Abstract and Figures

System of interest (SoI) failures can sometimes be traced to an unexpected behavior occurring within another system that is a member of the system of systems (SoS) with the SoI. This article presents a method for use when designing an SoI that helps to analyze an SoS for unexpected behaviors from existing SoS members during the SoI's conceptual functional modeling phase of system architecture. The concept of irrationality initiators—unanticipated or unexpected failure flows emitted from one system that adversely impact an SoI, which appear to be impossible or irrational to engineers developing the new system—is introduced and implemented in a quantitative risk analysis method. The method is implemented in the failure flow identification and propagation framework to yield a probability distribution of failure paths through an SoI in the SoS. An example of a network of autonomous vehicles operating in a partially denied environment is presented to demonstrate the method. The method presented in this paper allows practitioners to more easily identify potential failure paths and prioritize fixing vulnerabilities in an SoI during functional modeling when significant changes can still be made with minimal impact to cost and schedule.
Content may be subject to copyright.
Received: 15 December 2018 Revised: 14 October 2019 Accepted: 16 October 2019
DOI: 10.1002/sys.21520
A method of identifying and analyzing irrational system
behavior in a system of systems
Douglas L. Van Bossuyt1Bryan M. O’Halloran1Ryan M. Arlitt2
1Department of Systems Engineering, Naval
Postgraduate School, Monterey, California, USA
2Department of Mechanical Engineering,
TechnicalUniversity of Denmark, Lyngby,
Douglas L. Van Bossuyt, Department of Sys-
tems Engineering, Naval PostgradauteSchool,
Monterey,CA 93943, USA.
Email: douglas.vanbossuyt@nps.edu
System of interest (SoI) failures can sometimes be traced to an unexpected behavior occurring
within another system that is a member of the system of systems (SoS) with the SoI. This article
presents a method for use when designing an SoI that helps to analyze an SoS for unexpected
behaviors from existing SoS members during the SoI’s conceptual functional modeling phase of
system architecture. The concept of irrationality initiators—unanticipated or unexpected failure
flows emitted from one system that adversely impact an SoI, which appear to be impossible or irra-
tional to engineers developing the new system—is introduced and implemented in a quantitative
risk analysis method. The method is implemented in the failure flow identification and propagation
framework to yield a probability distribution of failure paths through an SoI in the SoS. An example
of a network of autonomous vehicles operating in a partially denied environment is presented to
demonstrate the method. The method presented in this paper allows practitioners to more easily
identify potential failure paths and prioritize fixing vulnerabilities in an SoI during functional
modeling when significant changes can still be made with minimal impact to cost and schedule.
failure analysis, irrationality, irrational system behavior, risk analysis, systems engineering, system
modeling, system of systems
In spite of extensive efforts undertaken during the design of systems,
system failures continue to occur regularly. This is demonstrated
by a multitude of system failure examples making headline news.
Over a period of 52 years (1957-2009), there were over 400 publicly
documented mission failures in the space industry, including satellites,
crewed spacecraft, and rockets.1Since the introduction of the com-
mercial airline industry, there have been a reported 154 984 deaths as
the result of 26 152 accidents.2According to Ref. 3, there have been a
total of 25 major dam failures documented, 16 of which have occurred
in the last 50 years. The nuclear power industry has observed over 200
significant failures, several of which have resulted mitigations exceed-
ing one billion U.S. dollars.4Recent events in the aviation industry5
emphasize that failures occur even in newly designed systems with
strong regulatory oversight. In short: systems routinely fail regardless
of system type, purpose, age, design approach used, industry, or the
era in which it was designed and built. Regardless of our best design
and analysis of systems, we as practitioners and researchers continue
to be surprised by emergent (unpredicted, unexpected, discounted,
or seemingly illogical or irrational) system failures. While we would
like to believe that the systems we design will behave exactly how
we predicted and observed during the design and testing portion of
the systems engineering process, the literature and the popular press
show that this is often not true.
Within the context of system failures, harmful emergent system
behaviors have been observed in engineered systems for many
decades.6Over time, more simple-to-understand emergent system
behaviors have been corrected for and are no longer a significant
issue.7However, efforts to systematically understand the underlying
causes of the emergent behaviors and design systems to minimize
the potential for harm have only been undertaken in the last few
decades.8,9 The majority of industry work and academic research has
focused on events that have previously been observed, and expected
and predictable events.10 As a result of efforts to address such events,
modern systems are much less likely to fail from single point failures
or from commonly occurring failures caused by multiple component
failures; such failures have largely been identified and corrected.11,12
The failures that are now observed in systems are often as a result
of multiple failure events occurring together to develop an emergent
Systems Engineering. 2019;22:519–537. c
2019 Wiley Periodicals, Inc. 519wileyonlinelibrary.com/journal/sys
system behavior that has previously not been predicted or observed,13
or which had been ruled out through previous analysis as unlikely to
occur.14 For example, a recent collision on Singapore’s Mass Rapid
Transit system resulted in 38 injuries and was a result of a series
of unexpected interactions across multiple systems and subsys-
tems in the signaling system that led to a series of undetected and
progressively degraded operation conditions.15
We believe that if the systems engineering community wishes to
continue to increase the robustness, resilience, interoperability, and
survivability of system of systems (SoSs) in an effort to improve the
probability of an SoS completing its mission successfully, a better
understanding of how failures are initiated in system of interest (SoIs)
by other members of an SoS that lead to SoI failure is needed. Already,
there have been some efforts that begin to address the problem with
most focusing on the more cost-effective conceptual phase of system
engineering when architectural trade-off studies of potential system
architectures are conducted and before significant component design
work has begun.16 For instance, there is a proposed method to analyze
SoS early on in the design cycle via SoS modeling.17 There are many
different ways to model SoS, such as the functional basis for engi-
neering design (FBED)18 functional modeling taxonomy, which can be
used to make functional architectures. A better understanding of what
potential failure events have a higher likelihood of occurrence can help
determine priorities for mitigating such potential failure events.19 One
way to model potential failure events is to use functional models to pre-
dict the likelihood of failure of a system.20 An SoS architecture can be
iterated many times until an acceptable system failure probability has
been reached.21 Using methods such as the family of methods devel-
oped from failure flow identification and propagation (FFIP),20,22–25
failure propagation can be assessed at a functional level through a
system. Probabilistic risk assessment (PRA) methods can also be useful
to understand system failure propagation, especially for systems with
high redundancy and failure mitigation systems.10 Many of the above
mentioned methods and approaches fall under the umbrella of model-
based systems engineering, which has been heavily advocated by the
International Council on Systems Engineering among others for sev-
eral decades.26 The INCOSE Systems Engineering Book of Knowledge
also includes several relevant sections on safety engineering (including
several variations of hazard analysis) and reliability, availability, and
maintainability that help to improve SOSs in those respective areas.26
Within the systems engineering V model,27 the method presented
in this paper is specifically meant to be used in the system architecture
phase of design—near the front end of the V model. In specific, the
conceptual phase of system architecture where functional models are
being developed from requirements, design reference missions, and
other similar information28 is where the below introduced method
is targeted for use. The early conceptual functional modeling stage
of system architecture within the systems engineering process is an
opportune time to uncover potential unexpected or unanticipated
system behaviors, the corresponding initiating events in an SoI, and
their impacts on SoIs. Large changes to SoI system architecture can
be made at this stage without significant adverse impact on schedule
and budget.16 The conceptual phase of system architecture also often
precedes hazard analysis, failure modes effects and criticality analysis
(FMECA), PRA, and other similar methods of failure and risk analysis
although FFIP and uncoupled failure flow state reasoner (UFFSR) are
conducted on functional models during conceptual design.
The method presented in this paper is intended for use on SoS and
SoI typically used by the U.S. Department of Defense (DoD), such as
groups of autonomous vehicles operating in an SoS configuration;
adaptive force packages that include surface vessels, underwater
assets, airplanes, autonomous vehicles of a variety of types, and other
related systems operating as an SoS (often in support of a mission
objective and in relation to mission engineering29); forward operating
base complexes where ground vehicles, living quarters, maintenance
depots, munitions storage, autonomous vehicles, and other systems
are present and can be considered an SoS; and other similar systems.
While the method we present below may be useful for other SoSs,
such as microgrids, cyber SoS (eg, fully software-based SoS—note: the
previous examples that are within the scope of this method do include
cyber-physical elements and are not excluded from consideration),
and primarily human-based SoS (eg, a company of soldiers and their
equipment) among other examples, this is not the primary focus of our
presented method. Further, while irrational behaviors of humans can
be incorporated to some extent in the method through the FBED flow
set, our primary focus is explicitly not on human-system interaction
but instead is primarily on the systems themselves.
