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METHODOLOGY AND THEORY
System failure behavior and
maintenance decision making
using, RCA, FMEA and FM
Rajiv Kumar Sharma
Department of Mechanical Engineering, NIT Hamirpur, India, and
Pooja Sharma
Department of Computer Science and Engineering, NIT Hamirpur, India
Abstract
Purpose – The purpose of this paper is to permit the system reliability analysts/managers/engineers
to model, analyze and predict the behavior of industrial systems in a more realistic and consistent
manner and plan suitable maintenance strategies accordingly.
Design/methodology/approach – Root cause analysis (RCA), failure mode effect analysis (FMEA)
and fuzzy methodology (FM) have been used by the authors to build an integrated framework, to
facilitate the reliability/system analysts in maintenance planning. The factors contributing to system
unreliability were analyzed using RCA and FMEA. The uncertainty related to performance of system
is modeled using fuzzy synthesis of information.
Findings – The in-depth analysis of system is carried out using RCA and FMEA. The discrepancies
associated with the traditional procedure of risk ranking in FMEA are modeled using decision making
system based on fuzzy methodology. Further, to cope up with imprecise, uncertain and subjective
information related to system performance, the system behavior is quantified by fuzzy synthesis of
information.
Originality/value – The complementary adoption of the techniques as discussed in the study will
help the maintenance engineers/managers/practitioners to plan/adapt suitable maintenance practices
to improve system reliability and maintainability aspects after understanding the failure behavior of
component(s) in the system.
Keywords Failure modes and effects analysis, Fuzzy control, Systems analysis, Maintenance,
Decision making
Paper type Research paper
1. Introduction
Needless to say failure is nearly an unavoidable phenomenon in mechanical
systems/components. One can observe various kinds of failures in past under various
circumstances such as nuclear explosions (Chernobyl nuclear disaster, 1986), Industrial
plant leakages (Union carbide plant, Bhopal 1984, oil pipeline at Jesse Nigeria, 1998),
aero plane crashes, and electrical network shutdowns etc. which may be due to human
error, poor maintenance, inadequate testing/inspection. Further, with the advances in
technology and growing intricacy of technological systems the job of reliability/system
analyst has become more challenging. As they have to study, characterize, compute,
and analyze the behavior of system using various techniques (Modarres and
Kaminsky, 1999; Ebeling, 2001; Madu, 2005; Aksu et al., 2006. Madu (2005) in his paper
on “strategic value of reliability and maintainability” emphasized on the need of
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1355-2511.htm
JQME
16,1
64
Journal of Quality in Maintenance
Engineering
Vol. 16 No. 1, 2010
pp. 64-88
qEmerald Group Publishing Limited
1355-2511
DOI 10.1108/13552511011030336
maintaining the equipment in good condition in order to eliminate the sudden and
sporadic failures resulting in production loss. Various techniques such as RCA, FMEA
and Pareto charts were discussed to uncover the problems related to system
unreliability. Aksu et al.(2006) in their work presented complementarily application of
fault tree analysis (FTA), failure mode and effect analysis (FMEA) and Markov
Analysis (MA) for reliability and availability estimation of Pod propulsion systems.
Numerous researchers such as Teng and Ho (1996); Sankar and Prabhu (2001); Xu et al.
(2002); Guimara
˜es and Lapa (2007); Sharma et al. (2005a, b); Sharma et al. (2008) carried
out FMEA research focused on improving traditional FMEA limitations by using
different schemes to identify and prioritize failure causes in engineering systems.
But according to Fonseca and Knapp (2001) in reliability and maintainability
studies a small number of researchers have seriously addressed the issue of handling
uncertainties especially related with failure data of systems. The traditional analytical
techniques (mathematical and statistical models) needs large amount of data, which is
difficult to obtain because of constraints i.e. rare events of components, human errors
and economic considerations for estimation of the failure /repair characteristics of the
system. Even if data is available, it is often inaccurate and thus, subjected to
uncertainty, i.e. historical records can only represent the past behavior but may be
unable to predict the future behavior of the equipment. Further, age, adverse operating
conditions and the vagaries of manufacturing /production processes affects each
part/unit of system differently (Fonseca and Knapp, 2001; Knezevic and Odoom, 2001;
Sergaki and Kalaitzakis, 2002). However, it may be difficult or even impossible to
establish rational database to accommodate all operating and environmental
conditions. In the absence of accurate data, rough (approximate) estimates of
probabilities can be worked out. The estimates provided by experts or engineers are
inherently subjective and to establish a rational method for reliability assessment, such
subjective estimates should be merged with statistical randomness.
