
fessional airline pilots using special psychodiagnostic equipment, i.e., tests. These tests
are based on a chronometric approach to measuring cognitive functions [
11
]. For the
purpose of this study, an electronic Complex Reactionmeter Drenovac (CRD) [
12
] system of
standardized chronometric cognitive tests is used. Personal (subjective) self-assessments of
each subject’s current state of fatigue were also used. The aim was to identify and quantify
elements that affect the appearance of fatigue.
The second part of this study includes a statistical analysis of the results obtained
with the CRD equipment and from the subjective fatigue scales. A statistical analysis was
performed using the analysis of variance (ANOVA) function in the Statistica 10 software.
In the third and final part of this study, causal modeling methods are used to determine
correlations among flight crew fatigue indicators, the subjective perception of fatigue, and
the defined workload settings. Recent studies focusing on developing predictive safety
management methodologies in aviation have revealed new possibilities. A conceptual
model of predictive safety management methodology was developed in [
13
]; this approach
defines the steps and tools of predictive safety management, i.e., the usage of predictive
(forecasting) and causal modeling methods [
14
–
16
] to identify potential hazards in aviation,
as well as their causal relations. This can help define efficient mitigation measures to
prevent or reduce the number of future hazards from turning into adverse events.
Hence, the main objective of this research is to find the correlations among the mea-
sured flight crew fatigue indicators, indicators of the subjective perception of fatigue, and
workload settings in flight operations. For the purpose of finding these correlations, the
IBM SPSS Statistics 27 software [17] was used.
2. Background on Research Related to the Impact of Fatigue in Flight Operations
Fatigue is defined as the result of personal and work-related factors [
7
,
18
–
20
]. Personal
factors are related to age, chronotype (morning type, evening type) [
21
], gender, genetic
Aerospace 2023,10, 856 3 of 42
predisposition, and personality, which have an impact on tolerance to shift work [
22
].
Individual lifestyle regarding physical activity or inactivity, e.g., the time spent in front of a
television or computer, has an effect on the length and quality of sleep [
23
,
24
]. For the flight
crew, work-related factors refer to shift work that includes early/late/night duties [
25
],
unpredictable monthly crew schedules (duties can change due to operational reasons,
sickness, or other reasons), time zone crossings, standby duties, and others. The listed
factors, together with the major biological mechanisms affecting periods of wakefulness
and drowsiness (the circadian rhythm, homeostatic sleep pressure, and sleep inertia), can
lead to sleep loss and sleep debt. Sleep is a biological need; its main mechanisms are
homeostatic sleep pressure and circadian rhythm. A recent study of fatigue phenomena
discovered molecular mechanisms controlling the circadian rhythm [
26
]. A small sleep
debt is needed to fall asleep (“The probability of falling asleep means a combination of
two opposing forces: our burden of sleep minus the level of excitement” [
27
]), but great
sleep debt can lead to falling asleep while driving. Performance, as measured by reaction
time or the number of mistakes in a given task, is worse among individuals who are sleep
deprived [
28
]. One study showed slow reaction time and poor performance of motorcycle
driving [
29
] because of sleep deprivation. Fatigue has physical manifestations (general
feeling of tiredness, decreased alertness, an irresistible desire for sleep, microsleep, lethargy,
and prolonged reaction time) and mental manifestations (difficulty with memorizing,
forgetting information and actions, a lack of concentration, slow understanding, poor
decision-making, and apathy).
In flight operations, fatigue can be a cause of inaccurate flight procedures, missed
radio calls, missed or slow responses to system warnings, routine tasks being performed
inaccurately or being forgotten, a loss of situational awareness, microsleeping and task
fixation, and poor communication among crew members [1,2,11].
In addition, fatigue may affect judgment or performance in the critical phases of flight
(take-off/landing), as well as making it difficult to remain alert when the workload is
reduced (cruising). Some of the identified causes of fatigue in short-haul operations include
restricted sleep due to early duty reporting times, multiple high workload periods during
the duty day, multiple sectors, long duty hours, restricted sleep due to short rest breaks,
and high-density airspace. Workload elements that may be able to mitigate fatigue risk in
flight operations include the length of duty, total flight time, number of sectors, rest period
duration, time of day, pattern of duty, rest facilities (management of sleep during layover
periods), number of time-zone transitions, and number of consecutive duty days [11,30].
In Europe, traditional fatigue management approaches and ways to protect crew
members from excessive fatigue levels are described in the Flight Time Limitations (FTL)
regulations [
25
]. However, restrictions on work hours are different from country to country
giving rise to inconsistencies in terms of restrictions on permitted flight duty, length of
rest periods, and other FTL elements [
3
,
4
]. Furthermore, the prescriptive nature of these
limitations prohibits some elements in a crew’s schedules but allows others that can be
very fatigue-inducing. Although the EU FTL [
25
] promotes active fatigue risk management
systems, it does not oblige airlines to apply a FRMS except in certain specific cases (e.g., the
use of reduced rest operations).
At the same time, EU FTL also requires airlines to ensure that flight duty periods are
planned in a way that enables crew members: to remain sufficiently free from fatigue so
that they can operate at a satisfactory level of safety; to take into account the relationship
between the frequencies and pattern of flight duty and rest periods and consider the
cumulative effects of undertaking long duty hours interspersed with minimum rest; to
allocate duty patterns which avoid undesirable practices such as alternating day/night
duties in order to minimize serious disruptions of established sleep/work patterns; to
provide rest periods of sufficient duration, especially after long flights crossing multiple
time zones; and to enable crew members to overcome the effects of their previous duties by
the time they start a new flight duty period [11,25].
Aerospace 2023,10, 856 4 of 42
In the USA, regulations pertaining to the fatigue risk management systems for aviation
safety are overseen by the Federal Aviation Administration (FAA). Basic FRMS concepts
are prescribed to ensure that aviation industry employees perform their duties safely. They
provide information on the components of an FRMS applied to aviation, describe how to
implement an FRMS within aviation operations, and define an FRMS as an operator-specific
process. While all FRMSs have common elements, the specifics can be tailored according to
a given set of conditions. It provides detailed guidance on how to prepare for the FRMS
approval process, develop the required documentation, develop and apply fatigue risk
management and safety assurance processes, collect and analyze data, and develop flight
crew FRMS operations procedures [31].
Within a FRMS, the most commonly used methods to measure and objectivate flight
crew fatigue are [9,11]:
•Subjective fatigue scales (Samn Perelli, Karolinska);
•Psychomotor vigilance tests;
•Actigraphy;
•Predictive models (biomathematical algorithms);
•Sleep diaries.
One of the main data sources for fatigue research, especially in flight operations, is
subjective fatigue scales. The application of subjective scales is described in recent research
regarding flight crew fatigue and the effect of the length of duty and time of day. In
some such studies, pilots reported their subjective fatigue levels using the Samn Perelli
scale [
32
,
33
]. The subjective objectification of fatigue is also commonly used in fatigue
reporting that can, in turn, be used as a data collection tool [7].
Other studies have used methods such as actigraphy, sleep diaries, performance
vigilance tests, and biomathematical predictive models, where the influence of fatigue was
studied via different quantification methods [
34
–
37
]. Predictive models, which warn crew
planners about fatigue risk (usually by displaying warning messages and color schemes),
can be found in modern crew management software.
Besides objectivation methods of quantifying flight crew fatigue, cognitive abilities
which deteriorate as fatigue increases, can be measured using chronometric approaches,
e.g., an electronic CRD system of standardized chronometric cognitive tests. CRD series
have been used in various studies since 1969 [
38
]. Information regarding the instruments,
methodology, measuring parameters, etc. used in such tests is provided in the CRD
handbook [
38
]. CRD series have been used for study on psychomotor disturbances in scuba
divers [
39
]. Another study showed differences between the working abilities of a driver,
a train operator, and a dispatcher during day and night shifts [
40
,
41
]. CRD series have
also been used to evaluate the psychomotor abilities of military pilots [
42
] and in research
regarding workloads and work efficiency over certain periods of time [
43
,
44
]. Recent
research has included several innovative approaches, such as assessing the sleep patterns
of flight attendants during the off-duty period using a photovoice technique [
45
], studying
new tools for use by pilots and the aviation industry to manage risks pertaining to work-
related stress and wellbeing [
46
], analyzing the workloads of aircraft pilots using Heart Rate
Variability (HRV) and the NASA Task Load Index questionnaire [
47
], applying multimodal
analyses of eye movements and fatigue in a simulated glass cockpit environment [
48
],
studying work type influence on fatigue among air traffic controllers based on data-driven
PERCLOS detection [
49
], identifying pilot fatigue status based on functional near-infrared
spectroscopy [
50
], examining fatigue among different crew compositions on long-haul
flights during the COVID-19 pandemic [
51
], and examining fatigue, work overload, and
sleepiness on a sample of commercial airline pilots [52].
For the purpose of finding correlations among various sets of indicators, causal mod-
eling techniques and methods are used. These methods use datasets of collected data and
build causal models that show causal relations among them. Using causal models, specifi-
cally, detected causal relations (impacts), it is possible to determine which variables should
be modified to obtain the desired performance of targeted indicator(s). Previous research
Aerospace 2023,10, 856 5 of 42
regarding causality and its variations has focused on causal time series analyses [
53
–
55
], the
causes and origins of human error [
56
], assumptions and methods for turning observations
into causal knowledge [
57
], the human perception of the relationship between cause and
effect [
58
], the role that human factors play in major aviation accidents [
59
], the use of
causal models to control and manage aircraft accident risk [
60
], graphical causal models
that can serve as powerful tools for detecting interrelations between variables [
61
], and
others. Recent studies have used causal modeling methods to identify causal relationships
among aviation hazards in order to define efficient measures to prevent future hazards
from turning into adverse events [14–16].
Against the described research background, this paper discusses the use of multiple
methods, i.e., objectivation methods such as CRD tests and subjective self-assessment
fatigue scales to collect data on flight crew fatigue; statistical analysis methods to analyze
collected data; causal modeling methods to detect correlations among the obtained fatigue
indicators; and subjective self-assessment results and indicators of workload settings in
flight operations.
3. Data Collection and Methods
This chapter presents the process of data collection regarding flight crew fatigue
using objectivation methods, i.e., an electronic CRD system of standardized chronometric
cognitive tests and subjective fatigue scales that capture the subjective perception of fatigue
by flight crews. The statistical methods used to analyze the collected data are described,
as well as the causal modeling methods used to detect correlations among the obtained
fatigue indicators, subjective self-assessments, and workload settings.
3.1. Collecting Data on Flight Crew Fatigue—Objectivation Methods
The data collected for this study were obtained by using an electronic CRD system
of standardized chronometric cognitive tests and subjective fatigue scales that capture the
subjective perception of fatigue by flight crews.
The tasks in the CRD tests were based on the measurement of reaction times by CDR
measuring instruments [
34
]. These tests are intended for the chronometric measurement
of the effectiveness of mental and psychomotor functions and to determine the dynamic
features and functional disturbances in mental processing. The efficiency of task-solving in
the CRD tests is shown by indicators expressed in time (milliseconds).
The individual mechanisms of the stimulus content processing system, as well as
the actualization and management of psychomotor activity, comprise special procedures
to extract and connect reaction time components with situational factors, which appear
in each test.
Numerous studies regarding the CRD series test measurements have established to
assess the following [38,62–65]:
•Perception, i.e., responding to changes in the attributes of sound and light signals;
•
Differentiation, i.e., distinguishing the features of light and sound signals and visual
constructs (characters);
•
Recognition (identification), i.e., extracting content from an unstructured stimulus context;
•
Visual orientation, i.e., navigating in space using the visual landmarks, finding the
latent location of a signal, etc.;
•Spatial visualization, i.e., recognition of characters rotated in space;
•
Short-term operational memory, i.e., coverage of sensory memory, the ability to update
short-term operational memory;
•
Learning, i.e., memorizing a path through a maze with nine alternative choice points;
•
Operational opinion, i.e., coordinated action of the hands and feet according to patterns
of light and sound stimuli;
•Conclusion (reasoning);
•Discovering relationships (AHA-phenomenon);
•Convergent thinking;
Aerospace 2023,10, 856 6 of 42
•Troubleshooting;
•
Simple reactions of individual limbs to different attributes (volume, frequency) of light
and sound stimuli (by pressing or releasing pedal buttons); and
•
Complex psychomotor reactions of different combinations of extremities (arms and
legs) to different complex sets of light and sound signals.
When the motor response to the stimulus content is in the form of a movement, then
the reaction time depends on the limb used to perform the movement. In the experiments,
a difference in the speed of the same movement performed with the right or left hand
was identified.
For sound, the required duration of the stimulus was shortened by 8.7%, and with
light, by 10%, i.e., faster reaction times were observed for sound than for light [
66
]. The
longer latency time of sensory components to a light signal than a sound signal is a result of
the different duration of the conversion of the signal into a stimulus (energy transformation
of electromagnetic waves, chemical reactions of visual purpura on the retina, initiation and
generation of the receptor potential). It takes 8 to 10 msec for sound stimulus, and 20 to
40 msec for light stimulus, to reach the cortex [66].
Reaction time is prolonged (slowed down) when the subject is tired [
50
]. Mental
fatigue, especially sleepiness, has the greatest influence [
67
]. Sleep deprivation impacts in
a similar way [
28
]. However, besides causing slower reaction times, it also increases the
likelihood of errors, for example, missing a response to stimulus.
Four CRD devices were used in this study. Additionally, five CRD tests were used, in
the following order:
•CRD 13: Spatial visualization test;
•CRD 241: Identifying progressive series of numbers;
•CRD 23: Complex convergent visual orientation;
•CRD 324: Actualization of short-term memory;
•CRD 422: Operative thinking with sound stimuli.
In this study, all measurements were made anonymously with four male pilots of an
average age of 42 years (+/
−
two years); all had been professional airline pilots for the last
11 years (standard deviation of 4.7 years) and had an average of 6305 flight hours (standard
deviation of 2532 flight hours) [
11
]. There was one captain and one co-pilot of a DH4-type
aircraft and one captain and one co-pilot of a A319/A320-type aircraft. The pilots were
familiarized with the methods used in the study, as well as with the CRD equipment and
tests. Pilots underwent training before taking the actual tests in order to avoid the effect of
learning how to do the tests, because the aim was to measure the drop in mental potential
due to fatigue.
Measurements, during which pilots completed a full set of tests (i.e., the five CRD tests
previously described) and filled out subjective surveys (self-assessment tables of emotional
state, energy level, self-confidence, and anxiety level), were performed before or after a
duty period. Tests were done in an improvised “CRD laboratory”, i.e., a room in their base
airport where pilots checked-in and checked-out (pre-flight and post-flight duty), as shown
in Figure 1. The average duration of testing on the CRD consoles was about 15 min [
11
].
All tests were recorded with a video camera.
A protocol was established with specific rules that were followed during the perfor-
mance of all tests:
•Each test was recorded with a camera;
•Each test was preceded by a short practice task;
•There were no breaks between tests;
•The results and tactics of solving the task could be discussed with the subjects;
•Every test started with the call “NOW”–“GET READY, WE BEGIN, NOW!”
The protocol included training the subjects, i.e., familiarizing them with the tests.
Training included 10 repetitions of the tests over a period of three to four days. The protocol
included the instructions and a description of each test.
Aerospace 2023,10, 856 7 of 42
Aerospace 2023, 10, 856 7 of 44
(a) (b)
Figure 1. CRD system: (a) CRD consoles; (b) CRD laboratory (Source: [11,12]).
A protocol was established with specific rules that were followed during the perfor-
mance of all tests:
• Each test was recorded with a camera;
• Each test was preceded by a short practice task;
• There were no breaks between tests;
• The results and tactics of solving the task could be discussed with the subjects;
• Every test started with the call “NOW”–“GET READY, WE BEGIN, NOW!”
The protocol included training the subjects, i.e., familiarizing them with the tests.
Training included 10 repetitions of the tests over a period of three to four days. The pro-
tocol included the instructions and a description of each test.
CRD 13 or “Spatial visualization test” examines the speed and accuracy of recogniz-
ing characters that appear in varying sizes and different positions in space. A signal panel
is located in the upper part of the instrument. On that panel, in the central part, there are
12 signal lights arranged in three rows and four columns. In each task, a large number of
signal lights that outline some kind of shape, are lit simultaneously, i.e., a line, a fork, a
triangle, a quadrilateral, a pentagon, or others. The same characters in different tasks
could be of different sizes and rotated differently in space. On the control panel, drawings
of these characters are located below the answer keys. In the upper row, the characters are
formed from open lines, and in the lower row, they are formed from geometric characters.
The subject has to look at them carefully and try to remember where they are. The answer
is given by pressing the button under which a given character is drawn. While solving the
tasks, the subject has to try to recognize the character formed by a group of lit signal lights
as quickly as possible, and quickly find and press the button above the drawing of the
appropriate character among the answer keys. While solving the test, the importance of
accuracy and speed is emphasized. The test contains 35 tasks. After correctly solving a
task, a new task immediately appears. If a new task does not appear, it means that the
correct answer was not provided. In such cases, the subject has to check where the error
occurred and press the key with the correct answer before continuing to the next task.
CRD 241 or “Test of identifying progressive series of numbers” examines the speed
and accuracy of assessing a series of 40 three-digit numbers ranging from 101 to 140, ar-
ranged in random order on the signal control panel. The task is to find the numbers in
order from the smallest (101) to the largest (140). The position of an individual number on
the signal control panel is indicated by pressing the button located below the respective
number. If the position of a certain number is correctly found, a return sound signal “BIP”
is obtained, but if the wrong key is pressed, the sound signal is absent. A single number
Figure 1. CRD system: (a) CRD consoles; (b) CRD laboratory (Source: [11,12]).
CRD 13 or “Spatial visualization test” examines the speed and accuracy of recognizing
characters that appear in varying sizes and different positions in space. A signal panel is
located in the upper part of the instrument. On that panel, in the central part, there are
12 signal lights arranged in three rows and four columns. In each task, a large number of
signal lights that outline some kind of shape, are lit simultaneously, i.e., a line, a fork, a
triangle, a quadrilateral, a pentagon, or others. The same characters in different tasks could
be of different sizes and rotated differently in space. On the control panel, drawings of
these characters are located below the answer keys. In the upper row, the characters are
formed from open lines, and in the lower row, they are formed from geometric characters.