In spite of the significant advances made in understanding how
failures propagate through SoIs and SoS, SoI failure events caused by
other systems within the SoS are often still missed.30–32 As far as we
are aware, the analysis how one or more systems within an SoS can
behave in unpredicted or unanticipated ways that result in initiating
failure events in an SoI are not being well analyzed within existing
failure analysis methods during conceptual functional modeling during
the system architecture phase of systems design for the specific types
of SoS mentioned above. Thus, there currently exists no practicable
way for practitioners to identify and analyze potential system unan-
ticipated or unpredicted system behaviors within an SoS that create
failure initiating events in an SoI.
1.1 Specific contributions
This article contributes an analysis method that helps the practitioner
consider irrational system behavior of member systems within an
SoS and their impacts on an SoI in the form of “irrationality initators”
(failure initiating events caused by unanticipated or unpredicted sys-
tem behaviors—described in detail in the methodology section). The
method is intended to be used in early system modeling where concep-
tual functional architectures are developed. An analysis of potential
effects (ie, the method) caused by “irrational system behaviors” (system
behaviors that are unanticipated or unpredicted by the SoI systems
engineers—described in detail in the methodology section) originating
in one or more systems and adversely affecting the SoI through “irra-
tionality initiators” is conducted using several techniques. The result
of the analysis can then be used to further develop and refine the SoI
system architecture to improve SoI robustness to irrational system
The method developed in this article relies upon several bodies of
work, including systems modeling, failure analysis, and probability
assessment. This section provides background and discusses related
efforts of relevance to the method presented here.
Systems modeling is a family of techniques used to develop
models of systems for the purposes of system representation and
simulation. Many system modeling techniques are available to the
practitioner, such as the Integrated Computer Aided Manufacturing
(Icam) DEFinition for Function Modeling (IDEF0) language33 that
has seen significant use in the systems engineering community. The
Universal Modeling Language and its offspring, the System Modeling
Language,34–36 are seeing increased usage especially within the
DoD. Other modeling languages, such as Refs. 37 and 38,are also
available and with varying levels of adoption. This article uses the
FBED18,39 functional hierarchical modeling language to represent
systems. The FBED models system functions and flows where func-
tions defined are the actions that a system can take (eg, transport
energy, convert rotational energy to electrical energy, etc) and flows
are defined as material, energy, or signal moving within the system
(eg, energy-chemical, signal-control-discrete, etc), into or out of a
system boundary, or between systems in the case of an SoS. The FBED
function and flow taxonomies are each decomposed into primary,
secondary, and tertiary categories where each deeper level has an
increased level of specificity. System components are abstracted to a
functional level to give engineers the freedom to consider functionality
of a system without being locked into a specific component architec-
ture. The abstraction of functions from components and the derivation
of component solutions from functions is a well understood and
established practice from the original and subsequent development
of FBED.40 FBED is an established National Institute of Standards
standard that helped to unify several disparate efforts in functional
modeling for engineering design.18,39 This places FBED as a modeling
language primarily suited for conceptual modeling. However, we have
observed FBED being used to analyze existing designs as well.
Failure analysis is performed to understand how a system may
degrade or fail primarily during operation although the analysis can
also be performed for other phases of the system life cycle, such as
maintenance. Failure modes and effects analysis (FMEA)41 and its
extension, FMECA,42 are heavily used in private industry43 and in
the DoD, where MIL-STD-882E prescribes FMECA to conduct hazard
analysis.44 FMEA calculates a risk priority number (RPN) by multiply-
ing the probability of a failure event happening, the ability to detect
the event before it happens, and the severity of the event on 1-10
scales with the RPN being on a 1-1000 scale to prioritize the order in
which potential failure events should be mitigated. However, FMEA
and FMECA are ill-suited to identify emergent system behaviors, such
as multiple component failures that lead to a system-level failure and
that have not been observed before in operating systems.45,46
PRA combines fault tree analysis47 and event tree analysis48
to produce failure event sequences that generally include multiple
components or subsystem failures in sequence to cause a system-level
failure. Initiating events are the probability of an event occurring that
initiates a potential system failure.49 However, valid initiating events
can be erroneously discounted as being possible or are sufficiently
beyond prior experience of engineers conducting the PRA that such
initiating events can fail to be included in the analysis.30,31
Cut-sets are produced by PRA, which can then be used to analyze
failure events that require multiple events to occur to lead to failure
(usually system failure although failure can be defined differently
depending upon the application).50 The production of cut-sets is often
truncated when the probability of an event occurring falls below a pre-
determined threshold.51 This can occasionally lead to low probability
but high consequence failure events from being missed in analysis
conducted using PRA.52
Unpredicted or unanticipated system behavior can occur in sys-
tems for many different reasons.53 A significant body of research has
been developed to understand unanticipated or unpredicted system
behaviors54–56 and address such system behaviors through increasing
system robustness and resiliency to both external and internal failure
initiating events.57–59 However, we have found scant evidence of work
being done to understand unexpected or unpredicted system behavior
within the context of an SoS.
Several efforts havebeen made to combine functional modeling and
failure analysis, such as a method of developing FMEAs for functional
models.60 The FFIP method20,22 uses a probabilistic approach to
analyze functional models for failure propagation. In recent years,
FFIP has been extended with methods, such as the UFFSR24 that
evaluates failure flows that do not travel along nominal flow pathways,
TAB L E 1 Comparison of existing risk, reliability, safety, and related methods presented to identify gaps in existing methodologies
Method capability Proposed method PRA FMEA/FMECA FFIP Hazard analysis Nan et al.
Identifies all irrationality initiators Y N N N N N
Identify failure propagation paths within
Quantifying failure probability outcomes Y Y Y N Y Y
Iterate functional model with results Y N N N N N
Propagate uncoupled failure flows Y N N N N N
Note: Note that instead of referencing multiple hazard analyses, the term hazard analysis encompasses the intent of the methods enclosed in MIL-STD-
882E.44 Examples methods include preliminary hazard analysis (PHA), functional hazard analysis (FHA), system hazard analysis (SHA), subsystem hazard
analysis (SSHA), Nan et al., etc. Note that irrationality initiators are described in detail in the methodology section. In short: an irrationality initiator is an
initiating event in an SoI that is induced by another system within the SoS behaving in an unpredicted or unanticipated manner.
and a functional Bayesian approach to developing prognostic and
health monitoring subsystems that can detect incipient failures while
they still can be corrected.23 In the FFIP family of methods, initiating
events are developed in a similar way to initiating events in PRA, which
leads to unexpected or unpredicted initiating events often not being
considered. The FFIP family of methods produces cut-sets similar to
those developed by PRA and handles truncation of analysis in a similar
Nan et. al. developed a method of analyzing supervisory control and
data acquisition (SCADA) systems and the systems under the SCADA’s
control in critical infrastructure to identify vulnerabilities. The method
investigates inderdependencies of four types, including physical, cyber,
geographic, and logic. However, Nan et al. does not conduct the analy-
sis at the functional level of system architecture nor is it an exhaustive
flow-based method of identifying potential initiating events.61
The method presented in this section has been developed specifically
for use during conceptual design of a system that is part of an SoS when
architectural trade-off studies are performed. Significant alterations
in a system’s design at this stage of the design process are relatively
inexpensive to perform and take relatively little time to implement.
A high-level flow chart is provided in Figure 1 to graphically show the
five steps of the methodology.
Note that a demonstration of the method is provided in the Case
Study and Results section of this article (Section 4). We have omitted
examples within the Methodology section and instead direct the inter-
ested reader to the Case Study and Results section. It should also be
noted that the case study is a fictionalized case study and is intended
only to demonstrate the methodology presented in this section.
3.1 Model the systems within the SoS
The first step is to model the SoI within the SoS and their connections
to one another. FBED18 is our preferred functional modeling method
and is used throughout this article. However, many equally valid meth-
ods are available.34–38 In concert with developing functional models,
physical component solutions to functions can be developed. Having
component solutions to functions (either a one to one correlation or
a many to one correlation if component solutions have not been down
selected yet) at this stage in the design process allows mapping of what
happens when a physical component fails to the function it fulfills. An
example of a function to component mapping is the function transfer
liquid, which may be fulfilled by the component pipe or the component
canal among other possible component solutions.