To this effect, both probabilistic and non-probabilistic methods available in literature
are used to treat the element of uncertainty in reliability analysis. Based on mature
scientific theory, the probabilistic methods deals with uncertainty which is essentially
random in nature but of an ordered kind. For instance, Bayesian methodology, appeared
in late 1970s is widely used in probabilistic risk assessment, an exercise aimed at
estimating the probability and consequences of accidents for the facility/process under
study. In the Bayesian framework, the analyst’s uncertainties in the parameters due to
lack of knowledge are expressed via probability distributions (Cizelj et al., 2001; Aven
and Kvaløy, 2002). The non-probabilistic/inexact reasoning methods on the other hand
study problems which are not probabilistic but cause uncertainty due to imprecision
associated with the complexity of the systems as well as vagueness of human judgment.
These methods are still developing and often use fuzzy sets, possibility theory and belief
functions.For instance, in their work Sii et al. (2001) presented a novel risk assessment
technique based on fuzzy reasoning for maritime safety management system. Sergaki
and Kalaitzakis (2002) in their work developed a fuzzy relational database model for
manipulating the data required for criticality ranking of components in thermal powers
plants. Liu et al. (2005) in their work proposed a framework for modeling, analyzing and
synthesising system safety of engineering systems on the basis of rule based inference
methodology using evidential reasoning. The framework has been applied to model
system safety of an offshore and marine engineering system. Thus, it is observed from
System failure
behavior
65
the studies that owing to its sound logic, effectiveness in quantifying the vagueness and
imprecision in human judgment, the fuzzy methodology can be used as an effective tool
by the reliability analysts to encounter real life problems.
Recently, fuzzy methodology has been widely applied in:
.fault diagnosis (Liu et al., 2009; Mustapha et al., 2004);
.structural reliability (Savoia, 2002; Biondini et al., 2004);
.software reliability (Popstojanova and Trivedi, 2001);
.human reliability (Konstandinidou et al., 2006);
.safety and risk engineering (Sii et al., 2001; Guimara
˜es and Lapa, 2005); and
.quality (Liang and Weng, 2002; Yang et al., 2003).
In the words of Cai (1996), “Undoubtedly fuzzy methodology in system failure
engineering is noticeable and growing area and is still lying in speculative research
period and is premature”. Also, Elasyed (2000) in his paper on “Perspectives and
challenges for research in quality and reliability engineering”;stressed up on the need
for development of new and efficient methods for quality engineering and reliability
estimation and prediction of systems.
Hence, in the present paper authors simultaneously adopt three methodologies i.e.
RCA, FMEA, and FM (shown in Figure 1) to build an integrated framework for
Figure 1.
Framework for failure
analysis and maintenance
decisions
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failure analysis of systems, which could prove beneficial to maintenance
engineers/managers dealing with analysis, design and optimization, of both
reliability and maintainability issues. An industrial case from paper industry is
undertaken to discuss the proposed framework. In the qualitative framework, RCA
is used to provide comprehensive classification of causes related to failure of paper
machine. To quantify the sources of unreliability related to process problems a
detailed FMEA analysis of forming unit is carried out by listing all potential failure
modes, their causes and effect on system performance. The numerical values of
parameters i.e. O
f
,SandO
d
obtained from expert elicitation is used to compute the
RPN score for each failure cause. The discrepancies associated with the traditional
procedure of risk ranking were modeled using decision support system based on
fuzzy methodology. In the quantitative framework various parameters of system
interest to maintenance managers are determined using fuzzy synthesis of system
information.