The subject has to look at them carefully and try to remember where they are. The answer
is given by pressing the button under which a given character is drawn. While solving
the tasks, the subject has to try to recognize the character formed by a group of lit signal
lights as quickly as possible, and quickly find and press the button above the drawing of
the appropriate character among the answer keys. While solving the test, the importance
of accuracy and speed is emphasized. The test contains 35 tasks. After correctly solving
a task, a new task immediately appears. If a new task does not appear, it means that the
correct answer was not provided. In such cases, the subject has to check where the error
occurred and press the key with the correct answer before continuing to the next task.
CRD 241 or “Test of identifying progressive series of numbers” examines the speed and
accuracy of assessing a series of 40 three-digit numbers ranging from 101 to 140, arranged
in random order on the signal control panel. The task is to find the numbers in order from
the smallest (101) to the largest (140). The position of an individual number on the signal
control panel is indicated by pressing the button located below the respective number. If
the position of a certain number is correctly found, a return sound signal “BIP” is obtained,
but if the wrong key is pressed, the sound signal is absent. A single number must not be
skipped, because all answers after the skipped number would be considered errors. While
solving the test, the importance of accuracy and speed was emphasized.
CRD 23 or “Test of complex convergent visual orientation” examines the speed and
accuracy of complex navigation in space. In each task, three signal lights are lit simultane-
ously, which are combined to make two intersections of the columns and rows in which the
answer keys are located. The task is to quickly determine the columns and rows that these
lights define when the signal lights come on and to find the intersection of these columns
and rows. The answer must be given by simultaneously pressing both buttons located
in those places. It is important to press the answer keys simultaneously with both hands.
The answer will not be valid if one key is pressed before the other. While solving the test,
the importance of accuracy and speed was emphasized. The test contains 35 tasks. After
correctly solving a task, a new task immediately appears. If a new task does not appear,
Aerospace 2023,10, 856 8 of 42
it means that the previous task was not answered correctly. In this case, it is necessary to
check that task, press the keys with the correct answer, and then continue to the next task.
CRD 324 or “Actualization of short-term memory” examines the speed and accuracy
of operational memory, i.e., recall. The task consists of noticing the place where the light
signal appears and finding the key to turn it off among the answer keys in the lower
row. At the same time, the subject must remember a sequence of signal connections and
answer keys. The position of the answer key can be vertically below, to the left, or to
the right of the light. In this test, the signal lights are lit up in a random order, and the
answers are given by alternately pressing the keys according to the principle “LEFT, RIGHT,
RIGHT, DOWN”.
CRD 422 or “Operative thinking with sound stimuli” involves the use of a main signal-
control panel and connection elements, i.e., headphones (speakers) and pedals. The CRD
422 test measures operational thinking and coordinating the work of both hands and legs
depending on an emitted pitch. In this test, one of the two predetermined sound signals is
emitted. For a higher pitch, it is necessary to simultaneously press the large button in the
left corner of the control panel with the left hand and the right foot pedal with the right
foot. For a lower pitch, subjects must simultaneously press the large button in the right
corner of the control panel with the right hand and the left foot pedal with the left foot.
The task design in the CRD series tests is based on the concept of reaction time
measurement. These tests are intended for chronometric measurements of the efficiency of
performing mental and psychomotor functions, as well as the determination of dynamic
characteristics and functional interferences in the process of mental processing [38].
Independent variables (inputs) are related to:
•Workload (flight hours, duty hours, rest periods, number of sectors);
•
Time of the day (when the CRD tests were performed; this was used to study the
influence of circadian rhythm);
•
Subjective self-assessments (results of the subjective perception of fatigue, considered
to be both independent and dependent variables).
Dependent variables (outputs/targets) are:
•CRD fatigue indicators (results of the CRD tests);
•
Subjective self-assessments (results of the subjective perception of fatigue, considered
to be both independent and dependent variables).
Independent variables are divided into the following seven groups:
1. Time of the day (consisting of one indicator: Time of the day);
2. Start or end of the shift (consisting of one indicator: Check In/Check Out);
3.
Days off (consisting of three indicators: Number of days (F) in the previous 7 days,
Number of days (F) in the previous 28 days, and Number of days (F) in the previous
28 days);
4.
Rest (consisting of four indicators: Rest length, Local night, Number of local nights in
the 48 h before flight duty, and Changes in schedule);
5.
Cumulative workload (consisting of six indicators: Sectors in the previous 7 days,
Sectors in the previous 28 days, Flight time in the previous 7 days, Flight time in the
previous 28 days, Duty time in the previous 7 days, and Duty time in the previous
28 days);
6.
Individual flight duty (consisting of eight indicators: Flight duty time, Duty time,
Flight time in flight duty, Average duration of a sector, Average duration of air-
craft ground handling, Split duty, Change of aircraft during flight duty period, and
Multi-day shifts);
7.
Subjective self-assessment (consisting of four indicators: Self-assessment of emotional
state, Self-assessment of energy level, Self-assessment of self-confidence, and Self-
assessment of anxiety level).
Aerospace 2023,10, 856 9 of 42
Independent variables represent the workload elements and the results of the subjec-
tive self-assessment scales, which are described in Table 1. For the purpose of detecting
correlations among all variables, the independent variables (indicators) are designated
with labels, i.e., Time of the day is X1, Start or end of the shift is X2, Number of F days
in the previous 7 days is X3, Number of F days in the previous 28 days is X4, Number of
individual F days in the previous 28 days is X5, Rest length is X6, Local night in a daily rest
is X7, Number of local nights in the 48 h before flight duty is X8, Changes in the schedule
is X9, Sectors in the previous 7 days is X10, Sectors in the previous 28 days is X11, Flight
time in the previous 7 days is X12, Flight time in the previous 28 days is X13, Duty time in
the previous 7 days is X14, Duty time in the previous 28 days is X15, Flight duty time is
X16, Duty time is X17, Flight time in flight duty is X18, Average duration of a sector is X19,
Average duration of aircraft ground handling is X20, Split duty is X21, Change of aircraft
during flight duty period is X22, Multi-day shifts is X23, Self-assessment of emotional state
is S1, Self-assessment of energy level is S2, Self-assessment of self-confidence is S3, and
Self-assessment of anxiety level is S4.
The results of the CRD measurement include the CRD measures and fatigue indicators.
These are considered dependent variables, and they include the following: Number of
errors (Nerr), Total test-solving time (Ttot), Minimum test-solving time (Tmin), Maximum
test-solving time (Tmax), Total ballast (Btot), Initial ballast (Bin), Final ballast (Bfin), and
Fatigue index (Bfin/Bin). A dependent variable, i.e., Number of errors (Nerr), is an integer
that indicates the number of errors. Other variables, i.e., Total test-solving time (Ttot),
Minimum test-solving time (Tmin), Maximum test-solving time (Tmax), Total ballast (Btot),
Initial ballast (Bin), and Final ballast (Bfin), are time indicators measured in milliseconds.
For the purpose of detecting correlations among all variables, the dependent variables
(indicators) are designated with labels, i.e., Number of errors (Nerr) is Y1, Total test-solving
time (Ttot) is Y2, Minimum test-solving time (Tmin) is Y3, Maximum test-solving time
(Tmax) is Y4, Total ballast (Btot) is Y5, Initial ballast (Bin) is Y6, Final ballast (Bfin) is Y7, and
Fatigue index (Bfin/Bin) is Y8.
Number of errors (Nerr) measures the accuracy of mental processing; a lower value in-
dicates a higher accuracy and vice versa. The Number of errors captures the coordination of
speed and accuracy in mental processing. The Number of errors also provides information
about the difficulty of the tasks.
Total test-solving time (Ttot) measures the total time required to solve a particular test
(it includes ballast, i.e., lost time due to the effect of systematic and random factors on the
speed of performing a certain mental activity). A lower value indicates a higher level of
efficiency and vice versa.
Minimum test-solving time (Tmin) measures the speed of mental processing, i.e., the
shortest task solving times in the individual tests. A lower value indicates a higher level of
efficiency and vice versa.
Maximum test-solving time (Tmax) measures the longest time required to solve a
particular task, i.e., an extremely long time to solve one or more tasks in a certain test. A
lower value indicates a higher level of efficiency and vice versa.
Total ballast (Btot) measures total lost time due to fluctuations in the speed of solving
similar tasks in individual tests; this represents the stability of mental processing, i.e., it is
an indicator of individual stability as a dynamic feature of mental processing. Lower values
indicate greater stability and vice versa. Btot is defined as the sum of the differences (Di)
between the time required to solve each individual task (Ti) and the individually shortest
time required to solve tasks in a certain test (Tmin), as shown in Figure 2.Di represents
the blocks of partial ballast (D1
. . .
Dn); it serves primarily to monitor the dynamics of
change in the speed of mental processing as a function of the performance of a particular
chronometric test, and cumulatively to derive the indicators of Initial ballast (Bin), and
Final ballast (Bfin). In other words, it is the overall indicator of the stability of the mental
processing of the test content by an individual.
Aerospace 2023,10, 856 10 of 42
Table 1.
The elements of workload and the results of subjective self-assessment scales–the indepen-
dent variables of CRD testing and subjective self-assessments.
Independent
Variables–Groups Label Name Description
Time of day X1 Time of the day Local time of testing at the beginning of the shift
(Check In–CI) or at the end of the shift (Check Out–CO)
Start or end of the shift
X2 Start or end of the shift
(Check In/Check Out–CI/CO)
Start of ’shift or Check In–CI,
or end of shift or Check Out–CO
Days off
X3 Number of F days in
the previous 7 days
Number of days off (F) in the previous 7 days, at the
beginning of the shift (CI) or at the end of the shift (CO)
X4 Number of F days in
the previous 28 days
Number of days off (F) in the previous 28 days, at the
beginning of the shift (CI) or at the end of the shift (CO)
X5 Number of individual F days in
the previous 28 days
Number of individual days off (F)
in the previous 28 days, at the beginning of the
shift (CI) or at the end of the shift (CO)
Rest
X6 Rest length Rest length before flying duty, at the start of a shift (CI)
or at the end of a shift (CO)
X7 Local night in a daily rest
Whether the rest before flight duty includes a local night
X8 Number of local nights in the
48 h before flight duty
How many local nights included rest
48 h before flight duty
X9 Changes in the schedule Changes in the schedule of crews in the previous
7 days by more than 1 h
Cumulative workload
X10 Sectors in the previous 7 days Number of sectors (flights) completed
in the previous 7 days
X11 Sectors in the previous 28 days Number of sectors (flights) performed
in the previous 28 days
X12 Flight time in the previous 7 days Total flight time (includes only flight time, not the time
of aircraft ground handling) in the previous 7 days
X13 Flight time in the previous 28 days Total flight time (includes flight time only, not the time
of aircraft ground handling) in the previous 28 days
X14 Duty time in the previous 7 days Total duty time (includes all time on duty–from CI to
CO and duties on the ground) in the previous 7 days
X15 Duty time in the previous 28 days Total duty time (includes all time on duty–from CI to
CO and duties on the ground) in the previous 28 days
Individual flight duty
X16 Flight duty time
Flight duty time for individual flight duty period (FDP)
X17 Duty time Duty time for individual flight duty period (FDP)
X18 Flight time in flight duty Flight time (Block Time) during the
individual flight duty period (FDP)
X19 Average duration of a sector Average duration of an individual sector (flight)
X20 Average duration of
aircraft ground handling
Average duration of the aircraft
ground handling (turnaround)
X21 Split duty Split duty
X22 Change of aircraft during
flight duty period Change of aircraft during flight duty period (FDP)
X23 Multi-day shifts Multi-day shifts
Subjective
self-assessment
S1 Self-assessment of emotional state Subjective self-assessment of emotional state
(scale from 1 to 10)
S2 Self-assessment of energy level Subjective self-assessment of energy level
(scale from 1 to 10)
S3 Self-assessment of self-confidence Subjective self-assessment of self-confidence
(scale from 1 to 10)
S4 Self-assessment of anxiety level Subjective self-assessment of anxiety level
(scale from 1 to 10)
Aerospace 2023,10, 856 11 of 42
Aerospace 2023, 10, 856 11 of 44
Maximum test-solving time (Tmax) measures the longest time required to solve a
particular task, i.e., an extremely long time to solve one or more tasks in a certain test. A
lower value indicates a higher level of efficiency and vice versa.
Total ballast (Btot) measures total lost time due to fluctuations in the speed of solving
similar tasks in individual tests; this represents the stability of mental processing, i.e., it is
an indicator of individual stability as a dynamic feature of mental processing. Lower val-
ues indicate greater stability and vice versa. Btot is defined as the sum of the differences
(Di) between the time required to solve each individual task (Ti) and the individually
shortest time required to solve tasks in a certain test (Tmin), as shown in Figure 2. Di rep-
resents the blocks of partial ballast (D1 … Dn); it serves primarily to monitor the dynamics
of change in the speed of mental processing as a function of the performance of a particu-
lar chronometric test, and cumulatively to derive the indicators of Initial ballast (Bin), and
Final ballast (Bfin). In other words, it is the overall indicator of the stability of the mental
processing of the test content by an individual.
Figure 2. Derivation of ballast Di from reaction time Ti.
Initial ballast (Bin) represents the working speed or starting ballast. In the first half
of the test, it contains information on the efficiency or interference of working speed.
Final ballast (Bfin) represents fatigue, i.e., it contains information about the transfer
of experience from the initial to the final part of the test.
Fatigue index (Bfin/Bin) is the quotient of Initial ballast (Bin) and Final ballast (Bfin);
it represents a derived indicator of the direction of changes in the speed (an acceleration
or a deceleration) of solving tasks in a particular test, i.e., it represents endurance and,
consequently, fatigue. Values of this indicator greater than 1 indicate the presence of fa-
tigue.
Table 2 shows an overview of all dependent variables, including the full name, label,
acronym, a short description, and meaning of each CRD fatigue indicator.
Table 2. Overview of the CRD fatigue indicators.
Name of the CDR
Fatigue Indicator Label Abbr. Short Description Meaning
Number of errors Y1 Nerr Number of errors: accuracy of mental pro-
cessing Lower value = higher accuracy
Total time Y2 Ttot Mental processing speed: total time required to
solve a test Lower value = higher level of efficiency
Minimum time Y3 Tmin Mental processing speed: the shortest task-solv-
ing time Lower value = higher level of efficiency
Maximum time Y4 Tmax Mental processing speed: the longest task-solv-
ing times Lower value = higher level of efficiency
Total ballast Y5 Btot Total lost time due to fluctuations in the speed
of solving similar tasks Lower value = greater stability
Initial ballast Y6 Bin Working speed or initial ballast Lower value = greater stability
Final ballast Y7 Bfin Fatigue or final ballast Lower value = greater stability
Fatigue index Y8 Bfin/Bin The quotient of Bfin and Bin Values greater than 1 indicate fatigue
The variables of subjective self-assessments represent the subjective results of self-
assessments regarding emotional state, energy level, self-confidence, and anxiety level.
The subjective self-assessment scale of emotional state comprises a ranking from 1 to
10, as shown in Table 3, where the worst was 1, i.e., “I am completely depressed, and
everything is black”, and the best was 10, i.e., “I feel unusually joyful and energetic”.
Figure 2. Derivation of ballast Di from reaction time Ti.
Initial ballast (Bin) represents the working speed or starting ballast. In the first half of
the test, it contains information on the efficiency or interference of working speed.
Final ballast (Bfin) represents fatigue, i.e., it contains information about the transfer of
experience from the initial to the final part of the test.
Fatigue index (Bfin/Bin) is the quotient of Initial ballast (Bin) and Final ballast (Bfin);
it represents a derived indicator of the direction of changes in the speed (an acceleration
or a deceleration) of solving tasks in a particular test, i.e., it represents endurance and,
consequently, fatigue. Values of this indicator greater than 1 indicate the presence of fatigue.
Table 2shows an overview of all dependent variables, including the full name, label,
acronym, a short description, and meaning of each CRD fatigue indicator.
Table 2. Overview of the CRD fatigue indicators.
Name of the CDR
Fatigue Indicator Label Abbr. Short Description Meaning
Number of errors Y1 Nerr Number of errors: accuracy
of mental processing Lower value = higher accuracy
Total time Y2 Ttot Mental processing speed: total time
required to solve a test Lower value = higher level of efficiency
Minimum time Y3 Tmin Mental processing speed:
the shortest task-solving time Lower value = higher level of efficiency
Maximum time Y4 Tmax Mental processing speed:
the longest task-solving times Lower value = higher level of efficiency
Total ballast Y5 Btot
Total lost time due to fluctuations in the
speed of solving similar tasks Lower value = greater stability
Initial ballast Y6 Bin Working speed or initial ballast Lower value = greater stability
Final ballast Y7 Bfin Fatigue or final ballast Lower value = greater stability
Fatigue index Y8 Bfin/Bin The quotient of Bfin and Bin Values greater than 1 indicate fatigue
The variables of subjective self-assessments represent the subjective results of self-
assessments regarding emotional state, energy level, self-confidence, and anxiety level.
The subjective self-assessment scale of emotional state comprises a ranking from
1 to 10, as shown in Table 3, where the worst was 1, i.e., “I am completely depressed, and
everything is black”, and the best was 10, i.e., “I feel unusually joyful and energetic”.
The subjective self-assessment scale for energy level comprises a ranking from
1 to 10
,
as shown in Table 4, where the worst was 1, i.e., “I’m completely exhausted, unable to make
the least effort”, while 10 was the best, i.e., “I feel great energy and see no obstacles”.
Table 3. Self-assessment scale of emotional state.
Rank Description of an Emotional State
1 I am completely depressed, and everything is black.
2 I am discouraged and feel very bad.
3 I am depressed and feeling down.
4 I feel uncomfortable.
5 I’m a little moody.
6 I’m not in a particularly good mood, I almost feel fine.
7 I am fine and feel a slight positive excitement.
8 I feel very well.
9 I am in a very positive mood, I feel great.
10 I feel unusually joyful and energetic.
Aerospace 2023,10, 856 12 of 42
Table 4. Self-assessment scale of energy level.