3.2 Identify potential irrational system behaviors
Based on observations in the literature and in our professional prac-
tices, we propose considering emergent system behaviors that were
not previously predicted or were discounted as being highly unlikely
to be what we term “irrational system behaviors.” We further refine
the definition of irrational system behaviors as unexpected behaviors
within a system that emit potential failure initiating events that other
systems within an SoS may in turn receive as inputs and thus cause
failures in the other systems. In short: irrational system behaviors are
system behaviors that have not been previously observed or predicted
(no prior knowledge or discounted as being a potential threat) by other
systems within an SoS, and have not been analyzed through routine
means of system simulation and hazard/failure analysis.
An example of potential irrational system behavior is a compressed
air delivery network SoS with a compressor, an air cleaning system,
a distribution system, and multiple compressed air use systems (eg,
venturi chillers, pneumatic solenoid valves, pneumatic rotary motors,
pneumatic cylinders, etc). While the SoS is designed with the expecta-
tion that contaminants such as water and compressor oil may bypass
the air cleaning system and would then be caught by filters on the
compressed air use systems, the SoS is not designed for and does not
expect the compressor to deliver corrosive gas. Such an irrational
system behavior may occur, for instance, because of an acetylene tank
unexpectedly venting near the compressor’s air intake. This may lead
FIGURE 1 High-level overview of the proposed
to multiple failure events in the systems that receive compressed air in
the SoS as unexpected corrosion occurs.
While an argument can be made that our definition of irrational sys-
tem behavior could also be described as unexpected or unanticipated
system behavior, we specifically use the word “irrational” to call prac-
titioners’ attentions to this phenomenon. In our professional practice,
on multiple occasions, we have observed senior systems engineers and
subject matter experts caught off guard by failure events caused by
other systems than the SoI (SoI–the system being designed to enter
an existing or proposed SoS) within an SoS. Within the context of SoS,
many practitioners we have discussed the concept of irrational system
behavior have their own stories of other systems within an SoS behav-
ing completely irrationally and impacting their SoIs when compared
with the practitioners’ understanding of how the other systems should
behave. We have personally witnessed in several industries that, in
spite of (a) excellent requirements, interface management strategies,
and comprehensive work products, and (b) outstanding hazard, failure,
reliability, and related analyses, irrational system behaviors continue
to occur that impact SoIs. While it may appear that irrational system
behaviors occur with high frequency, it is important to be clear that
these are in fact rare events. However, the consequences of irra-
tional system behaviors are significant enough to warrant study and
development of the methodology presented in this article.
Even when logical and probabilistic approaches for analyzing an
SoI within the SoS are used, the approaches often fail to uncover
potential emergent SoI system behaviors that are initiated by
irrational system behaviors of other systems within the SoS. The
aforementioned issue happens in spite of extensive guidance on
searching for potentially overlooked initiating events.30,62 In cases
where potential failure scenarios caused by irrational system behav-
iors have been identified, organizations that conduct system failure
and risk analysis can sometimes discount such scenarios and not
rigorously analyze the potential outcomes.63,64 The problem of not
identifying or discounting identified emergent system behaviors is
compounded as SoS are developed by connecting multiple systems
together. As the number of systems in an SoS increases, the likelihood
of irrational system behaviors increases. Irrational system behaviors
can occur in one or more systems within an SoS.65–67 In short, SoS can
have irrational system behaviors that may result in severe negative
outcomes to individual systems within an SoS or to the entire SoS.
One specific goal of this work is to identify irrational systems behav-
iors. In order to identify these behaviors, it is useful to understand
how systems can behave irrationally. The study of irrational behavior
began with investigating irrational behavior of people such as in the
context of economic models.68,69 Irrational behavior of people (also
often called irrationality) can take different forms and have different
causes, such as visceral reactions70 to events, psychosis,71 actions
taken under duress,72 or even intentional irrationality.73,74 Engineers
are no exception to irrational behavior; design engineers can appear to
behave irrationally in their risk-based design decisions although such
irrationality can sometimes be explained by the individual personal
utility function of a specific engineer.75 While some argue that humans
are the only true source of irrational system behaviors, we are using
the phrase “irrational system behavior” in a different context, as
described above. However, examining the context of irrational behav-
ior of humans is useful in conceptualizing how systems can appear
to behave irrationally to an outside observer or even to the subject
matter expert of the system behaving irrationally.
Decision theory and utility theory have been used to help under-
stand how people can appear to behave irrationally,76–81 including how
neural systems work82,83 Through the application of utility and deci-
sion theory, it is now possible to develop system models that deviate
from the expected value theorem and instead match a specific utility
function of either an individual or an organization.84 We contend
that (much like humans) while a system may appear to be behaving
irrationally to an outside observer, the system’s utility function may be
different from the observer’s expectation. In other words, the system
is behaving normally based on its own internal utility function but
appears to an external observer to be behaving irrationally.
From our proposed definition of irrational system behavior devel-
oped above, we further refine the definition of irrational system
behavior to specifically refer to functional flows that exit a system
boundary being unreasonable or illogical when compared to expected
and previously experienced system behavior. We define unreasonable
or illogical behavior as deviation from preprogrammed behaviors and
rational expectations;85 unresponsiveness to incentives;74 and/or
deviation from self-interest, self-preservation, and/or SoS self interest
and preservation.86 We further refine the definition of irrational
system behavior in the context of this article to specifically be a failure
flow class20,22 that exits a system boundary and that would not nor-
mally be anticipated through common failure analysis techniques, such
as hazard analysis,87 FMEAandtherelatedFMECA,
41 PRA,10FFIP,20
UFFSR,24 and other similar methods. Thus, irrational system behavior
produces potential initiating events for the SoI within an SoS. Another
way to conceptualize irrational system behavior is that it is similar
to Black Swan events as described by Taleb13,88 although irrational
system behavior is focused specifically on failure initiating events,
while Black Swan events generally refer to system-level failure.
An initiating event is an event that initiates an incipient failure
within an SoI that may propagate through the SoI until (a) the SoI has
failed, (b) the SoI is operating in a stable but degraded condition, (c) the
SoI recovers to a nominal operating state after a period of degraded
performance, or (d) the SoI mitigates the incipient failure. Initiating
events are used in PRA, FFIP, and other quantitative failure and risk
analysis methods. While standard procedures are available to identify
potential initiating events that may affect a system,49 a practitioner
may discount initiating events that are outside of prior experiences
with a system or that seem irrational.30–32
We propose supplementing existing methods of identifying initi-
ating events (eg, Ref. 49) by introducing the concept of irrationality
initiators, which we define as irrational system behavior within an SoS
that creates initiating events within an SoI. In other words, irrationality
initiators are caused by irrational system behavior of one or more sys-
tems within an SoS that emit unexpected system boundary-crossing
failure flows. The failure flows become irrationality initiators when
they encounter the SoI in the SoS. Irrationality initiators may follow
nominal flow paths between systems such as a data link between two
systems or irrationality initiators may affect the SoI by propagating via
uncoupled flow paths.24 We distinguish irrationality initiators from
failure flows that turn into ordinary initiating events to specifically
denote that irrationality initiators are initiating events originating out-
side of the SoI and caused by irrational system behavior of other sys-
tems within the SoS. Irrationality initiators are not caused by the envi-
ronment and do not include expected and/or understood failure flows
from other systems within the SoS that are already captured through
existing methods of initiating event analysis. As is the case with ordi-
nary initiating events, an irrationality initiator may also cause a failure
to propagate through an SoI and may result in one of several system
end states, including partially failed or degraded performance of the
SoI; failure of the SoI; after an initial period of disruption, the SoI recov-
ers to a nominal state; or a nominal SoI state. To reiterate, in the context
of an SoS, an SoI acquires irrationality initiators from other systems
within the SoS. It should be noted that an SoI receiving irrational ini-
tiators may in turn generate its own irrational system behaviors, which
may turn into irrationality initiators in other systems within the SoS.
Based on the proposed definitions of irrational system behavior
and irrationality initiators developed above, we propose the following
approach, as shown in Figure 2, to identify irrationality initiators. The
approach starts with all potential flows from the FBED flow set18,39
before reducing down to potential flows that may happen within a
specific SoS.
Step 2, Part 1: Start with all secondary and tertiary flow descriptions
from FBED. Each flow may conceivably be an irrationality initiator
coming from a generic black box system within an SoS. From a con-
ceptual standpoint, it is irrelevant if a failure flow is being emitted by
a function or a linked component within the models—in this step, the
failure flows are considered to be emitted from a black box system
model. Note that the use of the abstracted FBED flows is intentional;
abstracting away from physical components and subsystems to the
functional level can help practitioners to consider potential new ini-
tiating event sources that otherwise may be missed.
Step 2, Part 2: Remove all flows from the list of potential irrationality
initiators that are already modeled as initiating events through other
failure analysis methods, such as FFIP and PRA.