2. Failure analysis techniques
For failure analysis variety of methods exists in literature. These include root cause
analysis (RCA), reliability block diagrams (RBDs), Monte Carlo simulation (MCS),
Markov modeling (MM), failure mode and effect analysis (FMEA), fault tree analysis
(FTA) and Petrinets (PN) (Misra and Weber, 1989; Singer, 1990; Modarres and
Kaminsky, 1999; O’Connor, 2001; Bowles, 2003; Adamyan and David, 2004). Although
extensive literature exists on the theory behind these techniques, the contemporary
adaptation of these to the problem of reliability analysis is new and, hence, the section
sums up a brief overview of only those techniques, which are used to analyze the
system behavior in the study.
2.1 Root cause analysis
RCA is common terminology found in the reliability literature to avoid future
occurrence of failures by pinpointing the causes of problems Madu (2005), Sharma et al.
(2005a). It provides comprehensive classification of causes related to 4 M’s i.e. man,
machine, materials and methods and thus helps in establishing a knowledge base to
deal with problems related to process/product reliability, availability and
maintainability. With respect to man inadequate training, operator’s errors and
attitude, can contribute to unreliability and with respect to machine problems such as,
poor calibrations or misalignments may result in loss in operational efficiency.
Obivously the method helps to brainstorm the problems related with a particular
process/product reliability and maintainability.
2.2 Failure mode and effect analysis
FMEA is yet another powerful tool used by system safety and reliability engineers to
identify critical components /parts/functions whose failure will lead to undesirable
outcomes such as production loss, injury or even an accident. FMEA was developed at
Grumman Aircraft Corporation in the 1950 and 1960s (Coutinho, 1964) and was first
applied to naval aircraft flight control systems at Grumman. Since then, it has been
extensively used as a powerful technique for system safety and reliability analysis of
products and processes in wide range of industries – particularly aerospace, nuclear,
automotive and medical (O’Connor, 2001; Ebeling, 2001; Bowles, 2003; Sharma et al.,
System failure
behavior
67
2005a).The main objective of FMEA is to discover and prioritize the potential failure
modes (by computing respective RPN), which pose a detrimental effect on the system
and its performance. The approach involves statistical data collection especially
related with the frequency of subcomponent failures and their likelihood of
non-detectability and severity it imposes on system performance. The results of the
analysis help managers and engineers to identify the failure modes, their causes and
correct them during the stages of design and production. The critically debated
disadvantage of FMEA based on RPN analysis is that various sets of failure
occurrence probability [O
f
,], severity [S] and detectability [O
d
] may produce an identical
value, however, the risk implication may be totally different which may result in
high-risk events may go unnoticed. The other disadvantage of the RPN ranking
method is that it neglects the relative importance among O
f
, S and O
d
. The three factors
are assumed to have the same importance but in real practical applications the relative
importance among the factors exists.
To address these disadvantages related to traditional FMEA, a fuzzy decision
making system is provided in the paper to prioritize the failure causes.
2.3 Fault tree and Petrinets
A fault tree is used to analyze the probabilities associated with the various failure
causes and their effects on system performance. FTA starts by identifying a problem
(an accident or an undesirable event) and all possible ways that the problem (failure
occurs). Since 1960 the tool has been widely used for obtaining reliability information
about the complex systems. Obtaining minimal cut sets is a tedious process in a fault
tree model consisting of large number of gates and basic events. Contrary to fault trees,
Petrinets can more efficiently derive the minimal cut and path sets. Also, the
absorption property of Petrinets helps to simplify the Petrinet model and determine
minimal cut set and path sets by reorganizing the transitions which is possible as long
as the firing time is not taken into consideration i.e. transfer of tokens does not take
place (static condition) (Singer, 1990; Liu and Chiou, 1997; Adamyan and David, 2002).
Similar to fault tree, Petrinets makes use of digraph to describe cause and effect
relationship between conditions and events. Petri nets have two types of nodes named
place “P” and transition “T”. Formally Petrinet, a directed bipartite graph is defined by
a six-tuple N¼[T, P, A, M
0
, I (t), O (t)] (Peterson, 1999).
Where:
T¼{t
1
,t
2
,...,t
n
}: a set of transitions, each transition representing an event or
an action.