Rank Description of an Energy Level
1 I am completely exhausted, unable to make the least effort.
2 I’m terribly tired, incapable of any activity.
3 I am very tired, without energy, immobile.
4 I’m pretty tired, apathetic, wishing for a good night’s sleep.
5 I do not have enough energy, I get tired easily.
6 I feel quite fresh.
7 I’m fresh and I have a lot of energy.
8 I have a lot of energy, I feel the need for action.
9 I have great energy and a strong need for action.
10 I feel great energy and see no obstacles.
The subjective self-assessment scale of self-confidence comprised a ranking from
1 to 10
, as shown in Table 5, where the worst was 1, i.e., “I am unable to muster the strength
to do anything”, while 10 was the best, i.e., “Nothing is impossible for me, I can accomplish
anything I want”.
Table 5. Self-assessment scale of self-confidence.
Rank Description of Self-Confidence
1 I am unable to muster the strength to do anything.
2 I feel unhappy and sad, tired, and incompetent.
3 I am broken and not capable of taking action.
4 It seems to me that I am not capable of anything.
5
It’s as if my knowledge and abilities are insufficient to meet the demands placed on me.
6
I think that I am capable and that I have the knowledge to meet the demands placed on me.
7
It seems to me that my knowledge and abilities are greater than the demands placed on me.
8 I am completely confident in my knowledge and abilities.
9 I am confident in my abilities to perform important and responsible tasks.
10 Nothing is impossible for me, I can accomplish anything I want.
The subjective self-assessment scale of anxiety level comprised a ranking from
1 to 10
,
as shown in Table 6, where the worst was 1, i.e., “I’m completely freaked out, scared”,
while 10 was the best, i.e.,: “I am completely calm and peaceful”.
Table 6. Self-assessment scale of anxiety level.
Rank Description of an Anxiety Level
1 I’m completely freaked out, scared.
2 I am terribly disturbed and worried, imbued with fear.
3 I am very insecure, completely devastated by hopelessness.
4 I’m scared and upset, irritated and nervous.
5 I feel constrained and a little anxious.
6 Nothing particularly bothers me.
7 I am sure of myself, and nothing is bothering me.
8 I feel good without trying to.
9 I am cool, self-confident and do not get excited.
10 I am completely calm and peaceful.
A sample of the collected data regarding flight crew fatigue, i.e., independent and
dependent variables obtained using the described objectivation methods, is presented
in Appendix A.
3.2. Statistical Analysis of Collected Data on Flight Crew Fatigue
After the measurements were completed and the chronometric data had been collected,
a statistical analysis of the data was conducted. Before the statistical analysis began, it
Aerospace 2023,10, 856 13 of 42
was necessary to convert the original results of the CRD measurements expressed in time
indicators (milliseconds) into standard statistical measures (T scale) for the purpose of
normalizing the data.
The need to transpose the original measures into the standardized measures stems
from the fact that chronometric data are asymmetrically distributed, and the normalization
of their distribution is necessary, because statistical analysis assumes a normal distribution
of data. This procedure also eliminated the individual differences among subjects. To
this end, we converted Ttot,Tmin,Tmax,Btot,Bin, and Bfin data, which were originally
expressed in milliseconds; meanwhile, the total number of errors (Nerr) and the fatigue
index (Bfin/Bin) retained the original values.
At the same time, it is necessary to emphasize that shorter times in the aforementioned
variables indicate a higher degree efficiency of mental processing and vice versa, which
means that a lower value on the T scale also represents a higher degree of efficiency of
mental processing and vice versa. Dependent variables Nerr and Bfin/Bin are expressed in
their original values in further analysis, whereby a lower number of errors indicates greater
accuracy of mental processing, while for Bfin/Bin, i.e., the fatigue index, values greater
than 1 (when Bfin is greater than Bin) indicate the presence of fatigue.
Conversion to the T scale consists of two steps, as follows.
Step I: conversion of the original measurement results (values) into Z values according
to the formula:
Z value = (average of original value)/(standard deviation of original value). (1)
Step II: conversion of the Z value into the T value according to the formula:
T value = 50 + 10*Z. (2)
A sample of the Ttot,Tmin,Tmax,Btot,Bin, and Bfin indicators converted into T scale
values, i.e., TtotZ,TminZ,TmaxZ,BtotZ,BinZ, and BfinZ, is shown in Table 7.
Table 7. Sample of the original values for the CRD fatigue indicators converted into T scale values.
CDR
Test ID
Original Values in Milliseconds Transposed Values (T Scale)
Ttot Tmin Tmax Btot Bin Bfin TtotZ TminZ TmaxZ BtotZ BinZ BfinZ
979 14.128 271 635 4.643 1.943 2.701 0.4122 0.3102 −
0.0981
0.2927 0.1703 0.3291
1638 13.504 289 551 3.389 1.407 1.983 0.0193 0.8737 −
0.5959
−0.7616 −0.7683 −0.6124
568 11.186 223 505 3.381 1.178 2.204 −
1.4404
−
1.1923
−
0.8685
−0.7683 −1.1692 −0.3226
578 11.665 214 487 4.175 1.689 2.486 −
1.1387
−
1.4740
−
0.9751
−0.1007 −0.2736 0.0478
548 12.886 223 716 5.081 2.467 2.615 −
0.3699
−
1.1923
0.3819 0.6610 1.0878 0.2163
1628 10.930 223 451 3.125 1.066 2.060 −
1.6016
−
1.1923
−
1.1885
−0.9835 −1.3654 −0.5114
1658 12.292 228 572 3.661 1.752 1.909 −
0.7439
−
1.0358
−
0.4714
−0.5329 −0.1633 −0.7088
916 37.260 753 2.288 10.905 5.439 5.467 0.4438 0.4813 1.0960 0.1126 0.5999 −0.2759
1239 29.045 495 1.348 11.720 5.010 6.711 −
1.1814
−
1.7623
−
0.9139
0.4123 0.2674 0.4578
1360 30.130 661 1.232 6.995 2.893 4.103 −
0.9668
−
0.3187
−
1.1620
−1.3254 −1.3737 −1.0803
493 43.882 949 2.185 10.667 4.653 6.015 1.7539 2.1859 0.8757 0.0250 −0.0094 0.0473
518 41.860 870 1.847 11.410 4.983 6.427 1.3539 1.4988 0.1530 0.2983 0.2468 0.2906
821 35.656 803 2.092 7.551 2.384 5.168 0.1265 0.9162 0.6769 −1.1209 −1.7683 −0.4522
1219 30.285 636 1.342 8.025 2.997 5.028 −
0.9361
−
0.5361
−
0.9268
−0.9466 −1.2927 −0.5345
1340 30.819 548 2.833 11.639 6.509 5.130 −
0.8305
−
1.3014
2.2613 0.3825 1.4298 −0.4743
1350 31.650 592 2.201 10.930 4.063 6.867 −
0.6661
−
0.9188
0.9099 0.1218 −0.4664 0.5501
679 36.821 785 1.732 9.346 3.577 5.770 0.3570 0.7596 −
0.0929
−0.4608 −0.8435 −0.0972
1025 35.159 736 1.631 9.399 4.008 5.391 0.0282 0.3335 −
0.3088
−0.4413 −0.5090 −0.3204
681 56.385 1.173 3.834 15.330 4.264 11.067 1.2261 1.4732 1.1554 0.3564 −0.6829 1.0013
1027 50.804 991 2.541 16.119 7.853 8.267 0.3674 −
0.0624
−
0.2212
0.5078 0.6553 0.2413
1221 42.338 848 2.369 12.658 5.371 7.287 −
0.9353
−
1.2690
−
0.4044
−0.1563 −0.2700 −0.0245
1342 44.056 824 2.368 15.216 6.685 8.531 −
0.6709
−
1.4715
−
0.4054
0.3346 0.2200 0.3131
1352 42.238 907 2.406 10.493 4.240 6.254 −
0.9507
−
0.7712
−
0.3650
−0.5717 −0.6919 −0.3050
1362 41.639 843 1.668 12.134 5.900 6.235 −
1.0428
−
1.3112
−
1.1507
−0.2568 −0.0729 −0.3102
Aerospace 2023,10, 856 14 of 42
After the normalization of the collected data, a statistical analysis was performed
using ANOVA in the Statistica 10 software. The results are presented in Chapter 4 and
accompanying appendices.
3.3. Causal Modeling Methods
The aim of this research was to detect correlations among flight crew fatigue indicators,
subjective self-assessments (the subjective perception of fatigue), and workload parameters.
It is possible to improve the flight crew planning processes in flight operations and mitigate
the risk of fatigue by identifying causal links among flight crew fatigue indicators, subjective
self-assessments, and workload settings, collected via the CRD testing.
IBM SPSS Statistics is an analytics software [
17
] that can be used to analyze all data
in one or more datasets and identify causal links among variables (indicators). The SPSS
Statistics 27 version of the software was used for this study.
Causal models can be generated once a dataset has been prepared correctly using
the function called “Create Temporal Causal Model”. The Temporal Causal Model (TCM)
detects causal links among all indicators (variables) in a dataset—in this case, among
flight crew fatigue indicators, subjective self-assessments, and workload settings—and
presents them in a circular or impact diagram. The causal modeling results are presented
in Chapter 4.
4. Results
Correlations among flight crew fatigue indicators, subjective self-assessments, and
workload settings were detected, based on the CRD measurements, statistical analyses of
the collected data, and the causal modeling of the relevant dataset. The obtained results are
presented in this chapter.
4.1. Statistical Analysis Results of Flight Crew Fatigue Indicators
After the normalization of the collected data, a statistical analysis was performed
for the independent variables outlined in Table 1, Section 3.1, using the ANOVA of the
Statistica 10 software.
Independent variables, as previously described, are divided into the following groups:
•
Time of day when the measurement was made, i.e., how the time of day when the
measurement was conducted affects the dynamics of mental processing;
•
The beginning or the end of the shift, i.e., the dynamics of mental processing at the
beginning or end of the shift;
•
Subjective scales of self-assessment (scales of the energy level, emotional state, self-
confidence, and anxiety level), i.e., the dynamics of mental processing in relation to a
subject’s subjective self-assessment;
•
Days off, i.e., the influence of the number of days off on the dynamics of
mental processing
;
•Rest, i.e., the influence of fatigue on the dynamics of mental processing;
•
Cumulative workload, i.e., the impact of cumulative workload on the dynamics of
mental processing;
•
Individual flight duty, i.e., the influence of the elements of individual flight duty on
the dynamics of mental processing.
The CRD dependent variables or the CRD measurements results were grouped
as follows:
•Speed indicators: Ttot,Tmin and Tmax;
•Stability indicators: Btot,Bin,Bfin and Bfin/Bin;
•Reliability indicator: Nerr.
As described previously, based on CRD tests, data were collected. The total number of
conducted tests was 1182, which produced a large database of information. The tests were
conducted in a period of about one year. Parallel to conducting each test, subjects filled
out the subjective fatigue tests to provide information about their subjective perception of
Aerospace 2023,10, 856 15 of 42
fatigue. Subjects also filled out questionnaires regarding their workloads prior to taking the
tests. The workload settings data and results of the subjective fatigue tests were defined as
independent variables, while the CRD measures were defined as dependent variables. The
aim of the statistical analysis was to examine whether the independent variables affected
the dependent variables, i.e., CRD measures. The main hypothesis which was repeated for
each independent variable assumed that these have no effect on the dependent variables,
i.e., efficiency of mental processing.
Samples of the conducted statistical analysis of the CRD dependent variables are
presented in Appendix B, showing also an analysis of the independent variable “Average
duration of a sector”, while in Appendix C, and analysis of the independent variable
“Subjective self-assessment of the anxiety level” is provided.
The overall results of the statistical analysis are presented in the following table
and graphs.
Table 8shows the dependent variables of the CRD tests, i.e., the number of measure-
ments when the difference was statistically significant (statistical significance at a level of
less than 0.05), which totaled in 268 instances.
Table 8.
The number of measurements that were statistically significant as per each CRD test and the
dependent variables (Source: Own elaboration based on Statistica 10 ANOVA analysis).
Dependent Variable CDR13 CDR23 CDR241 CDR324 CDR422 Total
Nerr 4 12 2 6 13 37
Ttot 16 7 6 9 13 51
Tmin 7 6 9 8 1 31
Tmax 4 3 3 2 9 21
Btot 11 3 5 3 11 33
Bin 9 6 6 4 9 34
Bfin 6 1 8 3 10 28
Bfin/Bin 5 11 11 4 2 33
Total 62 49 50 39 68 268
According to our statistical analysis, CRD 422 and CRD 13 were the most sensitive
chronometric instruments in this study in terms of the number of dependent variables,
with statistical significance at a level of less than 0.05, as shown in Figure 3.
Aerospace 2023, 10, 856 16 of 44
Table 8. The number of measurements that were statistically significant as per each CRD test and
the dependent variables (Source: Own elaboration based on Statistica 10 ANOVA analysis).
Dependent
Variable CDR13 CDR23 CDR241 CDR324 CDR422 Total
Nerr 4 12 2 6 13 37
Ttot 16 7 6 9 13 51
Tmin 7 6 9 8 1 31
Tmax 4 3 3 2 9 21
Btot 11 3 5 3 11 33
Bin 9 6 6 4 9 34
Bfin 6 1 8 3 10 28
Bfin/Bin 5 11 11 4 2 33
Total 62 49 50 39 68 268
Figure 3. The number of CRD tests with statistical significance (Source: Own elaboration based on
Statistica 10 ANOVA analysis).
Figure 4. The number of dependent variables with statistical significance (Source: Own elaboration
based on Statistica 10 ANOVA analysis).
Figure 3.
The number of CRD tests with statistical significance (Source: Own elaboration based on
Statistica 10 ANOVA analysis).
The dependent variable with the most statistical significance at a level of less than
0.05 was Total test time, i.e., Ttot, while the least was Maximum test-solving time, i.e., Tmax,
as shown in Figure 4.
Aerospace 2023,10, 856 16 of 42
Aerospace 2023, 10, 856 16 of 44
Table 8. The number of measurements that were statistically significant as per each CRD test and
the dependent variables (Source: Own elaboration based on Statistica 10 ANOVA analysis).
Dependent
Variable CDR13 CDR23 CDR241 CDR324 CDR422 Total
Nerr 4 12 2 6 13 37
Ttot 16 7 6 9 13 51
Tmin 7 6 9 8 1 31
Tmax 4 3 3 2 9 21
Btot 11 3 5 3 11 33
Bin 9 6 6 4 9 34
Bfin 6 1 8 3 10 28
Bfin/Bin 5 11 11 4 2 33
Total 62 49 50 39 68 268
Figure 3. The number of CRD tests with statistical significance (Source: Own elaboration based on
Statistica 10 ANOVA analysis).
Figure 4. The number of dependent variables with statistical significance (Source: Own elaboration
based on Statistica 10 ANOVA analysis).
Figure 4.
The number of dependent variables with statistical significance (Source: Own elaboration
based on Statistica 10 ANOVA analysis).
The most statistically significant differences were recorded in the group of independent
variables for cumulative workload, followed by the group for individual flight duties,
as shown in Figure 5.
Aerospace 2023, 10, 856 17 of 44
The most statistically significant differences were recorded in the group of independ-
ent variables for cumulative workload, followed by the group for individual flight duties,
as shown in Figure 5.
Figure 5. The number of statistically significant differences for each group of independent variables
(Source: Own elaboration based on Statistica 10 ANOVA analysis).
The most statistically significant differences were recorded for the independent var-
iable “Duty time in the previous 28 days”, and the least for “Sectors in the previous 7
days”. Most (55.2%) of the statistically significant differences were recorded at the end of
the shift (Check-Out–CO), as shown in Figure 6.
Figure 6. The number of statistically significant differences for each of the independent variables
(Source: Own elaboration based on Statistica 10 ANOVA analysis).
Figure 7 shows the dependent variables in relation to the grouped CRD variables
regarding speed, stability, and reliability, according to the number of statistically signifi-
cant differences. CRD variables regarding speed include Total test-solving time (Ttot),
Minimum test-solving time (Tmin), and Maximum test-solving time (Tmax). CRD varia-
bles regarding stability include Total ballast (Btot), Initial Ballast (Bin), and Final ballast
(Bfin). The CRD variable regarding reliability is Number of errors (Nerr). Regarding the
Figure 5.
The number of statistically significant differences for each group of independent variables
(Source: Own elaboration based on Statistica 10 ANOVA analysis).
The most statistically significant differences were recorded for the independent vari-
able “Duty time in the previous 28 days”, and the least for “Sectors in the previous 7 days”.
Most (55.2%) of the statistically significant differences were recorded at the end of the shift
(Check-Out–CO), as shown in Figure 6.
Figure 7shows the dependent variables in relation to the grouped CRD variables
regarding speed, stability, and reliability, according to the number of statistically significant
differences. CRD variables regarding speed include Total test-solving time (Ttot), Minimum
test-solving time (Tmin), and Maximum test-solving time (Tmax). CRD variables regarding
stability include Total ballast (Btot), Initial Ballast (Bin), and Final ballast (Bfin). The CRD
variable regarding reliability is Number of errors (Nerr). Regarding the CRD indicators
measuring speed, most of the statistically significant differences were found for the indepen-
Aerospace 2023,10, 856 17 of 42
dent variables “Duty time in the previous 7 days” and “Duty time in the previous 28 days”.
For the CRD indicators measuring stability, most of the statistically significant differences
were found for the independent variables of “Changes in the schedule”, “Sectors in the
previous 28 days”, “Duty time in the previous 28 days”, and “Flight time in the previous
28 days”. For the CRD indicator measuring reliability, most of the statistically significant
differences were found for the independent variables “Sectors in the previous 28 days”,
“Duty time in the previous 7 days”, and “Self-assessment of emotional state”.
Aerospace 2023, 10, 856 17 of 44
The most statistically significant differences were recorded in the group of independ-
ent variables for cumulative workload, followed by the group for individual flight duties,
as shown in Figure 5.