Step 2, Part 3: Identify any potentially impossible candidate irra-
tionality initiators that cannot be emitted by the generic black box
system. Before eliminating a candidate irrationality initiator, the
practitioner must attempt to identify ways that the irrationality ini-
tiator may be able to be generated even if it is highly implausible
or unlikely. For instance, almost any material can produce spectral
emissions that would normally be unexpected with sufficient energy
applied to the material.
Step 2, Part 4: Assign probabilities of occurrence to each of the irra-
tionality initiators remaining on the list. We advocate that practi-
tioners follow initiating event probability guidance from PRA, such
as Refs. 10 and 49.
Now that potential irrationality initiators within an SoS that may
impact the SoI have been identified and probabilities assigned, the
flow paths by which the irrationality initiators enter the system must
be defined. Irrationality initiators may be introduced to a system
along nominal flow paths or along non-nominal flow paths, such as
the uncoupled failure flow paths advanced in the UFFSR method.24
Additions to or modifications of the failure model for a system may be
necessary to sufficiently capture irrationality initiator entry points.
3.3 Analysis of potential irrationality initiators
The next step in the method is to conduct failure analysis on the SoI
using the identified potential irrationality initiators. We advocate
for and use in the case study the FFIP family of failure analysis tools
to conduct failure analysis on the SoI. In order to produce a more
accurate analysis of potential irrationality initiators using FFIP and
FIGURE 2 Steps to developing irrationality
related tools, we recommend that the analysis be performed using
data collected from the proposed physical architecture that solves the
functional architecture of the SoI.
The number of potential failure scenarios, often called “cut-sets” in
PRA and sometimes in FFIP, resulting from the analysis of irrationality
initiators, is directly related to the number of irrationality initiators and
the functional model of the SoI. Each irrationality initiator may proceed
along many different flow paths in an SoI, causing functional failure
along the way, which in turn may lead to system failure. The number of
potential failure scenarios may further be expanded by having multiple
potential component solutions available for specific functions before
down-selection of component solutions has been conducted.
While probabilities for specific irrationality initiators were calcu-
lated in a prior step in the method, there are several options for how
irrationality initiators are analyzed based on what type of analysis
results a practitioner is interested in reviewing. These include an
uninformative prior and an informative prior. Further, irrationality
initiators that are either independent or dependent can be consid-
ered to provide additional insights into potential irrational failure
scenarios, such as when multiple irrationality initiators often occur
together. Informative and uninformative priors, and independent and
dependent irrationality initiators may be combined together. Further
explanation immediately follows:
3.3.1 Uninformative and informative priors
In order to understand the sensitivity of an SoI to irrationality initia-
tors, the uninformative prior sets all irrationality initiators to the same
probability of occurrence. It should be noted that using the uninforma-
tive prior approach does not allow for direct comparison of results with
other FFIP results. The results are specifically useful to understand
what high severity failure outcomes are present that otherwise may
be truncated during computation. The uninformative prior method
can also be used to perform a sensitivity analysis on the irrationality
initiators by changing their probabilities and comparing results. This
may help to identify irrationality initiators that are not particularly
sensitive to changes in their probabilities of occurrence and may also
identify specific irrationality initiators that warrant extended scrutiny
to ensure a higher degree of accuracy and realism in the probability
In contrast to the uninformative prior that uses arbitrarily assigned
probabilities to determine potential low probability but very severe
outcomes and to examine irrationality initiator probability sensitivity,
the informative prior uses probabilities of occurrence that were
already developed in a previous step of the methodology and that
are based in reality. This allows for direct comparison of irrationality
initiator-derived failure scenario probabilities with failure scenario
probabilities produced from FFIP.
In the event that a probability was unable to be developed previ-
ously because of a lack of information, we suggest using a probability
value that is 3x the highest probability of the highest known irra-
tionality initiator probability. Using a 3x higher probability may help
to ensure that any potential high consequence failure scenarios are
identified and will help to motivate the development of a better
estimation of the probability. If a failure scenario of a particular
irrationality initiator that used the 3x higher probability is sufficiently
probable, then this indicates the irrationality initiator probability
needs to be better understood. However, if no failure scenarios are
within a few orders of magnitude of the most likely failure scenario,
then this is an indication that there is likely no further refinement of
that irrationality initiator’s probability. It is worth noting that we do
not advocate for setting the multiplier higher than 3x for irrationality
initiators without well-founded probabilities. While such an approach
would almost certainly highlight every single potential failure scenario
caused by the irrationality initiator in question, setting the irrationality
initiator probability needlessly high without a rigorous analysis to
back up the choice is likely to overwhelm a user of this method with
many failure scenarios that masquerade as being of high likelihood
while in reality being of vanishingly small probability. This in turn
may lead to much wasted time and effort to disprove all of the failure
scenarios. The suggestion of a 3x multiplier is based on our prior
professional experience as risk analysts and reliability engineers and
from examining the sensitivity of several failure models to which we
have access to changing initiating event probabilities. While we believe
the 3x multiplier is a good starting point, we recommend that systems
engineering practitioners carefully examine the sensitivity of their
own systems to initiating event probabilities and make adjustments as
warranted and using their professional engineering judgment.
We recommend that both the informative and uninformative prior
methods are used to analyze irrationality initiators in the SoI. The
uninformative prior can shed light on potential high consequence
failure scenarios that otherwise may be missed and can also be used
to perform sensitivity studies on the irrationality initiators. The infor-
mative prior quantifies failure scenarios in a way that can be directly
compared with standard FFIP results. This may help practitioners to
prioritize where money and time is spent to mitigate potential issues.
3.3.2 Independent and dependent irrationality initiators
In almost every implementation of FFIP that we have encountered, ini-
tiating events are exclusively considered to be independent from each
other. The same is true in many PRA analyses. However, we suspect
based on our professional practice and observations that irrationality
initiators may have a higher likelihood of being dependent upon one
another to some extent. In other words, if one irrationality initiator
occurs, then it is more likely that another will occur at the same time.
We propose that irrationality initiators should be modeled both as
independent and dependent events. By analyzing multiple irrationality
initiators as single events, a practitioner can gain insight into scenarios
where a system in an SoS begins emitting many irrationality initiators.
This may help to identify “worst case scenarios” where completely
unanticipated emergent system behaviors occur due to the SoI receiv-
ing several irrationality initiators at once. Recent research on external
initiating events for autonomous robotic systems has indicated that
unique emergent system behaviors not predicted by other research
methods can be caused by several external initiating events simultane-
ously occurring and interacting with one another inside of an SoI.59,89
We suggest that all possible irrationality initiator-dependent com-
binations be investigated. For example, in the case of three irrationality
initiators [A, B, C], the following initiator-dependent combinations
should be investigated: [A & B], [A & C], [B & C], and [A, B, & C]. A gen-
eralized formula to determine the number of dependent combinations
is shown by Equation (1). Note that the formula intentionally subtracts
1 to acknowledge that the baseline case of no irrationality initiators
being present in the SoI is assumed to have been previously assessed.
2nn1 (1)
We recommend going through the the informative and uninforma-
tive prior analysis steps as described previously with the dependent
irrationality initiators. In the case of the informative prior, we recom-
mend conducting a thorough probability analysis of each dependent
combination. However, we recognize that this may be very difficult to
complete with any level of accuracy. In cases where analysis cannot
or is not completed for dependent combinations, we suggest using
the highest single probability of any of the irrationality initiators in
the dependent combination. In effect, this approach uses an OR logic
probability calculation, which we believe is a conservative approach
in this case. In many practical implementations of various types of risk
analysis (eg, PRA, FFIP, etc), the initiating event probabilities are often
assumed to be independent from each other, and in scenarios where
two initiating events occur simultaneously is generally considered
extremely unlikely. However, observation of improbable events occur-
ring with startling regularity suggests that perhaps the assumption
that initiating events are almost always independent is not entirely
valid.88 Thus, without having a better understanding of the true
likelihood of a specific dependent combination occurring, the highest
probability of an irrationality initiator within the dependent combi-
nation is an appropriate and conservative approach. Table 2 shows an
TAB L E 2 Comparison of methods of analysis for dependent and
independent and informative and uninformative approaches to
irrationality initiators
with FFIP
Identify high
consequence but
potentially low
Analyze several
initiators at
prior method
No Yes No
prior method
No Yes Ye s
prior method
Yes N o No
prior method
No No Yes
overview of the informative and uninformative, and the independent
and dependent priors and the benefits and limitations of each.
3.3.3 Specific guidance on modeling implementation with
We envision the method presented in this article to be used in concert
with a quantitative failure analysis technique, such as FFIP and PRA.