P¼{p
1
,p
2
,...,p
l
}: a set of places, where a place is used to represent either the
condition for the event or the consequences of the event.
A#{T £P} <{P £T} ¼a set of directed arcs that connect transitions to
places and places to transitions.
M
0
¼the initial marking of the system that represents initial state of the system.
I(t ¼{pj(p,t)[A}: a set of input places of a transition t.
O(t)¼{pj(t,p)[A}: a set of output places of a transition t.
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The basic symbols used in Petrinet model are defined as follows:
j¼Place, drawn as a circle.
–¼Transition, drawn as a bar.
"¼Arc, drawn as an arrow, between places and transitions.
†¼Token, drawn as a dot, contained in places.
Petrinet has two parts i.e. static and dynamic. The static part consists of Places (P),
Transitions (T) and Arrows (A). While the dynamic part is related with marking of
graph by tokens which are present, not present or evolves dynamically on firing of valid
transitions. As shown in Figure 2 (a), the static part and 2(b) the dynamic part i.e. before
firing there is one token in each of input places P
1
and P
2
but no token in output place P
3
.
Accordingly, the Petrinet marking is M ¼(1, 1, and 0). And after firing of transition
based on enabling rules the token moves from each of P
1
and P
2
to the output place P
3
.
From the literature studies it is observed that both Petri nets and fault tree methods
are used for software reliability analysis (Kumar and Aggarwal, 1993); analysis of
coherent fault trees (Hauptmanns, 2004) and fault diagnosis (Mustapha et al., 2004).
Exclusively in the field of reliability engineering the application of Petrinets has been
presented for reliability evaluation (Adamyan and David, 2002, 2004), Markov analysis
(German, 2000; Aneziris and Papazoglou, 2004; Schoenig et al., 2006) and stochastic
Figure 2.
System failure
behavior
69
modeling (Ciardo et al., 1994; Sahner and Trivedi, 1996) respectively. In the paper the
authors has used only the static part of Petrinet to model the quantitative behavior of
system. It is assumed that transitions are not timed i.e. the transfer of token from an
input place to output place does not takes place.
3. Brief overview of fuzzy concepts
The section presents brief overview of only those concepts related to fuzzy set theory,
which are of relevance in the study (Zimmermann, 1996; Kokso, 1999; Ross, 2000;
Tanaka, 2001).
Fuzzy sets, membership functions, Alpha cuts and linguistic variables
Crisp (classical) sets contain objects that satisfy precise properties of membership
functions. Only two possibilities whether an element belongs to, or not belongs to a set
exist. A crisp set “A” can be represented by a characteristic function m
A
/u¼{0, 1}.
MAðxÞ¼
1if x [A
0if x A
(ð1Þ
Where: U: universe of discourse, X: element of U, A: crisp set and M: characteristic
function.
On the other hand fuzzy sets contain objects that satisfy imprecise properties of
membership functions i.e. membership of an object in a fuzzy set can be partial.
Contrary to classical sets, fuzzy sets accommodate various degree of membership on
continuous interval [0, 1], where “0” conforms to no membership and “1”conforms to
full membership. Mathematically defined by Equation (2):
m
~
AðxÞ:U!½0;1ð2Þ
Where:
m
~
AðxÞ: Degree of membership of element x in fuzzy set ~
A
Various types of membership functions such as triangular, trapezoidal, gamma and
rectangular can be used for reliability analysis. However triangular membership functions
(TMF) are widely used for calculating and interpreting reliability data because of their
simplicity and understandability (Yadav et al., 2003; Bai and Asgarpoor, 2004). For
instance, imprecise or incomplete information such as low/high failure rate i.e. about 4 or
between 5 and 7 is well represented by triangular M.F. In the paper triangular membership
function is used as it not only conveys the behavior of various system parameters but also
reflect the dispersion of the data adequately. The dispersion takes care of inherent
variation in human performance, vagueness in system performance due to age and adverse
operating conditions. Thus, it becomes intuitive for the engineers to arrive at decisions.