Figure 5. The number of statistically significant differences for each group of independent variables
(Source: Own elaboration based on Statistica 10 ANOVA analysis).
The most statistically significant differences were recorded for the independent var-
iable “Duty time in the previous 28 days”, and the least for “Sectors in the previous 7
days”. Most (55.2%) of the statistically significant differences were recorded at the end of
the shift (Check-Out–CO), as shown in Figure 6.
Figure 6. The number of statistically significant differences for each of the independent variables
(Source: Own elaboration based on Statistica 10 ANOVA analysis).
Figure 7 shows the dependent variables in relation to the grouped CRD variables
regarding speed, stability, and reliability, according to the number of statistically signifi-
cant differences. CRD variables regarding speed include Total test-solving time (Ttot),
Minimum test-solving time (Tmin), and Maximum test-solving time (Tmax). CRD varia-
bles regarding stability include Total ballast (Btot), Initial Ballast (Bin), and Final ballast
(Bfin). The CRD variable regarding reliability is Number of errors (Nerr). Regarding the
Figure 6.
The number of statistically significant differences for each of the independent variables
(Source: Own elaboration based on Statistica 10 ANOVA analysis).
Aerospace 2023, 10, 856 18 of 44
CRD indicators measuring speed, most of the statistically significant differences were
found for the independent variables “Duty time in the previous 7 days” and “Duty time
in the previous 28 days”. For the CRD indicators measuring stability, most of the statisti-
cally significant differences were found for the independent variables of “Changes in the
schedule”, “Sectors in the previous 28 days”, “Duty time in the previous 28 days”, and
“Flight time in the previous 28 days”. For the CRD indicator measuring reliability, most
of the statistically significant differences were found for the independent variables “Sec-
tors in the previous 28 days”, “Duty time in the previous 7 days”, and “Self-assessment of
emotional state”.
Figure 7. The number of statistically significant differences per independent variable and per group
of CRD dependent variables (speed, stability, and reliability) (Source: Own elaboration based on
Statistica 10 ANOVA analysis).
4.2. Correlations Among Fatigue Indicators, Subjective Self-assessments, and Workload Settings
Using Temporal Causal Modeling
In this part, the aim was to create a causal model of a defined dataset of previously
described indicators in order to detect correlations among fatigue indicators, subjective
self-assessments, and workload settings. Detecting correlations among indicators implies
detecting the impacts (causes or effects) of indicators upon one another, which, in turn,
provides a possibility to improve the planning of future actions that may help mitigate
fatigue risk in flight operations.
To identify causal links among indicators, the IBM SPSS Statistics function “Create
Temporal Causal Modeling” was used. Table 9 shows all of the indicators in the observed
dataset, with their labels, names, and allocated roles.
Figure 7.
The number of statistically significant differences per independent variable and per group
of CRD dependent variables (speed, stability, and reliability) (Source: Own elaboration based on
Statistica 10 ANOVA analysis).
Aerospace 2023,10, 856 18 of 42
4.2. Correlations among Fatigue Indicators, Subjective Self-assessments, and Workload Settings
Using Temporal Causal Modeling
In this part, the aim was to create a causal model of a defined dataset of previously
described indicators in order to detect correlations among fatigue indicators, subjective
self-assessments, and workload settings. Detecting correlations among indicators implies
detecting the impacts (causes or effects) of indicators upon one another, which, in turn,
provides a possibility to improve the planning of future actions that may help mitigate
fatigue risk in flight operations.
To identify causal links among indicators, the IBM SPSS Statistics function “Create
Temporal Causal Modeling” was used. Table 9shows all of the indicators in the observed
dataset, with their labels, names, and allocated roles.
Table 9.
Variables of the observed dataset (collected data) of fatigue indicators, subjective self-
assessments, and workload settings (Source: Own elaboration using dataset from Appendix A).
Label Name Role
X1 Time of the day Independent variable (input)
X2
Start or end of the shift (Check In/Check Out–CI/CO)
Independent variable (input)
X3 Number of F days in the previous 7 days Independent variable (input)
X4 Number of F days in the previous 28 days Independent variable (input)
X5 Number of individual F days in the previous 28 days Independent variable (input)
X6 Rest length Independent variable (input)
X7 Local night in a daily rest Independent variable (input)
X8 Number of local nights in the 48 h before flight duty Independent variable (input)
X9 Changes in the schedule Independent variable (input)
X10 Sectors in the previous 7 days Independent variable (input)
X11 Sectors in the previous 28 days Independent variable (input)
X12 Flight time in the previous 7 days Independent variable (input)
X13 Flight time in the previous 28 days Independent variable (input)
X14 Duty time in the previous 7 days Independent variable (input)
X15 Duty time in the previous 28 days Independent variable (input)
X16 Flight duty time Independent variable (input)
X17 Duty time Independent variable (input)
X18 Flight time in flight duty Independent variable (input)
X19 Average duration of a sector Independent variable (input)
X20 Average duration of aircraft ground handling Independent variable (input)
X21 Split duty Independent variable (input)
X22 Change of aircraft during flight duty period Independent variable (input)
X23 Multi-day shifts Independent variable (input)
S1 Self-assessment of emotional state Independent and dependent variables (input/target, i.e., both)
S2 Self-assessment of energy level Independent and dependent variables (input/target, i.e., both)
S3 Self-assessment of self-confidence Independent and dependent variables (input/target, i.e., both)
S4 Self-assessment of anxiety level Independent and dependent variables (input/target, i.e., both)
Y1 Number of errors
Independent and dependent variables (input/target, i.e., both) *
Y2 Total time
Independent and dependent variables (input/target, i.e., both) *
Y3 Minimum time
Independent and dependent variables (input/target, i.e., both) *
Y4 Maximum time
Independent and dependent variables (input/target, i.e., both) *
Y5 Total ballast
Independent and dependent variables (input/target, i.e., both) *
Y6 Initial ballast
Independent and dependent variables (input/target, i.e., both) *
Y7 Final ballast
Independent and dependent variables (input/target, i.e., both) *
Y8 Fatigue index
Independent and dependent variables (input/target, i.e., both) *
* These indicators were initially determined to be dependent variables, but in the context of causal impacts, it
was concluded that they can also be independent variables influencing other variables, and hence, their role was
determined to be “both input and target” for the process of generating causal models.
For the purpose of detecting correlations among the defined indicators, a sample
dataset was used due to software limitations. The dataset used for this study included
135 entries for 23 indicators of workload settings (Xs), four indicators of subjective self-
Aerospace 2023,10, 856 19 of 42
assessments (Ss), and eight measured CRD indicators regarding mental processing,
i.e., fatigue indicators (Ys). The setup was made in such way that the independent variables,
i.e., workload settings indicators (Xs), were set as “inputs” in a temporal causal model, and
the dependent and independent variables, i.e., Ss and Ys, were set as “both inputs and
targets”. Variables X16 (Flight duty time), X17 (Duty time), X18 (Flight time in flight duty),
X19 (Average duration of a sector), X20 (Average duration of aircraft ground handling),
X21 (Split duty), and X22 (Change of aircraft during flight duty period) were excluded due
to the fact that their values were constant, i.e., equal to 0, or there were too many missing
values. The sample dataset is presented in Figure 8.
Aerospace 2023, 10, 856 20 of 44
due to the fact that their values were constant, i.e., equal to 0, or there were too many
missing values. The sample dataset is presented in Figure 8.
Figure 8. Sample of the dataset used to create a causal model of the observed flight crew fatigue
indicators (Source: Own elaboration using IBM SPSS and dataset from Appendix A).
Table 10 shows statistics for the causal models generated for each of the twelve target indicators,
obtained using the IBM SPSS Statistics function “Create Temporal Causal Modeling”. Model quality
(model fit) for all of the the built models was evaluated using the R-squared criterion, which can be
explained as the proportion of the variation in the dependent variable which is predictable from an
independent variable or variables. Different criteria can be used to do the “best fit” evaluation
(RMSE—Root Mean Squared Error, RMSPE—Root Mean Squared Percent Error, AIC—Akaike In-
formation Criterion, BIC—Bayesian Information Criterion, R-squared). In this case, R-squared was
selected, as it is the default in the software; the larger the R-squared value, the better the model.
Table 10 shows the fit statistics for all causal models of each target indicator in the observed dataset.
Table 10. Fit statistics for the causal models of each target indicator in the dataset (Source: Own
elaboration using IBM SPSS and dataset from Appendix A).
Model
for Target
Model Quality
RMSE RMSPE AIC BIC R-Squared
S1 0.50 0.03 –190.70 111.61 0.95
S2 0.41 0.03 –241.98 60.34 0.94
S3 0.53 0.03 –173.98 128.33 0.94
Y8 0.33 0.14 –296.80 5.52 0.94
Y2 0.52 1.70 –178.55 123.77 0.93
Y5 0.59 11.84 –149.04 153.27 0.93
S4 0.60 0.04 –144.94 157.37 0.93
Y4 0.73 2.20 –94.25 208.06 0.92
Y7 0.64 1.70 –127.44 174.87 0.92
Y1 1.39 0.23 71.05 373.37 0.92
Y3 0.61 1.29 –138.13 164.19 0.91
Y6 0.68 3.25 –110.43 191.88 0.91
Figure 8.
Sample of the dataset used to create a causal model of the observed flight crew fatigue
indicators (Source: Own elaboration using IBM SPSS and dataset from Appendix A).
Table 10 shows statistics for the causal models generated for each of the twelve
target indicators, obtained using the IBM SPSS Statistics function “Create Temporal Causal
Modeling”. Model quality (model fit) for all of the the built models was evaluated using
the R-squared criterion, which can be explained as the proportion of the variation in
the dependent variable which is predictable from an independent variable or variables.
Different criteria can be used to do the “best fit” evaluation (RMSE—Root Mean Squared
Error, RMSPE—Root Mean Squared Percent Error, AIC—Akaike Information Criterion,
BIC—Bayesian Information Criterion, R-squared). In this case, R-squared was selected, as it
is the default in the software; the larger the R-squared value, the better the model. Table 10
shows the fit statistics for all causal models of each target indicator in the observed dataset.
Figure 9shows the “overall model quality”, which shows the distribution of model
quality for all of the built models (from Table 10). As shown in Figure 9, the models
were of excellent quality, because 100% of them had R-squared values in the top interval
(0.88. 1). Figure 9provides confirmation that the applied TCM was of excellent quality,
with R-squared values ranging from 0.91 to 0.95; this means that the correlations detected
in the built TCM were strong.
Figure 10 shows the overall causal model system (TCM) of all causal links among
the flight crew fatigue indicators, subjective self-assessments, and workload settings pa-
rameters, obtained using the causal modeling functions of the IBM SPSS Statistics 27. For
example, TCM shows that indicator S2 (Self-assessment of the energy level) correlates with
X2 (Start or end of the shift (Check In/Check Out–CI/CO)), X3 (Number of days off in the
Aerospace 2023,10, 856 20 of 42
previous 7 days), X5 (Number of individual days off in the previous 28 days), X15 (Duty
time in the previous 28 days), S3 (Self-assessment of self-confidence), Y1 (Number of errors
or accuracy of mental processing), Y2 (Mental processing speed or total time required to
solve a test), and Y5 (Total ballast or total lost time due to fluctuations in the speed of
solving similar tasks).
Table 10.
Fit statistics for the causal models of each target indicator in the dataset (Source: Own
elaboration using IBM SPSS and dataset from Appendix A).
Model
for Target
Model Quality
RMSE RMSPE AIC BIC R-Squared
S1 0.50 0.03 −190.70 111.61 0.95
S2 0.41 0.03 −241.98 60.34 0.94
S3 0.53 0.03 −173.98 128.33 0.94
Y8 0.33 0.14 −296.80 5.52 0.94
Y2 0.52 1.70 −178.55 123.77 0.93
Y5 0.59 11.84 −149.04 153.27 0.93
S4 0.60 0.04 −144.94 157.37 0.93
Y4 0.73 2.20 −94.25 208.06 0.92
Y7 0.64 1.70 −127.44 174.87 0.92
Y1 1.39 0.23 71.05 373.37 0.92
Y3 0.61 1.29 −138.13 164.19 0.91
Y6 0.68 3.25 −110.43 191.88 0.91
Aerospace 2023, 10, 856 21 of 44
Figure 9 shows the “overall model quality”, which shows the distribution of model
quality for all of the built models (from Table 10). As shown in Figure 9, the models were
of excellent quality, because 100% of them had R-squared values in the top interval (0.88.
1). Figure 9 provides confirmation that the applied TCM was of excellent quality, with R-
squared values ranging from 0.91 to 0.95; this means that the correlations detected in the
built TCM were strong.
Figure 9. Overall model quality (Source: Own elaboration using IBM SPSS and dataset from the
Appendix A).
Figure 10 shows the overall causal model system (TCM) of all causal links among the
flight crew fatigue indicators, subjective self-assessments, and workload settings param-
eters, obtained using the causal modeling functions of the IBM SPSS Statistics 27. For ex-
ample, TCM shows that indicator S2 (Self-assessment of the energy level) correlates with
X2 (Start or end of the shift (Check In/Check Out–CI/CO)), X3 (Number of days off in the
previous 7 days), X5 (Number of individual days off in the previous 28 days), X15 (Duty
time in the previous 28 days), S3 (Self-assessment of self-confidence), Y1 (Number of er-
rors or accuracy of mental processing), Y2 (Mental processing speed or total time required
to solve a test), and Y5 (Total ballast or total lost time due to fluctuations in the speed of
solving similar tasks).
Figure 11 shows the direct impacts of target indicator Y8, i.e., Fatigue index. Figure
11a shows the correlations (links) with statistical significance values less than or equal to
0.05, while Figure 11b shows all of the detected correlations (impacts) of Y8. Figure 11a
shows all the links with statistical significance values less than or equal to 0.05. As shown
in these results, Y8 correlates with five workload settings indicators, namely X5 (Number
of individual days off in the previous 28 days), X6 (Rest length), X7 (Local night in daily
rest), X9 (Changes in the schedule), and X10 (Sectors in the previous 7 days). Additionally,
this correlates with three subjective self-assessment indicators, i.e., S2 (Self-assessment of
energy level), S3 (Self-assessment of self-confidence), and S4 (Self-assessment of anxiety
level), as well as with five other CRD indicators, namely, Y1 (Number of errors or accuracy
of mental processing), Y2 (Mental processing speed or total time required to solve a test),
Y4 (Maximum mental processing speed, i.e., the longest task-solving time), Y5 (Total bal-
last or total lost time due to fluctuations in the speed of solving similar tasks), and Y7
(Final ballast or final lost time due to fluctuations in the speed of solving similar tasks).
Figure 9.
Overall model quality (Source: Own elaboration using IBM SPSS and dataset from
the Appendix A).
Figure 11 shows the direct impacts of target indicator Y8, i.e., Fatigue index. Figure 11a
shows the correlations (links) with statistical significance values less than or equal to 0.05,
while Figure 11b shows all of the detected correlations (impacts) of Y8. Figure 11a shows
all the links with statistical significance values less than or equal to 0.05. As shown in
these results, Y8 correlates with five workload settings indicators, namely X5 (Number
of individual days off in the previous 28 days), X6 (Rest length), X7 (Local night in daily
rest), X9 (Changes in the schedule), and X10 (Sectors in the previous 7 days). Additionally,
this correlates with three subjective self-assessment indicators, i.e., S2 (Self-assessment of
energy level), S3 (Self-assessment of self-confidence), and S4 (Self-assessment of anxiety
level), as well as with five other CRD indicators, namely, Y1 (Number of errors or accuracy
of mental processing), Y2 (Mental processing speed or total time required to solve a test),
Aerospace 2023,10, 856 21 of 42
Y4 (Maximum mental processing speed, i.e., the longest task-solving time), Y5 (Total ballast
or total lost time due to fluctuations in the speed of solving similar tasks), and Y7 (Final
ballast or final lost time due to fluctuations in the speed of solving similar tasks).
Aerospace 2023, 10, 856 22 of 44
Figure 10. Temporal causal model of flight crew fatigue indicators, subjective self-assessments, and
workload settings parameters (Source: Own elaboration using IBM SPSS and dataset from Appen-
dix A).
(a) (b)
Figure 11. Direct impacts of target indicator Y8 (Fatigue index): (a) Links with statistical significance
values less than or equal to 0.05; (b) All links (Source: Own elaboration using IBM SPSS and dataset
from Appendix A).
Figure 12 shows an impact diagram of all indicators related to Y8, i.e., Fatigue index.
These include X2 (Start or end of the shift (Check In/Check Out)), X5 (Number of
Figure 10.
Temporal causal model of flight crew fatigue indicators, subjective self-assessments,
and workload settings parameters (Source: Own elaboration using IBM SPSS and dataset
from Appendix A).
Aerospace 2023, 10, 856 22 of 44
Figure 10. Temporal causal model of flight crew fatigue indicators, subjective self-assessments, and
workload settings parameters (Source: Own elaboration using IBM SPSS and dataset from Appen-
dix A).
(a) (b)
Figure 11. Direct impacts of target indicator Y8 (Fatigue index): (a) Links with statistical significance
values less than or equal to 0.05; (b) All links (Source: Own elaboration using IBM SPSS and dataset
from Appendix A).
Figure 12 shows an impact diagram of all indicators related to Y8, i.e., Fatigue index.
These include X2 (Start or end of the shift (Check In/Check Out)), X5 (Number of
Figure 11.
Direct impacts of target indicator Y8 (Fatigue index): (
a
) Links with statistical significance
values less than or equal to 0.05; (
b
) All links (Source: Own elaboration using IBM SPSS and dataset
from Appendix A).
Figure 12 shows an impact diagram of all indicators related to Y8, i.e., Fatigue index.
These include X2 (Start or end of the shift (Check In/Check Out)), X5 (Number of individual
Aerospace 2023,10, 856 22 of 42
days off in the previous 28 days), X6 (Rest length), X7 (Local night in daily rest), X9 (Changes
in the schedule), X10 (Sectors in the previous 7 days), X15 (Duty time in the previous
28 days), X23 (Multi-day shifts), S2 (Self-assessment of energy level), S3 (Self-assessment of
self-confidence), S4 (Self-assessment of anxiety level), Y1 (Number of errors or accuracy of
mental processing), Y2 (Mental processing speed or total time required to solve a test), and
Y4 (Maximum mental processing speed, i.e., the longest task-solving time).