While conducting a failure analysis with either technique is well under-
stood and documented in the literature, there are a few differences
and caveats to be aware of when using irrationality initiators. As
mentioned above, uninformative priors cannot be directly compared
to FFIP failure scenarios. However, informative priors can. Dependent
combinations of irrationality initiators can be compared with FFIP
results as long as they are not using uninformative priors.
Within the family of tools developed around the FFIP methodology,
each individual function’s response to all potential failure flows is
modeled. Results of a function receiving a failure flow can include: (a)
reduction, increase, or stoppage of nominal flows leaving the function;
(b) failure flows passing through the function and continuing on along
nominal or non-nominal flow paths; (c) failure flows being arrested
or rejected by the function and the function continuing to operate
nominally; (d) new failure flows being output by the function; or (e)
some combination of the above. A probability is developed for each
potential outcome which is then used to develop and calculate the
probability of specific failure sequences.
Irrationality initiators may enter a system through two flow path
types that cross the system boundary: nominal flow paths and non-
nominal flow paths. In the case of nominal flow paths, the core FFIP
method can be used to model how an irrationality initiator initiates a
failure that moves through a system. In the case of a non-nominal flow
path, the UFFSR methodology24 that extends FFIP is useful. UFFSR
can model uncoupled failure flow paths where a failure flow “jumps”
into or out of a system, or between functions in a system where no
nominal flow path exists. Because of this ability, UFFSR is particularly
useful when modeling irrationality initiators where they may enter
an SoI through non-nominal flow paths. Recent events, such as the
Deepwater Horizon, show that failure flows do not always travel
along the nominal flow path and may jump between unconnected
In summary, several analyses may be performed on irrationality
initiators depending upon the needs of the practitioner. We suggest
using all of the above approaches but acknowledge that there will be
specific instances where it may be appropriate to only use some of the
approaches. Implementing the analysis can be done in FFIP and with
the UFFSR extension to FFIP.
3.4 Analyze results of irrationality initiator failure
After developing failure scenarios specific to irrationality initiators in
the previous section, the results can now be analyzed to understand
the potential impacts of irrational system behavior on an SoI in an SoS.
The independent uninformative prior results can be used to identify
high consequence failure scenarios and to identify irrationality initia-
tors that are sensitive to changes in their probability values. These
results can be used to identify potential areas to invest more effort
in further developing knowledge of a specific irrationality initiator.
Potential high consequence failure scenarios identified through the
independent uninformative prior may also point to areas in the model
where further development and scrutiny is warranted. The dependent
uninformative prior failure scenario results provide similar informa-
tion as described in the above paragraph but with focus on dependent
combinations of irrationality initiators.
Failure scenario results from the independent informative prior can
be compared directly with FFIP results (if using the FFIP methodology
as the underlying failure analysis method). A comparison of the results
of the independent informative prior with FFIP results can reveal if
irrationality initiators are a significant or dominant contributor to
probability of system failure. Failure scenario results of the indepen-
dent informative prior can also be added to FFIP results to produce a
combined analysis that gives a more holistic view of potential SoI sys-
tem failure scenarios. It is important to maintain a list of irrationality
initiators that were assigned a generic probability of occurrence due
to no realistic probability being available–failure scenarios associated
with these specific irrationality initiators may be disproportionately
represented high in the results.
For both the informative and uninformative priors, the dependent
irrationality initiator combinations may provide insight into “worst
case scenarios,” where many irrationality initiators are emitted from
one or more systems within an SoS and impact the SoI at the same
time. An additional concern that may be uncovered from analyzing
dependent irrationality initiator combinations is a situation where
one or more irrationality initiators have passed into the SoI boundary
but the SoI continues to function normally. A subsequent irrationality
initiator that otherwise may have not caused the SoI to suffer a system
failure could now cause the weakened SoI to fail. A practical example
of this effect is a failed emergency brake in a car where the braking
functionality is not available in an emergency stopping situation if the
primary brakes have failed. The car can still brake under nominal oper-
ating conditions but the car will be unable to brake (excluding engine
braking, which may or may not be available depending on specifics
of the car configuration) if the primary braking system also suffers a
3.5 SoI design iteration
The insights that the analyses provide can then be used by practition-
ers to help guide improvements to an SoI to increase its robustness
to irrationality initiators. Improving robustness of the SoI within an
SoS can help to improve the reliability of the overall SoS and the
likelihood that the SoS will complete its mission. While an SoS will
never be without risk of failure due to a member system behaving
irrationally, failure risk can be sufficiently reduced to be manageable
and acceptable through careful analysis and improvement of the
constituent systems (eg, the SoI).
Following a thorough analysis of the results of the irrationality
initiator analysis method presented in this article, changes to the SoI
can be made to help prevent the irrational system behaviors of one
system from adversely impacting the SoI and SoS. There are many
options to protect an SoI from irrational system behaviors of another
system within the SoS. For instance, protection can be implemented
against uncoupled irrationality initiators.91 Redundant systems and
subsystems92,93 can be added to provide higher reliability. Sacrificial
subsystems or systems59 can be added to route failure flows caused by
irrationality initiators to a location where they can do the least harm.
Robustness and resilience of the SoI16,94,95 can be improved to better
deal with inputs to the SoI that go beyond the design basis of the SoI.
Changing SoI configuration or location can be used to decrease the
likelihood of irrationality initiators from occurring.96
After sufficient redesign of the SoI has been completed, the method
can be iterated upon to verify that irrationality initiator risk of failure
to the SoI and SoS has decreased to an acceptable level. If the risk of
SoI failure or SoS failure has not adequately decreased, further design
iterations are necessary. Once a system engineer or designer is satis-
fied that the SoI architecture is sufficiently robust against irrationality
initiators caused by another member of the SoS behaving irrationally,
the SoI architecture can be locked and the system engineering
process can continue to move forward in the systems engineering
In this section, we present a simplified and fictionalized case study to
demonstrate the method. The case study SoS and SoI is representative
of real systems in operation and/or being designed (such as Ref. 97 and
others), although certain details and contexts have been changed to
more clearly demonstrate the method and protect sensitive system
information. However, the system models and other details remain
representative of several existing fielded SoS and SoI. The case study
is only to be used for illustrative purposes and to demonstrate the
method presented in this article; no engineering conclusions on
existing or proposed SoS and SoI can be drawn from the case
study without a practitioner first conducting their own thorough
In the case study, an SoS that delivers sensitive supplies from a
logistics supply depot to a forward position has been operating for
some time. The SoS uses a small fleet of autonomous vehicles to
move supplies between the depot and the forward position through a
partially denied environment98 where there is poor and intermittent
global positioning system coverage, and other navigational aids, such
as way-point navigation beacons and celestial navigation, are unavail-
able. The autonomous vehicles have limited ability to track their
own positions internally and must receive regular position updates
to prevent excessive drift. To overcome a lack of positioning data,
the autonomous vehicles receive positioning information via a series
of radar stations that are able to localize the autonomous vehicles.
Two-way communications for command and control is also provided
FIGURE 3 SoS general physical configuration. Note that this figure is representative of a Department of Defense Architecture Framework
(DoDAF) 2.0 High-Level Operational Concept Graphic (OV-1)101
via the radar stations and links back to the logistics supply depot where
a control station is located. The radar stations are configured in a nodal
network. The location of the radar stations is not optimal due to the
topography of the area and hostile forces active in the area. Radar and
communications coverage does overlap in some areas and is desirable,
but much of the route the autonomous vehicles take only has single
radar station coverage. The supplies are sufficiently sensitive that if
positioning information is lost for more than 3 min or if a sufficiently
large deviation from the expected path is detected, it is assumed that
the autonomous vehicle may have been captured by hostile forces and
both the vehicle and the supplies aboard are destroyed.99,100 As long
as the autonomous vehicles remain on their intended path, there is no
threat of capture by hostile forces.
The existing autonomous vehicles in the SoS are reaching the end
of their service life and a defense contractor is developing a new fleet
of autonomous vehicles (the SoI for the case study) to begin service.
The radar stations and the control station are manufactured by other
contractors. The SoS integration is handled by another contractor, as
is often the case in defense SoS. While the defense contractor has an
understanding of how the other systems in the SoS are supposed to
operate and behave, the defense contractor desires to have a better
picture of potential threats to the SoI from irrational system behaviors
of the other systems. The defense contractor plans to use the knowl-
edge gained from investigating irrationality initiators to improve the
robustness and reliability of the SoI during the conceptual phase of
system architecture where functional models are being developed,
which will increase the likelihood of SoS mission success. Figure 3
shows the general SoS configuration.