The
a
cut of a fuzzy set M, denoted as ~
M
a
is the set of elements x of a universe of
discourse X for which the membership function of M is greater than or equal to
a
i.e.
~
M
a
¼{x[X;
m
MðxÞ$
a
;
a
[½0;1}
The alpha cut provides a convenient way of performing arithmetic operations on fuzzy
sets and fuzzy numbers including in applying extension principle. Consider a
triangular fuzzy number defined by triplets (m
1,
m
2,
m
3
) shown in Figure 3. With
introduction of
a
cuts, M
˜
a
¼[m
1(
a
)
,m
3(
a
)
]. The cut is used to define the interval of
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confidence of triangular membership function and is written as equation 3 (for details
refer to Kokso (1999) and Ross (2000)).
~
M
a
¼m22mð
a
Þ
1
a
þmð
a
Þ
1;2mð
a
Þ
32m2
a
þmð
a
Þ
3
ð3Þ
Moreover, when an event is imprecisely or vaguely defined, the experts would simply
say that the possibility of occurrence of a given event is “low”, “high”, and “fairly
high”. To estimate such subjective events linguistic expressions are used. The analyst
can use linguistic variables to assess and compute the events using well-defined fuzzy
membership functions (Tanaka, 2001). In the paper, the linguistic terms such as
“Remote”, “Low”, “Moderate”, “High”, and “Very high” are used to represent
probability of occurrence, severity and non-detectability in FMEA.
Fuzzy rule base and inference system
The rule base describes the criticality level of the system for each combination of input
variables. Often expressed in “If-Then” form [where, If:an antecedent which is
compared to the inputs and Then: a consequent, which is the result/output], they are
formulated in linguistic terms using two approaches
(1) Expert knowledge and expertise.
(2) Fuzzy model of the process.
For instance, the format of rules is defined as:
RI:Ifxis Mithen yis Ni;i¼1;2;3... Kð4Þ
where:
x¼the input linguistic variable.
M
i
¼the antecedent linguistic constants (qualitatively defined functions).
y¼the output linguistic variable.
N
i
¼the consequent linguistic constants.
By using the inference mechanism an output fuzzy set is obtained from the rules and the
input variables. There are two most common types of inference systems frequently used:
(1) the max-min inference; and
(2) the max-prod inference method (Zimmermann, 1996; Kokso, 1999; Ross, 2000).
Figure 3.
A triangular memership
function with
a
cut
System failure
behavior
71
Examples of t-norms are the minimum, oftenly called “mamdani implication” and the
product, called the Larsen implication. In the study mamdani’s max-min inference
method is used. For instance, a fuzzy rule expressed by equation (4) is represented by a
fuzzy relation R: (X x Y), which is computed by using Equation (5):
m
Rðx;yÞ¼I
m
AðxÞ;
m
BðyÞ
ð5Þ
Where, the operator Ican be either an implication or a conjunction operator.
Defuzzification
In order to obtain a crisp result from fuzzy output deffuzification is carried out. In the
literature various techniques for defuzzification such as centroid, bisector, middle of
the max, weighted average exist. The criterions for their selection are disambiguity
(result in unique value), plausibility (lie approximately in the middle of the area) and
computational simplicity (Ross, 2000; Zimmermann, 1996; Zadeh, 1996). In the study,
the centroid method is used for defuzzification as it gives mean value of the
parameters. Mathematically represented as (Equation 6):
Defuzzified value ¼y
R
m
B0ðyÞy:dy
y
R
m
B0ðyÞdy ð6Þ
Where, B0is the output fuzzy set, and
m
B0iis the membership function.
4. An illustration
As an example a case from process industry (paper mill) situated in northern part of
India (producing 180 tons of paper per day) is taken to discuss the failure behavior both
in qualitative and quantitative manner. There are many functional units in a paper mill
such as feeding, pulp preparation, pulp washing, screening, bleaching and preparation
of paper. The current analysis is based on the study of a real system (paper machine),
which is one of the main and most important functional units of the paper mill. It
consists of three main subunits defined as under:
(1) Sub unit 1 [SS
1
]. Forming. It consists of head box, wire mat and suction box as
three main components. Head box delivers stock (pulp þwater) in controlled
quantity to moving wire mat, supported by series of table and wire rolls. The
suction box (having six pumps) dewaters the pulp through vacuum action.