Aerospace 2023, 10, 856 23 of 44
individual days off in the previous 28 days), X6 (Rest length), X7 (Local night in daily rest),
X9 (Changes in the schedule), X10 (Sectors in the previous 7 days), X15 (Duty time in the
previous 28 days), X23 (Multi-day shifts), S2 (Self-assessment of energy level), S3 (Self-
assessment of self-confidence), S4 (Self-assessment of anxiety level), Y1 (Number of errors
or accuracy of mental processing), Y2 (Mental processing speed or total time required to
solve a test), and Y4 (Maximum mental processing speed, i.e., the longest task-solving
time).
Figure 12. Impact diagram: causes of Fatigue Index (Y8) (Source: Own elaboration using IBM SPSS
and dataset from Appendix A).
Figure 13 shows an impact diagram of all indicators affected by Y8, i.e., Fatigue In-
dex. These include S1 (Self-assessment of emotional state), S2 (Self-assessment of energy
level), S3 (Self-assessment of self-confidence), S4 (Self-assessment of anxiety level), Y1
(Number of errors or accuracy of mental processing), Y2 (Mental processing speed or total
time required to solve a test), Y3 (Minimum mental processing speed, i.e., the shortest
task-solving time), Y4 (Maximum mental processing speed, i.e., the longest task-solving
time), Y5 (Total ballast or total lost time due to fluctuations in the speed of solving similar
tasks), and Y7 (Final ballast or final lost time due to fluctuations in the speed of solving
similar tasks).
As previously mentioned, the focus of this study was to find correlations among
flight crew fatigue indicators, the subjective perception of fatigue, and workload settings.
Using causal modeling techniques, correlations were detected. Figure 14 shows all of the
detected correlations with specific emphasis on correlations regarding workload settings,
i.e., those labeled with Xs. In Figure 14a, these are clearly marked in red squares; in Figure
14b, the same ones are marked in red squares, while additional ones are marked in orange
squares. Those include X5 (Number of individual days off in the previous 28 days), X6
(Rest length), X7 (Local night in daily rest), X9 (Changes in the schedule), and X10 (Sectors
in the previous 7 days). The reason why these are of particular interest is because they
represent the independent variables which are susceptible to modification. Hence, finding
indicators of workload settings that impact the flight crew fatigue opens up the possibility
to modify them in order to mitigate fatigue risk.
Figure 12.
Impact diagram: causes of Fatigue Index (Y8) (Source: Own elaboration using IBM SPSS
and dataset from Appendix A).
Figure 13 shows an impact diagram of all indicators affected by Y8, i.e., Fatigue Index.
These include S1 (Self-assessment of emotional state), S2 (Self-assessment of energy level),
S3 (Self-assessment of self-confidence), S4 (Self-assessment of anxiety level), Y1 (Number of
errors or accuracy of mental processing), Y2 (Mental processing speed or total time required
to solve a test), Y3 (Minimum mental processing speed, i.e., the shortest task-solving time),
Y4 (Maximum mental processing speed, i.e., the longest task-solving time), Y5 (Total ballast
or total lost time due to fluctuations in the speed of solving similar tasks), and Y7 (Final
ballast or final lost time due to fluctuations in the speed of solving similar tasks).
Aerospace 2023, 10, 856 24 of 44
Figure 13. Impact diagram: effects of Fatigue Index (Y8) (Source: Own elaboration using IBM SPSS
and dataset from Appendix A).
(a) (b)
Figure 14. Direct impacts of workload setting on flight crew fatigue (Y8): (a) Links with significance
values less than or equal to 0.05; (b) All links (Source: Own elaboration using IBM SPSS and dataset
from the Appendix A).
5. Discussion
Due to the severity of fatigue risk in flight operations, it is necessary to constantly seek
and improve mitigation measures. As discussed in our review of the available literature, fa-
tigue issues in flight operations have been frequently addressed. Various methods had been
adopted to address fatigue related issues. The most commonly used methods include the ap-
plication of subjective scales in flight crew fatigue research as the main data collection tool,
such as in research done by Powell and others in 2007 and 2008. Other studies have included
methods such as the actigraphy, sleep diaries, performance vigilance tests, and biomathemat-
ical predictive models, such as in research done by Yi and Moochhala in 2013, Powell and
others in 2014, Gander and others in 2014, and Van den Berg and others in 2015. Recent
Figure 13.
Impact diagram: effects of Fatigue Index (Y8) (Source: Own elaboration using IBM SPSS
and dataset from Appendix A).
Aerospace 2023,10, 856 23 of 42
As previously mentioned, the focus of this study was to find correlations among flight
crew fatigue indicators, the subjective perception of fatigue, and workload settings. Using
causal modeling techniques, correlations were detected. Figure 14 shows all of the detected
correlations with specific emphasis on correlations regarding workload settings, i.e., those
labeled with Xs. In Figure 14a, these are clearly marked in red squares; in Figure 14b,
the same ones are marked in red squares, while additional ones are marked in orange
squares. Those include X5 (Number of individual days off in the previous 28 days), X6
(Rest length), X7 (Local night in daily rest), X9 (Changes in the schedule), and X10 (Sectors
in the previous 7 days). The reason why these are of particular interest is because they
represent the independent variables which are susceptible to modification. Hence, finding
indicators of workload settings that impact the flight crew fatigue opens up the possibility
to modify them in order to mitigate fatigue risk.
Aerospace 2023, 10, 856 24 of 44
Figure 13. Impact diagram: effects of Fatigue Index (Y8) (Source: Own elaboration using IBM SPSS
and dataset from Appendix A).
(a) (b)
Figure 14. Direct impacts of workload setting on flight crew fatigue (Y8): (a) Links with significance
values less than or equal to 0.05; (b) All links (Source: Own elaboration using IBM SPSS and dataset
from the Appendix A).
5. Discussion
Due to the severity of fatigue risk in flight operations, it is necessary to constantly seek
and improve mitigation measures. As discussed in our review of the available literature, fa-
tigue issues in flight operations have been frequently addressed. Various methods had been
adopted to address fatigue related issues. The most commonly used methods include the ap-
plication of subjective scales in flight crew fatigue research as the main data collection tool,
such as in research done by Powell and others in 2007 and 2008. Other studies have included
methods such as the actigraphy, sleep diaries, performance vigilance tests, and biomathemat-
ical predictive models, such as in research done by Yi and Moochhala in 2013, Powell and
others in 2014, Gander and others in 2014, and Van den Berg and others in 2015. Recent
Figure 14.
Direct impacts of workload setting on flight crew fatigue (Y8): (
a
) Links with significance
values less than or equal to 0.05; (
b
) All links (Source: Own elaboration using IBM SPSS and dataset
from the Appendix A).
5. Discussion
Due to the severity of fatigue risk in flight operations, it is necessary to constantly seek
and improve mitigation measures. As discussed in our review of the available literature,
fatigue issues in flight operations have been frequently addressed. Various methods had
been adopted to address fatigue related issues. The most commonly used methods include
the application of subjective scales in flight crew fatigue research as the main data collection
tool, such as in research done by Powell and others in 2007 and 2008. Other studies have
included methods such as the actigraphy, sleep diaries, performance vigilance tests, and
biomathematical predictive models, such as in research done by Yi and Moochhala in
2013, Powell and others in 2014, Gander and others in 2014, and Van den Berg and others
in 2015. Recent research has presented several innovative approaches regarding fatigue
and its effects on various aviation employees, such as that conducted by Laovoravit and
others in 2019, who used a photovoice technique, new tools to manage risks pertaining
to work-related stress and wellbeing by Cahill and others in 2020, the use of heart rate
or eye movement measuring equipment by Alaimo and others in 2020 and Naeeri and
others in 2021, data driven detection techniques by Zhang and others in 2021, near-infrared
spectroscopy by Pan and others in 2022, etc. Cognitive abilities that deteriorate as fatigue
increases can be measured with a chronometric approach to measuring cognitive functions,
i.e., an electronic CRD system of standardized chronometric cognitive tests, as defined
by Drenovac in 2009. CRD series have been used in various studies. CRD series have
Aerospace 2023,10, 856 24 of 42
been used to study psychomotor disturbances among practitioners in various fields. Some
studies have used CRD series to evaluate psychomotor abilities and to determine workload
and work efficiency during certain periods of time. Meanwhile, a few studies have shown
how causal modeling methods can be used to identify causal relations among aviation
hazards in order to define efficient mitigation measures to prevent future adverse events,
such as research conducted by Roelen in 2008, Liou and others in 2008, Sloman in 2015,
Rohrer in 2018, and Bartulovi´c in 2022. Since fatigue is defined as one of the most important
aviation hazards, the application of causal modeling techniques has been recognized and
implemented in the present study.
Hence, this paper used CRD tests to collect data regarding flight crew mental process-
ing and psychomotor abilities and to detect the presence of fatigue in the defined workload
settings. Subjective fatigue scales were used to additionally collect data on the subjective
perception of fatigue by flight crews. Finally, to find correlations among defined sets of in-
dicators, causal modeling techniques and methods were used. These methods use datasets
of collected data and build models that show causal relations among them. Using causal
models, specifically, detecting causal relations (impacts), it is possible to determine which
variables should be modified to obtain the desired performance of targeted indicator(s).
Against a research background related to the influence of fatigue on flight operations,
the focus of this paper was to use multiple methods, i.e., objectivation methods such as
CRD tests and subjective self-assessment fatigue scales to collect data on flight crew fatigue;
statistical analysis methods to analyze the collected data; and causal modeling methods
to detect correlations among the obtained fatigue indicators, subjective self-assessment
results, and indicators of workload settings in flight operations.
This research implemented a combination of fatigue objectivation methods, statistical
analysis tools, and causal modeling techniques to determine correlations among flight
crew fatigue indicators, indicators of the subjective perception of fatigue, and workload
settings in flight operations. Determining correlations among indicators provides useful
information on causal factors that trigger the appearance of fatigue in flight crews, making
it possible to modify those factors and define improved mitigation measures.
The first part of the study used objectivation methods to collect data on flight crew
fatigue, i.e., an electronic system of standardized chronometric cognitive tests (CRD tests)
and subjective self-assessment surveys on the subjective perception of fatigue (subjective
fatigue scales). CRD measurements were conducted using five CRD tests, i.e., CRD 13,
i.e., the Spatial visualization test, CRD 241, i.e., Identifying progressive series of num-
bers, CRD 23, i.e., Complex convergent visual orientation, CRD 324, i.e., Actualization of
short-term memory, and CRD 422, i.e., Operative thinking with sound stimuli. Subjects
underwent training before taking the actual tests in order to avoid the effect of learning,
because the aim was to measure any drop in mental potential due to fatigue. The indepen-
dent variables represent elements in the workload settings and the results of the subjective
self-assessment fatigue scales. All tests were performed anonymously with four male sub-
jects who had been professional airline pilots for the last 11 years. Tests were performed in
an improvised CRD laboratory, i.e., in a room of their base airport, where they checked-in
and checked-out (pre-flight and post-flight duty). The measurement produced a large
database of information regarding the speed, reliability, and stability of each pilot’s mental
processing and psychomotor capabilities. This database was used to conduct statistical
analyses to examine whether the independent variables of workload settings and subjective
states affected mental processing and, consequently, to determine the presence of fatigue.
After collecting and normalizing the data, in the second part of the study, a statis-
tical analysis was performed using the ANOVA of the Statistica 10 software. The main
hypothesis, repeated for each independent variable, was that there would be no effect on
the dependent variables (CRD measures), i.e., efficiency of mental processing. Most of the
hypotheses were disproven, i.e., statistical analysis showed that the independent variables
(workload settings and subjective states) had an effect on the dependent variables (CRD
measures); in other words, workload settings and subjective states affect the appearance
Aerospace 2023,10, 856 25 of 42
of fatigue. The results showed that CRD 422 (Operative thinking with sound stimuli) and
CRD 13 (Spatial visualization test) were the most sensitive chronometric instruments in
the study in terms of the number of dependent variables with statistical significance at a
level of less than 0.05. The most statistically significant differences were recorded in the
group of independent variables regarding cumulative workload, followed by the group
associated with individual flight duties. The most statistically significant differences were
recorded for the independent variables “Duty time in the previous 28 days”, “Flight time
in the previous 28 days”, “Duty time in the previous 7 days”, “Sectors in the previous
28 days”, and “Changes in the schedule”.
In the final part of the study, correlations were detected among measured flight crew
fatigue indicators, indicators of the subjective perception of fatigue, and workload settings,
using previously collected and analyzed data regarding flight crew fatigue. To identify
correlations (causal links) among all indicators in the dataset, the temporal causal modeling
tools in the IBM SPSS Statistics 27 software were used. The dataset used for this part of the
study included 135 entries for 23 indicators concerning workload settings, four indicators
concerning subjective self-assessments, and eight measured CRD indicators of mental
processing, i.e., fatigue indicators. The setup was made in such a way that the independent
variables, i.e., workload settings indicators, were the “inputs” in a temporal causal model
and the dependent and independent variables were “both inputs and targets”. A temporal
causal model of flight crew fatigue indicators, subjective self-assessments, and workload
settings parameters was created, with an excellent evaluation of the model fit using the
R-squared criterion (whose values ranged from 0.91 to 0.95). One indicator in the dataset
was of particular interest in this study: the Fatigue index (or Y8 in the dataset). The Fatigue
index is the quotient of the initial ballast and final ballast; it is derived indicator of the
direction of changes in the speed (an acceleration or deceleration) of solving tasks in a
particular test, i.e., it represents endurance, and consequently, fatigue. A value of this
index greater than 1 indicates the presence of fatigue. Hence, in the temporal causal model,
the focus was to observe which indicators correlated with this particular indicator. The
results showed that the Fatigue index correlates with five workload settings indicators,
namely “Number of individual days off in the previous 28 days”, “Rest length”, “Local
night in daily rest”, “Changes in the schedule”, and “Sectors in the previous 7 days”.
Additionally, it correlates with three subjective self-assessment indicators, i.e., “Energy
level”, “Self-confidence”, and “Anxiety level”; and five other CRD indicators, namely,
“Number of errors”, “Total test-solving time”, “Maximum test-solving time”, “Total ballast”,
and “Final ballast”.
The most interesting correlations were those related to the independent variables
of workload settings, i.e., the impacts of number of individual days off in the previous
28 days, rest length, local night in a daily rest, changes in the schedule, and sectors in the
previous 7 days, on fatigue. The reason why these were of particular interest is because
they may be modified. Detecting correlations among indicators showed the impacts (causes
or effects) of indicators upon one another, which, in turn, provides a foundation to improve
the planning of future actions that may help mitigate fatigue risk in flight operations.
6. Conclusions
The aim of this paper was to find correlations among the measured flight crew fatigue
indicators, indicators of the subjective perception of fatigue, and workload settings in
flight operations. Detecting correlations could help define improved mitigation measures
regarding fatigue risk in flight operations.
We described the objectivation methods used to collect data on flight crew fatigue,
i.e., with an electronic system of standardized chronometric cognitive tests (CRD tests)
and subjective self-assessment surveys on the subjective perception of fatigue (subjective
fatigue scales). Additionally, the various applied procedures were described.
A statistical analysis was performed using the ANOVA of the Statistica 10 software.
The main hypothesis was repeated for each independent variable was that there would
Aerospace 2023,10, 856 26 of 42
be no effect on the dependent variables (CRD measures), i.e., efficiency of mental pro-
cessing. Most of the hypotheses were disproven, i.e., our statistical analysis showed that
the independent variables (workload settings and subjective states) had an effect on the
dependent variables (CRD measures), or in other words, workload settings and subjective
states affected the appearance of fatigue.
The final part of the study aimed to detect correlations among measured flight crew
fatigue indicators, indicators of the subjective perception of fatigue, and workload settings
using previously collected and analyzed data on flight crew fatigue. Correlations were
detected showing the impact of specific workload and other elements; these could be used
to define improved mitigation measures regarding fatigue in flight operations.
7. Limitations and Future Research
There were some limitations to this study. It did not consider all possible elements
of workload settings that could impact the appearance of fatigue. Additionally, the study
was performed on the four male pilots of similar age and experience, and hence, it could
not be determined whether characteristics such as age, gender, or experience affected the
appearance of fatigue. Even though large number of tests were performed over a long
period of time, collecting data on a larger number (more than four) of pilots, as well as on
female and male pilots, with different ages, experience levels, and other characteristics,
might provide a better database to detect parameters affecting the appearance of fatigue.
In future, more extensive testing should be performed, and more elements concerning
the work environment and personal factors should be examined to obtain more information
regarding the presence of fatigue in flight operations. Finding indicators of workload
settings that impact flight crew fatigue opens up the possibility of modifying them in order
to mitigate fatigue risk. Further research will focus on simulating such modifications of
workload settings based the correlations defined in this study. The aim is to establish
improved workload settings that will have the least impact on fatigue, i.e., to mitigate
fatigue risk by preventing the conditions that lead to its appearance.
Author Contributions:
Conceptualization: D.B., S.S., D.F. and M.M.J.; methodology: D.B., S.S., D.F.
and M.M.J.; software: D.B., S.S., D.F. and M.M.J.; validation: D.B., S.S., D.F. and M.M.J.; formal
analysis: D.B., S.S., D.F. and M.M.J.; investigation: D.B., S.S., D.F. and M.M.J.; data curation: D.B., S.S.,
D.F. and M.M.J.; writing—original draft preparation: D.B., S.S., D.F. and M.M.J.; writing—review and
editing: D.B., S.S., D.F. and M.M.J.; visualization: D.B., S.S., D.F. and M.M.J.; supervision: D.B., S.S.,
D.F. and M.M.J. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Informed Consent Statement:
All subjects gave their informed consent for inclusion before they
participated in the study. All subjects involved in the study entered voluntarily, and the study was
conducted anonymously to protect the privacy of the subjects.