4.1 Model the systems within the SoS
The defense contractor chose to use a functional modeling approach
and FFIP as the underlying failure analysis tool for the irrationality
initiator analysis. A model of the SoS is shown in Figure 4. Note that
nominal flow paths are shown in the figure. An FFIP analysis of failure
scenarios for the SoS and SoI has already been performed. Further,
system solutions to functions within the SoS model have been chosen.
A simplified SoI (the new autonomous vehicles) system model devel-
oped with the FBED functional taxonomy is shown in Figure 5. An FFIP
analysis was conducted and the five most likely failure scenarios are
shown in Table 3. The FFIP family of methods examines how failures
move through a system from an initiating event through to either fail-
ure of the system (often defined by failure of a critical function or func-
tions and/or by a failure flow exiting the system boundary) or to ter-
mination of the failure flow without the failure flow causing system
failure.20,22,24 The probability of the failure outcome is calculated from
the probability that the failure flow (a) initiates, (b) passes through each
function, and (c) causes the system to fail and/or emit a failure flow.
Each failure scenario that FFIP identifies is treated as an independent
sequence of events from every other failure scenario similar to how
many implementations of PRA treat cut-sets as independent from one
another for the purposes of the associated probability statistics. Addi-
tionally, much like PRA, FFIP scenario outcome probabilities can be
added together to understand the overall probability of system failure.
The defense contractor has defined failure of the SoI (the autonomous
vehicles) as the cargo not reaching its final destination, which may
occur from the cargo being damaged, captured, destroyed, or lost.
FIGURE 4 SoS top-level model with major systems and flows between systems identified. Note that Data is used in place of the
Signal-Control-Discrete flow type. RADAR is used in place of the Energy-Electromagnetic flow type. Both substitutions have been made for ease
of understanding for readers who are not intimately familiar with FBED. Two autonomous vehicle systems (the SoIs) are shown in typical flow
connection configurations where one or more radar stations are connected to the autonomous vehicles
FIGURE 5 Simplified SoI (the new autonomous vehicle systems) functional model. Many functions and flows have been excluded from or
simplified in this functional model for brevity and ease of understanding the case study. The dashed border indicates the system boundary
4.2 Identify potential irrational system behaviors
The next step is to identify potential irrational system behaviors
that other systems might undertake in the SoS. For the purposes of
this case study, we are narrowing our focus specifically to the radar
stations. In a full analysis using the method presented in this article,
each member system in the SoS would be analyzed and all results
would be used throughout the analysis.
First, the full list of secondary and tertiary flows from FBED is
examined, as seen in Table 4. Next, the flows already represented
in the FFIP analysis conducted previously (Table 3) are struck from
consideration (shown in Table 4 by a horizontal strike-through line).
The third step is to validate that each remaining flow is somehow
possible to occur and remove from consideration any flows that are
absolutely impossible. This is represented in Table 4 by flows being
crossed out. Validation of the flows can be conducted in a variety
of different ways that the practitioner finds suitable to the task and
with a variety of different levels of fidelity. For instance, a workbook
could be developed for each flow similar to what is done for individual
initiating events in a nuclear PRA model.102 The flows that remain are
the irrationality initiators for the system. The final step is to develop
probabilities of occurrence for each irrationality initiator. Again,
there are a variety of ways these probabilities could be developed
depending on the specific situation. For instance, guidance is provided
in the nuclear power industry for the development of new initiating
events,102 resources are available in MIL-STD-882E to estimate
reliability of components and systems,44 and other methods are also
As an example of identifying irrationality initiators, we will now
examine the Signal-Status-Auditory (ie, noise) flow to determine if the
flow should be carried forward as an irrationality initiator for further
analysis. First, the flow is checked to verify that it was not already
captured in the FFIP analysis (Table 3). Then, the flow is analyzed to
determine its potential to reach the SoI (the new autonomous vehicles
that are under development). However, based on the physical layout of
the system, the SoI will never come close enough to the radar station
TAB L E 3 Truncated list of highest probability of failure FFIP
results from the SoI on a per unit basis
Failure propagation pathway Probability
Signal-Control-Discrete, Channel-Transmit,
Signal-Process, Convert Electrical Energy to
Mechanical Energy, Channel-Guide-Rotate
Provision-Supply, Signal-Process,
Signal-Control-Discrete, Channel-Export,
Signal-Control-Discrete, Channel-Transmit,
Signal-Process, Channel-Export,
Energy-Mechanical, Channel-Guide-Rotate,
Convert Electrical to Mechanical Energy,
Provision-Supply, Signal-Process,
Channel-Export, Provision-Store-Contain
Signal-Process, Channel-Transmit,
Provision-Supply, Convert Electrical to
Mechanical Energy, Channel-Guide-Rotate
for a noise generated by the radar station to impact the SoI. The
distance is too great for the loudest sound possible to be generated by
the radar station (eg, the radar station’s fuel source being detonated)
to reach the SoI with sufficient intensity to become an irrationality
initiator. Thus, the Signal-Status-Auditory flow can be struck from the
table of candidate irrationality initiators (Table 4). Had the flow not
been struck from the list of candidate irrationality initiators, the next
step would have been to quantify the likelihood of occurrence.
It should be noted that understanding if an irrational behavior-
induced failure flow under consideration for an SoI irrationality
initiator is not initially well understood, significant databases of
information exist in a variety of industries, which may aid systems
engineers to better understand the situation. For instance, the nuclear
power industry maintains significant databases of component part
failures spanning many decades.103 The petroleum industry maintains
similar databases.104 Mishap reports from similar systems to the SoI
After careful analysis, three flows remain as viable irrationality
initiators, including: Signal-Control-Analog, Material-Solid-Object,
and Energy-Electromagnetic-Solar, as shown in Table 4. To illustrate
how these three flows were determined to be irrationality initiators,
we will briefly focus on the Material-Solid-Object flow. The Material-
Solid-Object flow represents part or all of a radar station rolling off the
side of a mountain where it was placed and physically impacting the
SoI. While this may seem far-fetched, we have observed similar events
in our own professional practices. Several causes of this irrationality
initiator were identified such as a small landslide causing the radar
station to fall down the mountain, hostile forces rolling the radar off
the side of the mountain, abnormally high winds ripping one of the
communications dishes off of the radar station and blowing it down
the mountain, and other equally outlandish causes that nevertheless
cannot be completely ruled out. Next, analysis was conducted to
determine the probability of the Material-Solid-Object irrationality
initiator occurring. It was found to have a relatively high probability
TAB L E 4 Irrationality initiators are developed from the FBED
functional taxonomy flow set
Note: The three primary classes are material, signal, and energy. The sec-
ondary and tertiary classes have increasing levels of specificity. Note that
not all flows are represented at the tertiary level in FBED and some flows
may have several representations at the tertiary level. The flows that have
been identified as irrationality initiators in the case study are not struck out.
Probability of occurrence has been developed for the irrationality initiators
as explained in the text above.Refer to Refs. 18 and 39 for additional details
regarding the FBED flow set
FIGURE 6 SoI (the new autonomous vehicle system under development) high-level functional model with a potential irrationalityinitiator
failure scenario indicated by the dashed orange line. The SoI fails when the failure flow caused by the irrationality initiator reaches the
Provision-Store-Contain (Cargo) function via the Channel-Export function, which results in the cargo being destroyed
TAB L E 5 Irrationality initiator-dependent combinations for the SoI
(new autonomous vehicle system) on a per unit basis
Dependent grouping Probability
Signal-Control-Analog AND
Energy-Electromagnetic-Solar AND
Signal-Control-Analog AND
Signal-Control-Analog AND Material-Solid-Object 1E-2/day
Energy-Electromagnetic-Solar AND
of occurrence based on frequent windstorms observed in the area
and topographic features in the area, which may tend to funnel debris
down the mountains and into the path of the SoI.
A simplified FFIP failure analysis model is shown in Figure 6 of the
SoI (the new and under development autonomous vehicle system).
The orange dashed lines indicate one failure flow sequence moving
through the system at the functional level. The irrationality initiator
initially crosses the system boundary the system along a non-nominal
flow path before traveling along nominal flow paths to eventually
cause system failure. Additional development work not shown here
was completed on the system models to allow for analysis of the
irrationality initiator failure scenarios to be conducted.
4.3 Analyses of potential irrationality initiators
After developing the SoI system models and identifying the irrational-
ity initiators, analysis can be conducted on the SoI using the four
approaches outlined in the methodology section above (independent
and dependent irrationality initiators, uninformative and informative
priors uninformative prior). The three irrationality initiators and their
potential dependent combinations are shown in Table 5. A subset of
the results of analysis conducted using the FFIP family of tools with
the irrationality initiators is shown in Table 6.