(2) Sub unit 2 [SS
2
]Press. It consists of felt, upper and bottom rolls as main
components. The unit receives wet paper sheet from forming unit on to the felt,
which is further, carried through press rolls thereby reducing the moisture
content to almost 50 percent.
(3) Sub unit 3 [SS
3
]Dryer. It consists of felt, steam-heated rolls (dryers), in stages,
associated with steam handling systems as main components. The remaining
moisture content in the sheet is removed by means of heat and vapor transfer.
The failure of any subunit /components would cause the system to fail.
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4.1 Qualitative framework
To diagnose the unreliable aspects of the machine, root cause analysis (RCA) of paper
machine, as a system is carried out by listing all the possible causes related to the
machine units i.e. forming, press and dryer as shown in Figure 4.
Further, to quantify the sources of unreliability related to process problems and
identify potential system failure modes, their causes and effect on performance of the
system it is decided to conduct and failure mode and effect analysis of one of the unit
i.e. press unit, by breaking the unit into two sub-units i.e. press felts and press rolls. In
brief the methodology used to compute the scores related to failure of occurrence (O
f
),
likelihood of non-detection of failure (O
d
), and severity (S) of failure of various
components are discussed as follow (Sharma et al. 2005a).
Probability of occurrence of failure [O
f
]. Probability of occurrence of failure is
evaluated as a function of mean time between failures. The data related to mean time
between failures of components is obtained from previous historical records,
maintenance log-books and is then integrated with the experience of maintenance
personnel. For instance, if MTBF of component is between two to four months then
probability of occurrence of failure is high (occurrence rate 0.5-1 percent) with the score
Figure 4.
Root cause analysis
System failure
behavior
73
ranging between 7-8. Table I presents the linguistic assessment of probability of failure
occurrence with corresponding MTBF and scores assigned.
Probability of non-detection of failures [O
d
]. The chance of detecting a failure cause
or mechanism depends on various factors such as ability of operator or maintenance
personnel to detect failure through naked eye or by periodical inspection or with the
help of machine diagnostic aids such as automatic controls, alarms and sensors. For
instance, probability of non-detection of failure of a component through naked eye is
say, 0-5% is ranked 1 with non-detectability remote. The values of S
d
for various
failure causes reported in the study are evaluated according to the score reported in
Table I.
Severity of failure (S). Severity of failure is assessed by the possible outcome of
failure effect on the system performance. The severity of effect may be regarded as
remote, moderate or very high. In the study the data related to mean time to repair
(MTTR), effect on the quality of the product are used to obtain score for severity. For
instance, if MTTR of facility/component is less, say lies between 1/4-1/5 hours, than
effect may be regarded as remote. If external intervention is required for repairs, or
MTTR exceeds 1/2 days and there is appreciable deterioration in the quality of the
paper than effect may be regarded as high and if system degrades resulting in line shut
down /production stoppage than the severity may be regarded as very high.
Table II presents the traditional FMEA analysis for the press unit. The numerical
values of FMEA parameters i.e. O
f
, S and O
d
are obtained by using the discussed
methodology. Then, RPN number for each failure cause is evaluated by multiplying
the factor scores [O
f
£S£O
d
]. From Table II it is observed that causes PC
26
and
PC
28
produce an identical RPN i.e. 280, however, the occurrence rate and detectability
for both the causes are totally different. Also, PC
14
and PC
24
though represented by
different sets of linguistic terms produce identical RPN i.e. 180, which could be
misleading.
The above listed limitations of traditional FMEA are addressed by using fuzzy
decision making system (FDMS) developed using MATLAB based on fuzzy set
principles as discussed in section 3. The basic system architecture of FDMS consists of
three main modules i.e. knowledge base module and user input/output interface
module as shown in Figure 5.