Data Availability Statement:
Samples of data supporting reported results can be found in this paper,
in the Appendices. The entire database of collected data is not publicly available due to protection
of the privacy.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Sample of the data collected (results) regarding flight crew fatigue. i.e., CRD indicators–
the independent and dependent variables obtained using CRD equipment, are presented
in Table A1.
Aerospace 2023,10, 856 27 of 42
Table A1. Sample of CRD measurements (collected data).
CRD Test
CRD Test ID
Time of Day
Start or End of the Shift (CI/CO)
Number of Days off in the Previous 7 Days
Number of Days off in the Previous 28 Days
Number of Individual Days off in the Previous 28 Days
Rest Length
Local Night in a Daily Rest
Number of Local Nights in the 48 h before Flight Duty
Changes in the Schedule in the Previous 7 Days by More Than 1 h
Sectors in the Previous 7 Days
Sectors in the Previous 28 Days
Flight Time in the Previous 7 Days
Flight Time in the Previous 28 Days
Duty Time in the Previous 7 Days
Duty Time in the Previous 28 Days
Flight Duty Time
Duty Time
Flight Time in Flight Duty
Average Duration of a Sector (from Number of Sectors)
Average Duration of Aircraft Ground Handling
Split Duty
Change of Aircraft during Flight Duty Period
Multi-Day Shifts
Self-Assessment of the Emotional State
Self-Assessment of the Energy Level
Self-Assessment of Self-Confidence
Self-Assessment of the Anxiety Level
Number of Errors (Nerr)
Total Time (Ttot)
Minimum Time (Tmin)
Maximum Time (Tmax)
Total Ballast (Btot)
Initial Ballast (Bin)
Final Ballast (Bfin)
Fatigue Index (Bfin/Bin)
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 S1 S2 S3 S4 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8
CRD13 1325 17.43 1 1 5 3 14.50 1 2 0 6 30 6.22 39.22 20.65 80.02 9.43 9.93 4.65 4 3 0.00 0 0 8 6 8 8 2 29.831 464 1.388 13.591 5.989 7.602 1.2693
CRD23 1327 17.43 1 1 5 3 14.50 1 2 0 6 30 6.22 39.22 20.65 80.02 9.43 9.93 4.65 4 3 0.00 0 0 8 6 8 8 1 44.551 1.038 1.746 8.221 3.990 4.231 1.0604
CRD324 1328 17.43 1 1 5 3 14.50 1 2 0 6 30 6.22 39.22 20.65 80.02 9.43 9.93 4.65 4 3 0.00 0 0 8 6 8 8 0 18.181 130 801 10.381 5.871 4.510 0.7682
CRD13 1040 14.98 1 5 13 0 15.25 1 2 0 0 25 0.00 27.80 16.00 118.25 7.23 7.73 4.00 4 3 0.00 0 0 8 6 8 8 1 35.519 659 1.963 12.454 5.418 7.037 1.2988
CRD23 1042 14.98 1 5 13 0 15.25 1 2 0 0 25 0.00 27.80 16.00 118.25 7.23 7.73 4.00 4 3 0.00 0 0 8 6 8 8 1 52.686 1.155 2.337 12.261 3.513 8.749 2.4907
CRD241 1041 14.98 1 5 13 0 15.25 1 2 0 0 25 0.00 27.80 16.00 118.25 7.23 7.73 4.00 4 3 0.00 0 0 8 6 8 8 1 88.917 325 18.658 75.917 31.621 44.296 1.4008
CRD324 1043 14.98 1 5 13 0 15.25 1 2 0 0 25 0.00 27.80 16.00 118.25 7.23 7.73 4.00 4 3 0.00 0 0 8 6 8 8 1 23.516 181 781 12.656 6.957 5.699 0.8192
CDR422 1044 14.98 1 5 13 0 15.25 1 2 0 0 25 0.00 27.80 16.00 118.25 7.23 7.73 4.00 4 3 0.00 0 0 8 6 8 8 0 12.019 225 789 4.144 1.764 2.381 1.3499
CRD13 1335 17.77 1 2 6 3 63.25 1 2 1 9 38 9.50 47.88 52.10 166.98 10.02 10.52 7.00 4 3 0.00 0 0 8 6 8 6 0 33.117 625 2.070 11.242 7.365 3.878 0.5265
CRD23 1337 17.77 1 2 6 3 63.25 1 2 1 9 38 9.50 47.88 52.10 166.98 10.02 10.52 7.00 4 3 0.00 0 0 8 6 8 6 5 47.187 817 1.922 18.592 12.382 6.211 0.5016
CRD241 1336 17.77 1 2 6 3 63.25 1 2 1 9 38 9.50 47.88 52.10 166.98 10.02 10.52 7.00 4 3 0.00 0 0 8 6 8 6 0 69.316 180 5.898 62.116 35.460 26.656 0.7517
CRD324 1338 17.77 1 2 6 3 63.25 1 2 1 9 38 9.50 47.88 52.10 166.98 10.02 10.52 7.00 4 3 0.00 0 0 8 6 8 6 0 17.251 140 605 8.851 4.620 4.231 0.9158
CRD13 990 15.03 1 4 11 0 15.50 1 2 0 0 23 0.00 28.00 22.00 131.78 7.03 7.53 3.95 4 3 0.00 0 0 8 6 8 7 0 36.243 749 1.657 10.028 5.145 4.884 0.9493
CRD23 992 15.03 1 4 11 0 15.50 1 2 0 0 23 0.00 28.00 22.00 131.78 7.03 7.53 3.95 4 3 0.00 0 0 8 6 8 7 2 49.306 1.153 1.752 8.951 4.722 4.230 0.8958
CRD241 991 15.03 1 4 11 0 15.50 1 2 0 0 23 0.00 28.00 22.00 131.78 7.03 7.53 3.95 4 3 0.00 0 0 8 6 8 7 1 78.140 366 8.268 63.500 40.613 22.887 0.5635
CRD324 993 15.03 1 4 11 0 15.50 1 2 0 0 23 0.00 28.00 22.00 131.78 7.03 7.53 3.95 4 3 0.00 0 0 8 6 8 7 0 22.530 137 810 14.310 7.916 6.394 0.8077
CDR422 994 15.03 1 4 11 0 15.50 1 2 0 0 23 0.00 28.00 22.00 131.78 7.03 7.53 3.95 4 3 0.00 0 0 8 6 8 7 1 12.475 252 520 3.655 1.657 1.998 1.2058
CDR422 1339 17.77 1 2 6 3 63.25 1 2 1 9 38 9.50 47.88 52.10 166.98 10.02 10.52 7.00 4 3 0.00 0 0 8 6 8 6 0 11.353 239 513 2.988 1.700 1.289 0.7582
CDR422 1329 17.43 1 1 5 3 14.50 1 2 0 6 30 6.22 39.22 20.65 80.02 9.43 9.93 4.65 4 3 0.00 0 0 8 6 8 8 4 12.059 274 454 2.469 1.265 1.204 0.9518
CRD13 579 17.27 1 1 8 2 17.47 1 1 1 17 47 27.77 75.18 49.05 160.68 9.52 10.02 6.25 4 3 0.00 0 0 6 4 6 5 0 47.012 752 3.182 20.692 9.528 11.164 1.1717
CRD23 581 17.27 1 1 8 2 17.47 1 1 1 17 47 27.77 75.18 49.05 160.68 9.52 10.02 6.25 4 3 0.00 0 0 6 4 6 5 7 88.297 1.055 7.970 51.372 19.314 32.059 1.6599
CRD241 580 17.27 1 1 8 2 17.47 1 1 1 17 47 27.77 75.18 49.05 160.68 9.52 10.02 6.25 4 3 0.00 0 0 6 4 6 5 1 103.010 266 11.545 92.370 36.729 55.641 1.5149
CRD324 582 17.27 1 1 8 2 17.47 1 1 1 17 47 27.77 75.18 49.05 160.68 9.52 10.02 6.25 4 3 0.00 0 0 6 4 6 5 0 27.882 269 802 11.742 5.325 6.417 1.2051
Aerospace 2023,10, 856 28 of 42
Table A1. Cont.
CRD Test
CRD Test ID
Time of Day
Start or End of the Shift (CI/CO)
Number of Days off in the Previous 7 Days
Number of Days off in the Previous 28 Days
Number of Individual Days off in the Previous 28 Days
Rest Length
Local Night in a Daily Rest
Number of Local Nights in the 48 h before Flight Duty
Changes in the Schedule in the Previous 7 Days by More Than 1 h
Sectors in the Previous 7 Days
Sectors in the Previous 28 Days
Flight Time in the Previous 7 Days
Flight Time in the Previous 28 Days
Duty Time in the Previous 7 Days
Duty Time in the Previous 28 Days
Flight Duty Time
Duty Time
Flight Time in Flight Duty
Average Duration of a Sector (from Number of Sectors)
Average Duration of Aircraft Ground Handling
Split Duty
Change of Aircraft during Flight Duty Period
Multi-Day Shifts
Self-Assessment of the Emotional State
Self-Assessment of the Energy Level
Self-Assessment of Self-Confidence
Self-Assessment of the Anxiety Level
Number of Errors (Nerr)
Total Time (Ttot)
Minimum Time (Tmin)
Maximum Time (Tmax)
Total Ballast (Btot)
Initial Ballast (Bin)
Final Ballast (Bfin)
Fatigue Index (Bfin/Bin)
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 S1 S2 S3 S4 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8
CDR422 583 17.27 1 1 8 2 17.47 1 1 1 17 47 27.77 75.18 49.05 160.68 9.52 10.02 6.25 4 3 0.00 0 0 6 4 6 5 1 13.185 233 637 5.030 2.598 2.433 0.9365
CRD13 1000 17.47 1 3 11 0 16.47 1 2 0 4 27 3.95 31.95 29.53 131.73 9.47 9.97 4.62 4 3 0.00 0 0 8 6 8 7 0 36.384 750 2.054 10.134 6.247 3.887 0.6222
CRD23 1002 17.47 1 3 11 0 16.47 1 2 0 4 27 3.95 31.95 29.53 131.73 9.47 9.97 4.62 4 3 0.00 0 0 8 6 8 7 3 50.961 1.158 1.933 10.431 2.658 7.773 2.9244
CRD241 1001 17.47 1 3 11 0 16.47 1 2 0 4 27 3.95 31.95 29.53 131.73 9.47 9.97 4.62 4 3 0.00 0 0 8 6 8 7 0 74.526 265 6.275 63.926 32.960 30.966 0.9395
CRD324 1003 17.47 1 3 11 0 16.47 1 2 0 4 27 3.95 31.95 29.53 131.73 9.47 9.97 4.62 4 3 0.00 0 0 8 6 8 7 0 22.416 193 789 10.836 6.061 4.775 0.7878
CDR422 1004 17.47 1 3 11 0 16.47 1 2 0 4 27 3.95 31.95 29.53 131.73 9.47 9.97 4.62 4 3 0.00 0 0 8 6 8 7 0 12.500 279 678 2.735 1.456 1.280 0.8791
CRD13 1296 17.48 1 1 5 3 15.50 1 2 0 8 24 8.15 33.00 30.73 121.65 9.48 9.98 4.62 4 4 0.00 0 0 8 6 8 8 0 32.147 626 1.864 10.237 4.262 5.975 1.4019
CRD23 1298 17.48 1 1 5 3 15.50 1 2 0 8 24 8.15 33.00 30.73 121.65 9.48 9.98 4.62 4 4 0.00 0 0 8 6 8 8 6 54.279 1.097 1.657 15.884 9.469 6.416 0.6776
CRD241 1297 17.48 1 1 5 3 15.50 1 2 0 8 24 8.15 33.00 30.73 121.65 9.48 9.98 4.62 4 4 0.00 0 0 8 6 8 8 0 69.486 145 14.392 63.686 27.996 35.690 1.2748
CRD324 1299 17.48 1 1 5 3 15.50 1 2 0 8 24 8.15 33.00 30.73 121.65 9.48 9.98 4.62 4 4 0.00 0 0 8 6 8 8 0 21.701 185 852 10.601 5.970 4.631 0.7757
CRD13 1375 17.43 1 5 9 3 111.00 1 2 1 4 30 7.00 35.58 18.52 142.87 9.43 9.93 4.48 4 3 0.00 0 0 8 6 8 7 1 29.850 605 1.298 8.675 3.888 4.788 1.2315
CRD23 1377 17.43 1 5 9 3 111.00 1 2 1 4 30 7.00 35.58 18.52 142.87 9.43 9.93 4.48 4 3 0.00 0 0 8 6 8 7 6 46.493 905 2.044 14.818 5.293 9.526 1.7998
CRD241 1376 17.43 1 5 9 3 111.00 1 2 1 4 30 7.00 35.58 18.52 142.87 9.43 9.93 4.48 4 3 0.00 0 0 8 6 8 7 0 53.042 226 5.077 44.002 21.856 22.146 1.0133
CRD324 1378 17.43 1 5 9 3 111.00 1 2 1 4 30 7.00 35.58 18.52 142.87 9.43 9.93 4.48 4 3 0.00 0 0 8 6 8 7 0 16.935 135 616 8.835 4.717 4.118 0.8730
CDR422 1300 17.48 1 1 5 3 15.50 1 2 0 8 24 8.15 33.00 30.73 121.65 9.48 9.98 4.62 4 4 0.00 0 0 8 6 8 8 2 10.612 221 437 2.877 1.786 1.092 0.6113
CDR422 1379 17.43 1 5 9 3 111.00 1 2 1 4 30 7.00 35.58 18.52 142.87 9.43 9.93 4.48 4 3 0.00 0 0 8 6 8 7 1 11.088 233 463 2.933 1.277 1.657 1.2977
Aerospace 2023,10, 856 29 of 42
Table A1. Cont.
CRD Test
CRD Test ID
Time of Day
Start or End of the Shift (CI/CO)
Number of Days off in the Previous 7 Days
Number of Days off in the Previous 28 Days
Number of Individual Days off in the Previous 28 Days
Rest Length
Local Night in a Daily Rest
Number of Local Nights in the 48 h before Flight Duty
Changes in the Schedule in the Previous 7 Days by More Than 1 h
Sectors in the Previous 7 Days
Sectors in the Previous 28 Days
Flight Time in the Previous 7 Days
Flight Time in the Previous 28 Days
Duty Time in the Previous 7 Days
Duty Time in the Previous 28 Days
Flight Duty Time
Duty Time
Flight Time in Flight Duty
Average Duration of a Sector (from Number of Sectors)
Average Duration of Aircraft Ground Handling
Split Duty
Change of Aircraft during Flight Duty Period
Multi-Day Shifts
Self-Assessment of the Emotional State
Self-Assessment of the Energy Level
Self-Assessment of Self-Confidence
Self-Assessment of the Anxiety Level
Number of Errors (Nerr)
Total Time (Ttot)
Minimum Time (Tmin)
Maximum Time (Tmax)
Total Ballast (Btot)
Initial Ballast (Bin)
Final Ballast (Bfin)
Fatigue Index (Bfin/Bin)
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 S1 S2 S3 S4 Y1 Y2 Y3 Y4 Y5 Y6 Y7 Y8
CRD13 836 16.07 1 3 7 4 154.00 1 2 0 0 34 0.00 64.87 10.00 99.38 6.57 7.07 4.05 2 1 0.00 0 0 7 6 7 8 0 39.709 685 1.912 15.734 7.039 8.696 1.2354
CRD13 980 16.30 1 2 8 2 16.63 1 1 1 12 32 20.35 54.35 36.82 161.27 8.30 13.72 5.47 3 2 0.00 0 0 6 5 6 6 0 41.213 640 2.446 18.813 7.247 11.566 1.5960
CRD23 838 16.07 1 3 7 4 154.00 1 2 0 0 34 0.00 64.87 10.00 99.38 6.57 7.07 4.05 2 1 0.00 0 0 7 6 7 8 11 80.554 908 4.839 48.774 19.088 29.686 1.5552
CRD23 982 16.30 1 2 8 2 16.63 1 1 1 12 32 20.35 54.35 36.82 161.27 8.30 13.72 5.47 3 2 0.00 0 0 6 5 6 6 2 57.556 687 3.396 33.511 15.558 17.954 1.1540
CRD241 837 16.07 1 3 7 4 154.00 1 2 0 0 34 0.00 64.87 10.00 99.38 6.57 7.07 4.05 2 1 0.00 0 0 7 6 7 8 1 89.615 323 12.129 76.695 46.769 29.926 0.6399
CRD241 981 16.30 1 2 8 2 16.63 1 1 1 12 32 20.35 54.35 36.82 161.27 8.30 13.72 5.47 3 2 0.00 0 0 6 5 6 6 2 107.492 289 12.337 95.932 42.904 53.028 1.2360
CRD324 983 16.30 1 2 8 2 16.63 1 1 1 12 32 20.35 54.35 36.82 161.27 8.30 13.72 5.47 3 2 0.00 0 0 6 5 6 6 0 28.876 162 865 19.156 9.981 9.175 0.9192
CRD324 839 16.07 1 3 7 4 154.00 1 2 0 0 34 0.00 64.87 10.00 99.38 6.57 7.07 4.05 2 1 0.00 0 0 7 6 7 8 4 27.507 272 1.867 11.187 8.110 3.077 0.3794
CDR422 840 16.07 1 3 7 4 154.00 1 2 0 0 34 0.00 64.87 10.00 99.38 6.57 7.07 4.05 2 1 0.00 0 0 7 6 7 8 2 13.246 266 563 3.936 1.729 2.207 1.2765
CDR422 984 16.30 1 2 8 2 16.63 1 1 1 12 32 20.35 54.35 36.82 161.27 8.30 13.72 5.47 3 2 0.00 0 0 6 5 6 6 0 16.244 293 765 5.989 2.608 3.382 1.2968
CRD13 921 17.45 1 3 16 1 71.83 1 2 1 10 12 14.38 16.13 30.58 88.07 9.45 9.95 4.65 4 3 0.00 0 0 7 7 7 7 0 35.086 678 1.672 11.356 5.698 5.658 0.9930
CRD13 1214 15.77 1 2 13 4 16.33 0 1 0 2 24 3.32 28.83 25.93 57.98 9.93 11.92 5.10 3 2 0.00 0 0 6 6 6 6 0 33.632 649 1.509 10.917 4.814 6.104 1.2680
CRD13 1224 15.28 1 2 12 4 14.00 1 1 0 5 27 8.42 33.93 35.35 104.92 7.53 8.03 1.87 2 1 0.00 0 0 7 7 7 7 0 30.269 610 1.579 8.919 3.745 5.174 1.3816
CRD13 1345 14.92 1 5 18 0 14.25 1 2 0 4 12 4.42 12.40 16.75 63.07 7.17 7.67 4.07 4 3 0.00 0 0 8 8 8 8 0 30.003 581 1.478 9.668 4.740 4.929 1.0399
CRD13 1679 17.65 1 3 15 0 90.67 1 2 0 12 34 12.97 37.80 31.37 94.22 6.48 6.98 3.48 4 3 0.00 0 0 7 7 7 7 0 30.617 618 1.298 8.987 3.320 5.667 1.7069
CRD13 1355 17.67 1 4 18 0 16.33 1 2 1 8 12 8.48 12.52 24.42 63.23 9.92 10.42 6.97 4 3 0.00 0 0 6 6 6 6 0 30.458 536 1.540 11.698 6.013 5.685 0.9455
CRD13 816 16.48 1 3 13 3 41.92 1 2 1 6 26 10.53 34.85 32.62 119.17 6.07 6.57 3.42 4 3 0.00 0 0 6 6 6 6 0 33.481 755 1.445 7.056 3.165 3.892 1.2297
CRD13 1649 17.52 1 3 17 0 22.93 1 1 1 14 30 17.72 34.00 30.82 79.37 6.35 6.85 3.80 4 3 0.00 0 0 7 7 7 7 0 29.321 594 1.366 8.531 3.594 4.937 1.3737
Aerospace 2023,10, 856 30 of 42
Appendix B
The main hypothesis states: “Mental potential does not depend on the results of the
subjective self-assessment of the anxiety level”.