4.4 Analyze results of irrationality initiator failure
Failure scenarios produced from the independent uninformative prior
approach’s sensitivity analysis show a high sensitivity to change in
probability values for the Energy-Electromagnetic-Solar irrationality
initiator. This is a strong indication that additional resources should
be dedicated to evaluating the Energy-Electromagnetic-Solar irra-
tionality initiator to ensure the probability of occurrence is realistic
and conservative.
The dependent uninformative prior approach indicates that the
three irrationality initiators occurring at the same time result in a
much higher probability of system failure than other combinations
of irrationality initiators produce. This indicates that an SoI system
redesign may be needed to specifically protect against this scenario.
The Signal-Control-Analog irrationality initiator was identified as a
significant contributor to SoI system failure based on the independent
informative prior approach. This information can be used by a systems
engineer to make a decision on dedicating more resources toward
mitigating potential SoI system failures caused by this particular
irrationality initiator.
As with the earlier dependent uninformative prior results, the
dependent informative prior approach points toward the combination
of all three irrationality initiators has the potential for signifi-
cant SoI system failure events. However, because a more realistic
probability of occurrence is being used as part of the calculations, the
probability of the SoI system failure scenarios is lower than results
from the original FFIP analysis. In spite of this, the failure scenario out-
comes of the irrationality initiator combinations are significant enough
that a systems engineer may still wish to verify the probabilities before
deciding to discount the result.
TAB L E 6 A subset of failure scenarios caused by the irrationality initiators as developed through analysis using FFIP and related methods
Failure propagation pathway Probability
Independent uninformative prior method
Energy-Electromagnetic-Solar, Provision-Supply 4.3E-3/day
Energy-Electromagnetic-Solar, Provision-Store-Contain 2.6E-3/day
Material-Solid-Object, Channel-Guide-Rotate 1.2E-3/day
Material-Solid-Object, Channel-Export, Provision-Store-Contain 5.2E-4/day
Signal-Control-Analog, Channel-Transmit, Signal-Process, Channel-Export, Provision-Store-Contain 1.3E-4/day
Dependent uninformative prior method
Signal-Control-Analog AND Energy-Electromagnetic-Solar AND Material-Solid-Object,
Channel-Export, Provision-Store-Contain
Signal-Control-Analog AND Energy-Electromagnetic-Solar,Channel-Guide-Rotate 3.6E-3/day
Signal-Control-Analog AND Energy-Electromagnetic-Solar,Channel-Export, Provision-Store-Contain 8.7E-4/day
Signal-Control-Analog AND Energy-Electromagnetic-Solar,Provision-Store-Contain 5.9E-5/day
Signal-Control-Analog AND Energy-Electromagnetic-Solar,Signal-Process, Convert Electrical to
Mechanical Energy, Channel-Guide-Rotate
Independent informative prior method
Signal-Control-Analog, Channel-Transmit, Signal-Process, Channel-Export, Provision-Store-Contain 4.2E-4/day
Signal-Control-Analog, Channel-Transmit, Signal-Process, Provision-Supply,Convert Electrical to
mechanical Energy, Channel-Guide-Rotate
Material-Solid-Object, Channel-Export, Provision-Store-Contain 7.2E-5/day
Material-Solid-Object, Channel-Guide-Rotate 8.4E-5/day
Signal-Control-Analog, Channel-Transmit, Provision-Supply,Convert Electrical to Mechanical Energy,
Dependent informative prior method
Signal-Control-Analog AND Energy-Electromagnetic-Solar AND Material-Solid-Object,
Channel-Export, Provision-Store-Contain
Signal-Control-Analog AND Energy-Electromagnetic-Solar,Channel-Guide-Rotate 8.3E-5/day
Signal-Control-Analog AND Energy-Electromagnetic-Solar,Channel-Export, Provision-Store-Contain 7.2E-5/day
Signal-Control-Analog AND Energy-Electromagnetic-Solar,Provision-Store-Contain 5.1E-5/day
Signal-Control-Analog AND Energy-Electromagnetic-Solar,Signal-Process, Convert Electrical to
Mechanical Energy, Channel-Guide-Rotate
Note: The failure scenarios shown in the table are the highest probability for each of the four methods (independent uninformative prior,dependent uninfor-
mative prior, independent informative prior, and dependent informative prior)
Once this step has been completed, the systems engineer must
evaluate the SoI and SoS requirements to determine if specific risk,
reliability, and other relevant requirements have been satisfied in light
of the above analysis. If the requirements have been satisfied, then the
systems engineer can exist the method. However, if the requirements
have not been satisfied as evidenced by the above analysis, then the
systems engineer should proceed to the final step in the methodology.
4.5 SoI design iteration
Now that the results of the method have been analyzed, a redesign
of the SoI can be conducted to improve system reliability in the face
of irrational system behaviors of other systems that the SoI interacts
within the SoS. Many resources exist for practitioners to conduct
redesign efforts.16 After a redesign has been completed, a new analy-
sis should be conducted to verify the success of the redesign effort. We
omit further redesign efforts from the case study here in the interest
of brevity.
The method we present in this article raises several topics worthy
of discussion. This section reviews the benefits of the method as
well as limitations and drawbacks. Several questions of philosoph-
ical importance to users of the method are also covered. Based on
these discussion points, we present some potential future research
directions to further improve upon the method.
As has been mentioned above, the four analyses (independent
informative prior, dependent informative prior, independent uninfor-
mative prior, and dependent uninformative prior) each yields unique
insights that may be useful to a practitioner (see Table 2 for a sum-
mary). We advocate that each of the four analysis methods be used
during an irrational system behavior analysis but we also recognize
that such analysis may be too computationally expensive for very
complex systems or may be too time intensive for very large SoS. The
uninformative prior approaches help the practitioner to understand
sensitivity to changes in probability of occurrence of irrationality
initiators and to discover potentially significant failure scenarios,
which could otherwise be truncated as being of too low of probability.
The informative prior approaches produce failure scenarios that can
be compared directly to failure scenarios produced by FFIP. Further,
the failure scenarios can be added to the list of failure scenarios
that FFIP produces to give a more complete view of how an SoI may
fail. Treating irrationality initiators as independent events versus
dependent events allows a practitioner to investigate both situations
where only one irrationality initiator occurs and cases where multiple
irrationality initiators occur simultaneously. Looking at combinations
of irrationality initiators may help to find emergent system behaviors
that otherwise would have been missed because any one irrationality
initiator on its own might not have caused the failure to occur. Future
work may include conducting a detailed comparison of existing risk,
reliability, failure, safety, and other related analyses with the method
presented in this paper from the specific perspective of dependent
priors. This may help to reveal gaps in the understanding of how
emergent system behaviors occur due to several irrationality initiators
being dependent upon one another in ways that have not previously
been fully characterized.
The process of identifying and validating irrationality initiators
as being possible, and of developing realistic probabilities, can be
very challenging. However, it is not too dissimilar to the process
that is done for new nuclear power plant risk analysis to develop
initiating events.102 Where the method presented in this paper to
develop irrationality initiators differs from other established meth-
ods of developing initiating events is that irrationality initiators by
their very nature are rare events that either have not been seen
before or have been discounted as being likely enough to occur to
include in analysis. In this case, it can be a vexing problem to develop
realistic probabilities that are validated with any sort of quantita-
tive data. However, we believe that even with these limitations, the
method is useful enough for practitioners to adopt. The insights
gained could help to improve SoI and SoS reliability and robust-
ness by improving constituent systems’ (eg, the SoI) responses to
irrationality initiators.
No explicit guidance has been provided in this method on how to
deal with humans in an SoI or the SoS, other than the fact that they can
explicitly be modeled into the functional and physical models in FFIP.
While this might be sufficient, we recognize that in many situations
humans are the most likely point of failure. Humans tend to behave
in a manner that was not anticipated or expected.56,64,105–107 The
flows from FBED do contain human flows (eg, human energy)thatcan
be used to begin to develop irrationality initiators that are human
caused. However, acts of commission,108,109 acts of malice,31,110
and acts of irrationality, insanity, or calculated instability111,112 are
not well represented in existing human reliability analysis methods.
Further work is needed to more accurately assess potential irra-
tionality initiators caused by humans and is beyond the scope of
this article.
A potential computational benefit of the irrationality initiator
approach is breaking potential loop-backs in the analysis of failure
events. Loop-backs are a significant challenge in SoS that have a
high number of interconnections, and in systems with a large num-
ber of connections between functions.113 Transforming irrational
failure flows exiting a system into irrationality initiators enter-
ing an SoI helps to isolate the flows as a source of loop-backs in
the analysis.