For the purpose of answering this hypothesis, the statistical analysis of an independent
variable “Subjective self-assessment of the anxiety level” (at the end of the shift) and
obtained dependent variables, was performed by using ANOVA variance analysis of
Statistica 10, as presented below.
The results of subjective self-assessment of the anxiety level are divided into four
main groups:
1. Nothing particularly bothers me;
2. I am sure of myself, and nothing disturbs me;
3. I feel good, completely unforced;
4. I am cool, self-confident and do not get excited.
The statistical analysis was conducted for all CRD tests, i.e., CRD 13, CRD 23,
CRD 241
,
CRD 324, and CRD 422.
CRD 13–Statistical Analysis
Table A2 shows the frequency of the independent variable “Subjective self-assessment
of the anxiety level” divided among four defined groups. The data is collected using the
CRD 13 test.
Table A2. Frequency of “Subjective self-assessment of the anxiety level”–test CRD 13.
Rank Subjective Self-Assessment of the Anxiety Level N
6 Nothing particularly bothers me. 66
7 I am sure of myself, and nothing disturbs me. 51
8 I feel good, completely unforced. 113
9 I am cool, self-confident and do not get excited. 7
TOTAL 237
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that
analysis are shown in Table A3. There were no statistically significant differences recorded.
Table A3.
One-way ANOVA variance analysis of CRD 13 results for “Subjective self-assessment of
the anxiety level”.
Subjective Self-Assessment of the Anxiety Level Rank 6 Rank 7 Rank 8 Rank 9 F p
Ttot 13 average 51.86608 49.45236 49.23956 48.81355 1.059602 0.367014
Tmin 13 average 51.72231 49.95499 49.03078 50.32708 1.001294 0.393004
Tmax 13 average 51.01929 49.95327 49.28599 52.35323 0.542388 0.653739
Btot 13 average 51.49604 49.92260 49.38981 46.15887 0.969353 0.407900
Bin 13 average 51.10484 50.48862 49.39312 45.64711 0.881197 0.451502
Bfin 13 average 51.59082 49.40034 49.46050 47.98723 0.813211 0.487679
Nerr 13 average 0.454545 0.607843 0.814159 0.714286 1.368159 0.253222
Bfin/Bin 13 average 1.280427 1.191822 1.183713 1.349022 1.205296 0.308549
CRD 23–Statistical Analysis
Table A4 shows the frequency of the independent variable “Subjective self-assessment
of the anxiety level” divided among four defined groups. The data is collected using
CRD 23 test.
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that
analysis are shown in Table A5.
Aerospace 2023,10, 856 31 of 42
Table A4. Frequency of “Subjective self-assessment of the anxiety level”–test CRD 23.
Rank Subjective Self-Assessment of the Anxiety Level N
6 Nothing particularly bothers me. 66
7 I am sure of myself, and nothing disturbs me. 51
8 I feel good, completely unforced. 113
9 I am cool, self-confident and do not get excited. 7
TOTAL 237
Table A5.
One-way ANOVA variance analysis of CRD 23 results for “Subjective self-assessment of
the anxiety level”.
Subjective Self-Assessment of the Anxiety Level Rank 6 Rank 7 Rank 8 Rank 9 F p
Ttot 23 average 48.85532 51.19790 50.26323 47.25375 0.725835 0.537478
Tmin 23 average 49.51938 50.72190 50.16723 46.49723 0.429431 0.732104
Tmax 23 average 48.95780 50.94257 50.00549 53.14966 0.613273 0.607021
Btot 23 average 49.55692 51.23196 49.80738 47.31470 0.476483 0.698954
Bin 23 average 50.14412 50.62698 49.78275 45.84474 0.485707 0.692533
Bfin 23 average 49.06727 51.38598 49.97859 49.19941 0.525426 0.665224
Nerr 23 average 2.545455 2.686275 2.938053 3.428571 0.476525 0.698924
Bfin/Bin 23 average 1.294253 1.486982 1.658031 1.376961 4.351235 0.005263
***
*** Statistical significance at the promile level.
The ANOVA variance analysis showed statistically significant differences in the mental
efficiency at the promile level for the Bfin/Bin variable, i.e., Fatigue index.
Figure A1 shows One-way ANOVA analysis of a dependent variable Bfin/Bin and
independent variable “Subjective self-assessment of the anxiety level”.
Aerospace 2023, 10, 856 32 of 44
Table A4. Frequency of “Subjective self-assessment of the anxiety level”–test CRD 23.
Rank Subjective Self-Assessment of the Anxiety Level N
6 Nothing particularly bothers me. 66
7 I am sure of myself, and nothing disturbs me. 51
8 I feel good, completely unforced. 113
9 I am cool, self-confident and do not get excited. 7
TOTAL 237
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that anal-
ysis are shown in Table A5.
Table A5. One-way ANOVA variance analysis of CRD 23 results for “Subjective self-assessment of
the anxiety level”.
Subjective Self-Assessment
of the Anxiety Level Rank 6 Rank 7 Rank 8 Rank 9 F p
Ttot 23 average 48.85532 51.19790 50.26323 47.25375 0.725835 0.537478
Tmin 23 average 49.51938 50.72190 50.16723 46.49723 0.429431 0.732104
Tmax 23 average 48.95780 50.94257 50.00549 53.14966 0.613273 0.607021
Btot 23 average 49.55692 51.23196 49.80738 47.31470 0.476483 0.698954
Bin 23 average 50.14412 50.62698 49.78275 45.84474 0.485707 0.692533
Bfin 23 average 49.06727 51.38598 49.97859 49.19941 0.525426 0.665224
Nerr 23 average 2.545455 2.686275 2.938053 3.428571 0.476525 0.698924
Bfin/Bin 23 average 1.294253 1.486982 1.658031 1.376961 4.351235 0.005263 ***
*** Statistical significance at the promile level.
The ANOVA variance analysis showed statistically significant differences in the
mental efficiency at the promile level for the Bfin/Bin variable, i.e., Fatigue index.
Figure A1 shows One-way ANOVA analysis of a dependent variable Bfin/Bin and
independent variable “Subjective self-assessment of the anxiety level”.
Figure A1. One-way ANOVA analysis of a dependent variable Bfin/Bin and independent variable
“Subjective self-assessment of the anxiety level”–CRD 23.
Figure A1.
One-way ANOVA analysis of a dependent variable Bfin/Bin and independent variable
“Subjective self-assessment of the anxiety level”–CRD 23.
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statis-
tica 10, as shown in Table A6.
Aerospace 2023,10, 856 32 of 42
Table A6.
Post-hoc analysis of the Bfin/Bin and “Subjective self-assessment of the anxiety level” using
the Fisher LSD test.
Bfin/Bin 23 Average 1.2943 1.4870 1.6580 1.3770
Subjective self-assessment of the anxiety level 6 7 8 9
Rank 6 - 0.119042 0.000459 0.753108
Rank 7 0.119042 - 0.126228 0.679898
Rank 8 0.000459 0.126228 - 0.275881
Rank 9 0.753108 0.679898 0.275881 -
CRD 241–Statistical Analysis of Results
Table A7 shows the frequency of the independent variable “Subjective self-assessment
of the anxiety level” divided among four defined groups. The data is collected using
CRD 241 test.
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that
analysis are shown in Table A8.
Table A7. Frequency of “Subjective self-assessment of the anxiety level”–test CRD 241.
Rank Subjective Self-Assessment of the Anxiety Level N
6 Nothing particularly bothers me. 66
7 I am sure of myself, and nothing disturbs me. 50
8 I feel good, completely unforced. 112
9 I am cool, self-confident and do not get excited. 7
TOTAL 235
Table A8.
One-way ANOVA variance analysis of CRD 241 results for “Subjective self-assessment of
the anxiety level”.
Subjective Self-Assessment of the Anxiety Level Rank 6 Rank 7 Rank 8 Rank 9 F p
Ttot 241 average 49.45133 50.98986 49.69860 53.22693 0.498932 0.683381
Tmin 241 average 49.48946 53.54827 48.94247 46.58082 2.890495 0.036222 *
Tmax 241 average 49.93285 49.67687 50.00809 53.29366 0.266681 0.849374
Btot 241 average 49.45550 50.54446 49.85829 53.81896 0.455337 0.713776
Bin 241 average 49.96896 49.68779 49.65709 57.73228 1.451617 0.228573
Bfin 241 average 49.00320 51.48192 50.09892 47.83915 0.688825 0.559694
Nerr 241 average 0.439394 0.500000 0.464286 1.000000 1.061682 0.366133
Bfin/Bin 241 average 0.975712 0.962235 0.922333 0.897471 0.331003 0.802941
* Statistical significance at the level of 0.05.
The ANOVA variance analysis showed statistically significant differences in the mental
efficiency at the level less than 0.05 for a Tmin variable.
Figure A2 shows One-way ANOVA analysis of a dependent variable Tmin and inde-
pendent variable “Subjective self-assessment of the anxiety level”.
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statis-
tica 10, as shown in Table A9.
Table A9.
Post-hoc analysis of a Tmin and “Subjective self-assessment of the anxiety level” using the
Fisher LSD test.
Tmin 241 Average 49.489 53.548 48.942 46.581
Subjective self-assessment of the anxiety level 6 7 8 9
Rank 6 - 0.030140 0.722734 0.461611
Rank 7 0.030140 - 0.006841 0.083198
Rank 8 0.722734 0.006841 - 0.541868
Rank 9 0.461611 0.083198 0.541868 -
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Aerospace 2023, 10, 856 34 of 44
Figure A2. One-way ANOVA analysis of a dependent variable Tmin and independent variable
“Subjective self-assessment of the anxiety level”–CRD 241.
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Sta-
tistica 10, as shown in Table A9.
Table A9. Post-hoc analysis of a Tmin and “Subjective self-assessment of the anxiety level” using
the Fisher LSD test.
Tmin 241 Average 49.489 53.548 48.942 46.581
Subjective self-assessment of the anxiety level 6 7 8 9
Rank 6 - 0.030140 0.722734 0.461611
Rank 7 0.030140 - 0.006841 0.083198
Rank 8 0.722734 0.006841 - 0.541868
Rank 9 0.461611 0.083198 0.541868 -
CRD 324–Statistical Analysis of Results
Table A10 shows the frequency of the independent variable “Subjective self-assess-
ment of the anxiety level” divided among four defined groups. The data is collected using
CRD 324 test.
Table A10. Frequency of “Subjective self-assessment of the anxiety level”–test CRD 324.
Rank Subjective Self-Assessment of the Anxiety Level N
6 Nothing particularly bothers me. 66
7 I am sure of myself, and nothing disturbs me. 51
8 I feel good, completely unforced. 113
9 I am cool, self-confident and do not get excited. 7
TOTAL 237
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that anal-
ysis are shown in Table A11. There were no statistically significant differences recorded.
Figure A2.
One-way ANOVA analysis of a dependent variable Tmin and independent variable
“Subjective self-assessment of the anxiety level”–CRD 241.
CRD 324–Statistical Analysis of Results
Table A10 shows the frequency of the independent variable “Subjective self-assessment
of the anxiety level” divided among four defined groups. The data is collected using
CRD 324 test.
Table A10. Frequency of “Subjective self-assessment of the anxiety level”–test CRD 324.
Rank Subjective Self-Assessment of the Anxiety Level N
6 Nothing particularly bothers me. 66
7 I am sure of myself, and nothing disturbs me. 51
8 I feel good, completely unforced. 113
9 I am cool, self-confident and do not get excited. 7
TOTAL 237
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that
analysis are shown in Table A11. There were no statistically significant differences recorded.
Table A11.
One-way ANOVA variance analysis of CRD 324 results for “Subjective self-assessment of
the anxiety level”.
Subjective Self-Assessment of the Anxiety Level Rank 6 Rank 7 Rank 8 Rank 9 F p
Ttot 324 average 51.84290 49.75132 49.32941 45.17648 1.466267 0.224454
Tmin 324 average 49.59915 51.18520 49.67281 50.21860 0.310190 0.818013
Tmax 324 average 51.40444 47.38614 50.57715 47.27671 1.901583 0.130045
Btot 324 average 51.91536 48.15078 50.02267 45.34265 1.900614 0.130205
Bin 324 average 51.08235 47.56522 50.60690 48.16453 1.479798 0.220734
Bfin 324 average 52.26834 48.91284 49.52223 44.31641 2.186888 0.090303
Nerr 324 average 0.681818 0.509804 0.946903 0.714286 1.445621 0.230243
Bfin/Bin 324 average 0.979237 0.965446 0.933093 0.813493 1.372237 0.251961
Aerospace 2023,10, 856 34 of 42
CRD 422–Statistical Analysis of Results
Table A12 shows the frequency of the independent variable “Subjective self-assessment
of the anxiety level” divided among four defined groups. The data is collected using
CRD 422 test.
Table A12. Frequency of “Subjective self-assessment of the anxiety level”–test CRD 422.
Rank Subjective Self-Assessment of the Anxiety Level N
6 Nothing particularly bothers me. 64
7 I am sure of myself, and nothing disturbs me. 49
8 I feel good, completely unforced. 107
9 I am cool, self-confident and do not get excited. 7
TOTAL 227
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that
analysis are shown in Table A13.
Table A13.
One-way ANOVA variance analysis of CRD 422 results for “Subjective self-assessment of
the anxiety level”.
Subjective Self-Assessment of the Anxiety Level Rank 6 Rank 7 Rank 8 Rank 9 F p
Ttot 422 average 52.57760 48.59999 49.38563 44.61455 2.584625 0.054089
Tmin 422 average 50.83371 49.97814 49.68369 45.98683 0.552553 0.646934
Tmax 422 average 51.53672 47.83276 50.18826 47.56798 1.418019 0.238329
Btot 422 average 52.93341 47.80840 49.48861 46.35976 3.078866 0.028367 *
Bin 422 average 51.58117 48.81983 49.69173 48.74770 0.822149 0.482857
Bfin 422 average 53.46783 47.48592 49.37732 45.24409 4.418580 0.004846
***
Nerr 422 average 1.359375 2.142857 2.925234 5.285714 5.877577 0.000704
***
Bfin/Bin 422 average 1.486409 1.381196 1.334060 1.308132 1.464319 0.225126
* Statistical significance at the level of 0.05. *** Statistical significance at the promile level.
The ANOVA variance analysis showed statistically significant differences in the mental
efficiency at the level less than 0.05 for a Btot variable, and at the promile level for Bfin and
Nerr variables.
Figure A3 shows One-way ANOVA analysis of a dependent variable Nerr and in-
dependent variable “Subjective self-assessment of the anxiety level” (Figure A3a), and
One-way ANOVA analysis of dependent variables Btot and Bfin and an independent
variable “Subjective self-assessment of the anxiety level” (Figure A3b).
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statis-
tica 10, as shown in Table A14.
Table A14.
Post-hoc analysis of a Btot and “Subjective self-assessment of the anxiety level” using the
Fisher LSD test.
Btot 422 Average 52.933 47.808 49.489 46.360
Subjective self-assessment of the anxiety level 6 7 8 9
Rank 6 0.006943 0.028825 0.097011
Rank 7 0.006943 0.326633 0.717818
Rank 8 0.028825 0.326633 0.419140
Rank 9 0.097011 0.717818 0.419140
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Aerospace 2023, 10, 856 36 of 44
way ANOVA analysis of dependent variables Btot and Bfin and an independent variable
“Subjective self-assessment of the anxiety level” (Figure A3b).
(a) (b)
Figure A3. One-way ANOVA analysis of: (a) A dependent variable Nerr and an independent vari-
able “Subjective self-assessment of the anxiety level”; (b) Dependent variable Btot and Bfin and an
independent variable “Subjective self-assessment of the anxiety level”.
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Sta-
tistica 10, as shown in Table A14.
Table A14. Post-hoc analysis of a Btot and “Subjective self-assessment of the anxiety level” using
the Fisher LSD test.
Btot 422 Average 52.933 47.808 49.489 46.360
Subjective self-assessment of the anxiety level 6 7 8 9
Rank 6 0.006943 0.028825 0.097011
Rank 7 0.006943 0.326633 0.717818
Rank 8 0.028825 0.326633 0.419140
Rank 9 0.097011 0.717818 0.419140
Appendix C
The main hypothesis states: “The average duration of a sector does not affect the dy-
namics of mental processing”.
For the purpose of answering this hypothesis, the statistical analysis of an independ-
ent variable “Average duration of a sector” (at the end of the shift) and dependent varia-
bles, was performed using the ANOVA variance analysis of the Statistica 10, as presented
below.
The average duration of a sector is divided into four groups:
5. Duration of a sector from 00:40 to 01:01 h;
6. Duration of a sector from 01:03 to 01:23 h;
7. Duration of a sector from 01:25 to 01:45 h;
8. Duration of a sector from 01:46 to 03:35 h.
The statistical analysis was conducted for all CRD tests, i.e., CRD 13, CRD 23, CRD
241, CRD 324, and CRD 422.
Figure A3.
One-way ANOVA analysis of: (
a
) A dependent variable Nerr and an independent
variable “Subjective self-assessment of the anxiety level”; (
b
) Dependent variable Btot and Bfin and
an independent variable “Subjective self-assessment of the anxiety level”.
Appendix C
The main hypothesis states: “The average duration of a sector does not affect the
dynamics of mental processing”.
For the purpose of answering this hypothesis, the statistical analysis of an independent
variable “Average duration of a sector” (at the end of the shift) and dependent variables,
was performed using the ANOVA variance analysis of the Statistica 10, as presented below.
The average duration of a sector is divided into four groups:
5. Duration of a sector from 00:40 to 01:01 h;
6. Duration of a sector from 01:03 to 01:23 h;
7. Duration of a sector from 01:25 to 01:45 h;
8. Duration of a sector from 01:46 to 03:35 h.
The statistical analysis was conducted for all CRD tests, i.e., CRD 13, CRD 23,
CRD 241
,
CRD 324, and CRD 422.
CRD 13–Statistical Analysis
Table A15 shows the frequency of the independent variable “Average duration of a
sector” divided among four defined groups. The data is collected at the end of the shift,
using CRD 13 test.
Table A15. Frequency of “Average duration of a sector”–test CRD 13.
No. Average Duration of a Sector N
1 Duration of a sector from 00:40 to 01:01 h 26
2 Duration of a sector from 01:03 to 01:23 h 33
3 Duration of a sector from 01:25 to 01:45 h 35
4 Duration of a sector from 01:46 to 03:35 h 25
TOTAL 119
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that
analysis are shown in Table A16. There were no statistically significant differences recorded.
Aerospace 2023,10, 856 36 of 42
Table A16.
One-way ANOVA variance analysis–Differences in “the mental processing efficiency” on
CRD 13 for “Average duration of a sector”.
Average Duration
of a Sector
1. Duration of
a Sector from
00:40 to 01:01 h
2. Duration of
a Sector from
01:03 to 01:23 h
3. Duration of
a Sector from
01:25 to 01:45 h
4. Duration of
a Sector from
01:46 to 03:35 h
F p
Ttot 13 average 46.21642 49.82100 52.18436 51.87311 2.139983 0.099010
Tmin 13 average 46.56269 49.69505 52.19872 53.24869 2.166799 0.095745
Tmax 13 average 47.42146 49.84274 51.08324 51.99670 0.965515 0.411618
Btot 13 average 46.82196 50.14163 51.99055 50.97522 1.456805 0.230075
Bin 13 average 47.13370 50.02517 51.86160 51.26841 1.322296 0.270584
Bfin 13 average 47.27060 50.30616 51.53157 50.36400 0.943615 0.422077
Nerr 13 average 0.230769 0.545455 0.742857 0.520000 1.277792 0.285383
Bfin/Bin 13 average 1.214796 1.248883 1.124423 1.253408 0.775994 0.509711
CRD 23–Statistical Analysis
Table A17 shows the frequency of the independent variable “Average duration of a
sector” divided among four defined groups. The data is collected at the end of the shift,
using CRD 23 test.
Table A17. Frequency of “Average duration of a sector”–test CRD 23.
No. Average Duration of a Sector N
1 Duration of a sector from 00:40 to 01:01 h 26
2 Duration of a sector from 01:03 to 01:23 h 33
3 Duration of a sector from 01:25 to 01:45 h 35
4 Duration of a sector from 01:46 to 03:35 h 25
TOTAL 119
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that
analysis are shown in Table A18.
Table A18.
One-way ANOVA variance analysis–Differences in “mental processing efficiency” on
CRD 23 for “Average duration of a sector”.
Average Duration
of a Sector
1. Duration of
a Sector from
00:40 to 01:01 h
2. Duration of
a Sector from
01:03 to 01:23 h
3. Duration of
a Sector from
01:25 to 01:45 h
4. Duration of
a Sector from
01:46 to 03:35 h
F p
Ttot 23 average 47.00635 49.75537 50.01389 50.66006 0.834626 0.477514
Tmin 23 average 48.57642 50.86285 49.71041 51.27222 0.392667 0.758507
Tmax 23 average 46.57376 50.25681 52.40167 49.26574 1.659819 0.179595
Btot 23 average 47.55674 49.17855 50.53336 49.80169 0.531406 0.661632
Bin 23 average 49.01254 48.68330 51.56244 49.69549 0.706245 0.550188
Bfin 23 average 47.17548 49.73646 49.23677 50.02485 0.460498 0.710417
Nerr 23 average 1.692308 2.333333 3.228571 3.280000 2.816381 0.042277 *
Bfin/Bin 23 average 1.318085 1.570940 1.427197 1.495067 0.745533 0.527098
* Statistical significance at the level of 0.05.
The ANOVA variance analysis showed statistically significant differences in the mental
efficiency at the level less than 0.05 for Nerr variable.
Figure A4 shows the One-way ANOVA analysis of a dependent variable Nerr and an
independent variable “Average duration of a sector”.
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statis-
tica 10, as shown in Table A19.
Aerospace 2023,10, 856 37 of 42
Aerospace 2023, 10, 856 38 of 44
Table A18. One-way ANOVA variance analysis–Differences in “mental processing efficiency” on
CRD 23 for “Average duration of a sector”.
Average Duration of
a Sector
1. Duration of a
Sector from 00:40
to 01:01 h
2. Duration of a
Sector from 01:03
to 01:23 h
3. Duration of a
Sector from 01:25
to 01:45 h
4. Duration of a
Sector from 01:46
to 03:35 h
F p
Ttot 23 average 47.00635 49.75537 50.01389 50.66006 0.834626 0.477514
Tmin 23 average 48.57642 50.86285 49.71041 51.27222 0.392667 0.758507
Tmax 23 average 46.57376 50.25681 52.40167 49.26574 1.659819 0.179595
Btot 23 average 47.55674 49.17855 50.53336 49.80169 0.531406 0.661632
Bin 23 average 49.01254 48.68330 51.56244 49.69549 0.706245 0.550188
Bfin 23 average 47.17548 49.73646 49.23677 50.02485 0.460498 0.710417
Nerr 23 average 1.692308 2.333333 3.228571 3.280000 2.816381 0.042277 *
Bfin/Bin 23 average 1.318085 1.570940 1.427197 1.495067 0.745533 0.527098
* Statistical significance at the level of 0.05.
The ANOVA variance analysis showed statistically significant differences in the
mental efficiency at the level less than 0.05 for Nerr variable.
Figure A4 shows the One-way ANOVA analysis of a dependent variable Nerr and an
independent variable “Average duration of a sector”.
Figure A4. One-way ANOVA analysis of a dependent variable Nerr and an independent variable
“Average duration of a sector”–CRD 23.
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Sta-
tistica 10, as shown in Table A19.
Figure A4.
One-way ANOVA analysis of a dependent variable Nerr and an independent variable
“Average duration of a sector”–CRD 23.
Table A19.
Post-hoc analysis of a Nerr and an “Average duration of a sector” using the Fisher
LSD test.
Nerr 23 Average 1.692308 2.333333 3.228571 3.280000
Average duration of a sector 1 2 3 4
1. Duration of a sector from 00:40 to 01:01 h - 0.311167 0.015010 0.020025
2. Duration of a sector from 01:03 to 01:23 h 0.311167 - 0.127440 0.140080
3. Duration of a sector from 01:25 to 01:45 h 0.015010 0.127440 - 0.935005
4. Duration of a sector from 01:46 to 03:35 h 0.020025 0.140080 0.935005 -
CRD 241–Statistical Analysis of Results
Table A20 shows the frequency of the independent variable “Average duration of a
sector” divided among four defined groups. The data is collected at the end of the shift,
using CRD 241 test.
Table A20. Frequency of “Average duration of a sector”–test CRD 241.
No. Average Duration of a Sector N
1 Duration of a sector from 00:40 to 01:01 h 26
2 Duration of a sector from 01:03 to 01:23 h 32
3 Duration of a sector from 01:25 to 01:45 h 35
h Duration of a sector from 01:46 to 03:35 h 25
TOTAL 118
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that
analysis are shown in Table A21. There were no statistically significant differences recorded.
Aerospace 2023,10, 856 38 of 42
Table A21.
One-way ANOVA variance analysis–Differences in “the mental processing efficiency” on
CRD 241 for “Average duration of a sector”.
Average Duration
of a Sector
1. Duration of
a Sector from
00:40 to 01:01 h
2. Duration of
a Sector from
01:03 to 01:23 h
3. Duration of
a Sector from
01:25 to 01:45 h
4. Duration of
a Sector from
01:46 to 03:35 h
F p
Ttot 241 average 46.40752 49.08085 51.20806 50.74141 1.409193 0.243768
Tmin 241 average 47.47529 47.91140 52.49647 52.70048 2.222416 0.089358
Tmax 241 average 46.81067 49.15896 52.28729 49.34677 1.478612 0.224121
Btot 241 average 46.41095 49.38678 50.87664 50.47119 1.216198 0.307138
Bin 241 average 46.48104 49.45775 51.18209 51.18078 1.538701 0.208329
Bfin 241 average 47.52253 49.66491 50.45635 49.78640 0.459033 0.711447
Nerr 241 average 0.269231 0.500000 0.485714 0.680000 1.261576 0.291004
Bfin/Bin 241 average 0.874167 0.901808 0.999709 0.956845 0.656994 0.580192
CRD 324–Statistical Analysis of Results
Table A22 shows the frequency of the independent variable “Average duration of a
sector” divided among four defined groups. The data is collected at the end of the shift,
using CRD 324 test.
Table A22. Frequency of “Average duration of a sector”–test CRD 324.
No. Average Duration of a Sector N
1 Duration of a sector from 00:40 to 01:01 h 26
2 Duration of a sector from 01:03 to 01:23 h 33
3 Duration of a sector from 01:25 to 01:45 h 35
4 Duration of a sector from 01:46 to 03:35 h 25
TOTAL 119
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that
analysis are shown in Table A23.
Table A23.
One-way ANOVA variance analysis–Differences in “the mental processing efficiency” on
CRD 324 for “Average duration of a sector”.
Average Duration
of a Sector
1. Duration of
a Sector from
00:40 to 01:01 h
2. Duration of
a Sector from
01:03 to 01:23 h
3. Duration of
a Sector from
01:25 to 01:45 h
4. Duration of
a Sector from
01:46 to 03:35 h
F p
Ttot 324 average 48.11431 51.58547 53.64137 53.85030 2.083585 0.106238
Tmin 324 average 47.47785 50.58187 50.22000 51.72998 0.821143 0.484770
Tmax 324 average 48.27304 50.36144 52.92532 53.74278 1.409672 0.243576
Btot 324 average 51.76143 50.26904 54.02739 51.81702 0.718102 0.543141
Bin 324 average 50.87915 52.06397 52.39503 52.02470 0.107133 0.955773
Bfin 324 average 52.28071 48.14814 54.73094 51.01424 2.345741 0.076505
Nerr 324 average 0.346154 0.484848 1.228571 1.040000 2.936446 0.036324 *
Bfin/Bin 324 average 0.970464 0.865062 1.056610 0.950476 3.769393 0.012667 *
* Statistical significance at the level of 0.05.
The ANOVA variance analysis showed statistically significant differences in the mental
efficiency at the level less than 0.05 for Nerr and Bfin/Bin variables.
Figure A5 shows the One-way ANOVA analysis of a dependent variable Nerr and an
independent variable “Average duration of a sector” (Figure A5a), and One-way ANOVA
analysis of a dependent variable Bfin/Bin (Fatigue index) and an independent variable
“Average duration of a sector” (Figure A5b).
Aerospace 2023,10, 856 39 of 42
Aerospace 2023, 10, 856 40 of 44
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that anal-
ysis are shown in Table A23.
Table A23. One-way ANOVA variance analysis–Differences in “the mental processing efficiency”
on CRD 324 for “Average duration of a sector”.
Average Duration of
a Sector
1. Duration of a
Sector from 00:40
to 01:01 h
2. Duration of a
Sector from 01:03
to 01:23 h
3. Duration of a
Sector from 01:25
to 01:45 h
4. Duration of a
Sector from 01:46
to 03:35 h
F p
Ttot 324 average 48.11431 51.58547 53.64137 53.85030 2.083585 0.106238
Tmin 324 average 47.47785 50.58187 50.22000 51.72998 0.821143 0.484770
Tmax 324 average 48.27304 50.36144 52.92532 53.74278 1.409672 0.243576
Btot 324 average 51.76143 50.26904 54.02739 51.81702 0.718102 0.543141
Bin 324 average 50.87915 52.06397 52.39503 52.02470 0.107133 0.955773
Bfin 324 average 52.28071 48.14814 54.73094 51.01424 2.345741 0.076505
Nerr 324 average 0.346154 0.484848 1.228571 1.040000 2.936446 0.036324 *
Bfin/Bin 324 average 0.970464 0.865062 1.056610 0.950476 3.769393 0.012667 *
* Statistical significance at the level of 0.05.
The ANOVA variance analysis showed statistically significant differences in the
mental efficiency at the level less than 0.05 for Nerr and Bfin/Bin variables.
Figure A5 shows the One-way ANOVA analysis of a dependent variable Nerr and an
independent variable “Average duration of a sector” (Figure A5a), and One-way ANOVA
analysis of a dependent variable Bfin/Bin (Fatigue index) and an independent variable
“Average duration of a sector” (Figure A5b).
(a) (b)
Figure A5. One-way ANOVA analysis of: (a) A dependent variable Nerr and an independent vari-
able “Average duration of a sector”; (b) A dependent variable Bfin/Bin and an independent variable
“Average duration of a sector”.
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Sta-
tistica 10, as shown in Tables A24 and A25.
Figure A5.
One-way ANOVA analysis of: (
a
) A dependent variable Nerr and an independent variable
“Average duration of a sector”; (
b
) A dependent variable Bfin/Bin and an independent variable
“Average duration of a sector”.
Additionally, the post-hoc analysis was conducted using the Fisher LSD test of Statis-
tica 10, as shown in Tables A24 and A25.
Table A24.
Post-hoc analysis of a Nerr and an “Average duration of a sector” using the Fisher
LSD test.
Nerr 324 Average 0.34615 0.48485 1.2286 1.0400
Average duration of a sector 1 2 3 4
1. Duration of a sector from 00:40 to 01:01 h - 0.699777 0.014160 0.072826
2. Duration of a sector from 01:03 to 01:23 h 0.699777 - 0.026989 0.128674
3. Duration of a sector from 01:25 to 01:45 h 0.014160 0.026989 - 0.599660
4. Duration of a sector from 01:46 to 03:35 h 0.072826 0.128674 0.599660 -
Table A25.
Post-hoc analysis of a Bfin/Bin and an “Average duration of a sector” using the Fisher
LSD test.
Bfin/Bin 324 Average 0.97046 0.86506 1.0566 0.95048
Average duration of a sector 1 2 3 4
1. Duration of a sector from 00:40 to 01:01 h - 0.090919 0.160858 0.762692
2. Duration of a sector from 01:03 to 01:23 h 0.090919 - 0.001099 0.174490
3. Duration of a sector from 01:25 to 01:45 h 0.160858 0.001099 - 0.088281
4. Duration of a sector from 01:46 to 03:35 h 0.762692 0.174490 0.088281 -
CRD 422–Statistical Analysis of Results
Table A26 shows the frequency of the independent variable “Average duration of a
sector” divided among four defined groups. The data is collected at the end of the shift,
using CRD 422 test.
Table A26. Frequency of “Average duration of a sector”–test CRD 422.
No. Average Duration of a Sector N
1 Duration of a sector from 00:40 to 01:01 h 26
2 Duration of a sector from 01:03 to 01:23 h 31
3 Duration of a sector from 01:25 to 01:45 h 33
4 Duration of a sector from 01:46 to 03:35 h 25
TOTAL 115
Aerospace 2023,10, 856 40 of 42
In the next step, the ANOVA variance analysis of Statistica 10 was used to test the
significance of statistical differences in CRD dependent variables. The results of that
analysis are shown in Table A27. There were no statistically significant differences recorded.
Table A27.
One-way ANOVA variance analysis–Differences in “the mental processing efficiency” on
CRD 422 for “Average duration of a sector”.
Average Duration
of a Sector
1. Duration of
a Sector from
00:40 to 01:01 h
2. Duration of
a Sector from
01:03 to 01:23 h
3. Duration of
a Sector from
01:25 to 01:45 h
4. Duration of
a Sector from
01:46 to 03:35 h
F p
Ttot 422 average 48.32397 51.88769 54.40093 54.28714 2.148779 0.098147
Tmin 422 average 46.90232 50.28237 52.58701 53.40961 2.136707 0.099637
Tmax 422 average 50.02255 49.35864 51.90110 52.52097 0.519525 0.669711
Btot 422 average 50.78579 52.15440 54.09295 52.50808 0.430383 0.731639
Bin 422 average 49.81383 52.17682 53.60702 51.93453 0.572429 0.634319
Bfin 422 average 51.48297 51.69732 53.57845 52.31380 0.212872 0.887300
Nerr 422 average 1.115385 1.290323 2.000000 1.480000 0.894118 0.446668
Bfin/Bin 422 average 1.486102 1.318848 1.387670 1.385508 0.565700 0.638757
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