The FFIP family of methods is similar to PRA in that it can be very
computationally expensive (taking many computational resources for
long periods of time) to analyze large, complex SoIs. Truncation, as
discussed in the background and related work section, is heavily used
in this situation to reduce computational expense and time require-
ments. The computational requirements for the method presented in
this paper are on par with FFIP and PRA methods in computational
expense. Further fundamental research in computational efficiency
of probabilistic-based analysis methods is needed to reduce com-
putational expense of the method presented in this paper and many
other methods, such as FFIP and PRA. It is beyond the scope of this
research to quantitatively benchmark computational performance of
the method presented above.
FFIP was used throughout the methodology and case study sections
in this article. However,we have undertaken an initial proof-of-concept
study, which shows favorable results for implementing the method in
PRA. The main challenge in a PRA implementation is building out event
trees and failure trees that can accept irrationality initiators. Existing
event trees and fault trees may not sufficiently capture what happens
in a system when an irrationality initiator is introduced.
The issue of cost-effectiveness of implementing this method is an
open question that remains to be resolved not only for this method,
but also for the larger world of risk and failure analysis, reliability
analysis, and safety engineering.114 Safety engineering is generally
viewed as a cost center rather than a profit center. In our profes-
sional experience, and in the experience of safety engineers we have
discussed this issue with, it is rare to quantify savings from safety
analysis. From our discussions with leading system safety engineers
around the world who are affiliated with INCOSE,114 the issue of
justifying safety engineering is largely driven by regulatory compli-
ance. Certain well-known engineering ethics examples, such as the
Ford Pinto,115 highlight the situation that faces systems engineers and
high-level management and indicate a need for further study of this
important topic.
Note that we have intentionally omitted discussion of uncer-
tainty in this article. Methods of understanding and quantifying
uncertainty in probabilistic-based methods116–119 are appropriate to
implement in the method presented above. Including uncertainty
in probabilistic calculations may present interesting decision
points in an analysis conducted using the methodology presented
In summary, the method introduced in this article provides a way
for practitioners to begin identifying “unknown unknowns”120 that
may result in SoI and/or SoS failure. While there are some chal-
lenges in implementing the method, especially with regard to down-
selecting the irrationality initiators and developing realistic probability
statistics, the method produces useful results that can influence the
design of an SoI. As far as we are aware, analyzing all potential failure
flows that enter an SoI within an SoS in the context of irrational system
behavior is a novel approach.
One area of future expansion of the work is a validation of the
method presented here that uses controlled experiments conducted
with systems engineers to compare our method with existing method-
ologies to determine if our method improves SoI and SoS outcomes.
This proposed effort is likely a significant undertaking requiring a
large participant pool participating in lengthy controlled experiments
to achieve sufficient replicates, which will help to gain statistical
significance of the results. Other potential validation methods for new
system design methodologies, such as the mechanical design theory
and methodology (DTM) community’s Validation Square method,121
are not yet universally accepted by either the DTM community or the
systems engineering community.
The analysis technique presented above that uses the informative
and uninformative priors, and the dependent and independent irra-
tionality initiators, may be a useful starting point to further investigate
how emergent behaviors are initiated in complex systems. While many
systems have significant analysis and resources dedicated to inde-
pendent initiating events, less work is done to investigate dependent
events. In our professional practice, we have observed this is because
of the assumed relative rarity of dependent initiating events. However,
as many of the independent initiating events are now being effectively
addressed in design, dependent initiating events appear to us to be
becoming more important. Informative and uninformative priors may
also prove a very fruitful area of future research to help discover
high consequence, low probability initiating events that warrant
more attention and that may be discounted or truncated in analysis
methods, such as PRA.
Another potential fruitful line of future research is reversing
the analysis to start with assuming the SoI is behaving irrationally.
The analysis would then focus on the SoI’s impact within the rest
of the SoS. Insights from this approach may show system designers
how to reduce the likelihood of specific irrational failure flows from
exiting the SoI and potentially adversely affecting other systems. This
may help to improve the probability of an SoS successfully completing
its mission.
Focusing on human behaviors in an SoS that may cause irrationality
initiators may be a productive area of future research. The human
factors literature may provide a good starting point for further
investigations.122–125 The psychology and related literature on irra-
tional human behaviors may also be useful.126,127 There is also some
research in the engineering design community regarding functional
analysis of human errors.128
Some may find the usage of the term “irrational” to be controversial.
Other terms, such as “unexpected” and “not accounted for,” may be
more palatable for some readers. However, we have specifically
retained the term “irrational” to call attention to the issue that the
method presented above addresses. Until methodologies are devel-
oped that can automatically identify an exhaustive list of potential
system behaviors including behaviors that we have termed “irrational”
and behaviors that no one has either hypothesized or observed, we
believe that the use of the word “irrational” is appropriate.
This article introduces the concept of irrationality initiators as a
method to improve failure analysis while developing conceptual
functional models of an SoI in an SoS. Irrationality initiators allow
practitioners to closely examine potential irrational system behaviors
by other systems within an SoS that could have negative effects on
the SoI. This may result in discovering new and unexpected system
vulnerabilities. Once a failure scenario has been found that poses a
significant threat to the SoI’s continued operation or an SoS com-
pleting its mission (due to the failure of the SoI), a practitioner can
undertake a redesign of the SoI to make it more robust and reliable.
Multiple iterations of the method can result in potentially significant
improvements in the likelihood that an SoI remains functional in spite
of irrational system behaviors from other systems in the SoS and also
increases the likelihood that the SoS completes its intended mission.
Four different irrationality initiator analysis techniques are introduced
in this paper, including dependent and independent irrationality
initiators and uninformative and informative priors. Each analysis
technique provides a unique and useful perspective on potential
emergent system behaviors and potential consequences caused by the
irrationality initiators. While we demonstrated the method using FFIP
and its associated extensions, the method shows promise for being
useful with PRA as well. Other quantitative risk analysis methods may
also prove to be compatible with irrationality initiators.
This research is partially supported by the Naval Postgraduate School
(NPS), the Singapore University of Technology and Design (SUTD),
and Danmarks Tekniske Universitet. Any opinions or findings of this
work are the responsibility of the authors, and do not necessarily
reflect the views of the sponsors or collaborators. Please address all
correspondence to D.L. Van Bossuyt.
Dr. Arlittwas at the Singapore University of Technology and Design during
the initial development of this research prior to moving to Danmarks
Tekniske Universitet.
Douglas L. Van Bossuyt https://orcid.org/0000-0001-9910-371X
Ryan M. Arlitt https://orcid.org/0000-0003-3471-7387
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Professor in the Systems Engineering Depart-
ment at the Naval Postgraduate School. His
research focuses on understanding and miti-
gating deleterious emergent system behaviors
from a risk analysis and failure modeling perspective through the
development of system design methodologies targeted at the sys-
tem architecture phase of the system design process. He holds an
Honors Bachelor of Science in Mechanical Engineering, an Honor
Bachelor of Arts in International Studies, a Masters’ of Science in
Mechanical Engineering, and a PhD in Mechanical Engineering all
from Oregon State University.
DR.BRYAN M. O’HALLORAN is an Assistant
Professor in the Systems Engineering Depart-
ment at the Naval Postgraduate School (NPS)
and the Academic Associate for the Reliability
and Maintainability certificate program (cur-
riculum 242). Previously, he was a Senior Reliability and Systems
Safety Engineer at Raytheon Missile Systems (RMS) and the Lead
Reliability and Safety Engineer for hypersonic missile programs.
He holds a Bachelor of Science degree in Engineering Physics and a
Master of Science and Doctorate of Philosophy in Mechanical Engi-
neering from Oregon State University. His current research inter-
ests include risk, reliability, safety, and failure modeling in the early
design of complex systems.
DR.RYAN M. ARLITT is an Assistant Profes-
sor in the Department of Mechanical Engineer-
ing at the Technical University of Denmark.
His research focus is on understanding (a) how
successful designers solve complex conceptual
design challenges, and (b) how computational support can improve
the likelihood and quality of success in conceptual design and
beyond. He holds a PhD in Mechanical Engineering from Oregon
State University, and Bachelors and Masters Degrees in Interdis-
ciplinary Engineering and Systems Engineering, respectively, from
the Missouri University of Science and Technology.
How to cite this article: Van Bossuyt DL, O’Halloran BM,
Arlitt RM. A method of identifying and analyzing irrational
system behavior in a system of systems. Systems Engineering.
2019;22:519–537. https://doi.org/10.1002/sys.21520
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