Linguistic
terms
Score/
Rank no. MTBF
Occurrence
rate%
Severity effect Likelihood of non-
detection (%)
Remote 1 .3 years ,0.01 Not noticed 0-5
Low 2
3
1-3 years 0.01-0.1 Slight annoyance to operator 6-15
16-25
Moderate 4
5
6
0.4-1 year 0.1-0.5 Slight deterioration in
system performance
26-35
36-45
46-55
High 7
8
2-4months 0.5-1 Significant deterioration in
system performance
56-65
66-75
Very high 9
10
,2 months .1 Production loss and non-
conforming products
76-85
86-100
Table I.
Scale used for O
f
, S and O
d
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74
Component
Function Potential failure
mode Potential effect of failure Potential cause of failure O
f
SO
d
RPN
Press section
Press felts
To carry the sheet Excessive tension/
slippage
Web-breaks/loss in operation Vibrations [PC
11
] 5 8 8 320
Inadequate tension [PC
12
] 7 7 6 294
Broken internals [PC
13
] 4 6 7 168
Abrasion/worn-out
(prematurely)
(i) Deteriorate/degrade the
sheet
Abrasive materials. [PC
14
] 4 9 5 180
Corrosion. [PC
15
] 6 6 6 216
(ii) Loss of flow Scale buildup [PC
16
] 5 8 8 320
Insufficient cleaning/
maintenance. [PC
17
]
3 6 8 144
Press rolls To apply mechanical pressure
when felt and sheet sandwich
passes through loaded press rolls
(i) Sagging Loss in operation Non uniform loading of
stock [PC
21
]
8 8 8 512
(ii) Deflection Loss in operation Pull of felts [PC
22
] 7 9 7 441
(iii) Bearing seizure/
failure
Overheating with noise
Rolls fails to move
Scanty lubrication [PC
23
] 6 5 5 150
High temperature [PC
24
] 5 6 6 180
(iv) Buckling/
deformation
Stock jumps and creates
disturbance on wire
Misalignment [PC
25
] 8 9 9 648
Vibrations. [PC
26
] 5 8 7 280
(v) Improper
alignment
Felt failure (crush and curl
the paper)
Out of balance [PC
27
] 5 9 6 270
Improper maintenance
[PC
28
]
8 7 5 280
(vi) Rubber wear Degrade quality of sheet Vibrations [PC
29
] 5 6 8 240
Loss in Heat resistance
[PC
210
]
8 7 9 504
Table II.
Traditional FMEA for
press unit
System failure
behavior
75
The input parameters i.e. O
f
,SandO
d
, used in FMEA, were fuzzified using appropriate
membership functions to determine degree of membership in each input class. For the
output variable, riskiness/priority level both triangular and trapezoidal membership
functions were used (Figure 6(a) and 6 (b)). Multiple experts with different degree of
competencies were used to construct the membership function.
The resulting fuzzy inputs were evaluated in fuzzy inference engine, which makes
use of well-defined rule base. In the study, based on the membership functions of three
input variables O
f
,S,O
d
with, five fuzzy sets in each, a total of 125 rules can be
generated. However, these rules were combined (wherever possible) and the total
number of rules in rule base was reduced to 30.
Finally to express the riskiness/criticality level of the failure so that corrective or
remedial actions can be prioritized accordingly, defuzzification is done using centroid
method to obtain crisp ranking from the fuzzy conclusion set.
Figure 5.
Modules in fuzzy decision
making system
Figure 6.
Membership function
plots
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16,1
76
Discussion
The summary of the results obtained through traditional and fuzzy method is
presented in Table III. From Table III it is observed that for events PC
26
and PC
28
where O
f
,Sand O
d
are described by “Moderate, High” and “High”, and “High, High,
Moderate” respectively, the traditional FMEA output is 280 for both, this means that
both the events are prioritized at same rank i.e. fifth But the defuzzified outputs for
PC
26
and PC
28
are 0.664 and 0.660 respectively which shows that PC
26
should be
ranked higher than PC
28
. Also, for causes PC
14
&PC
24
which are represented by
different sets of linguistic terms i.e. Moderate, Very high and Moderate;Moderate,
Moderate and Moderate produce identical RPN i.e. 180. But FDMS output so obtained
is different for both of them.
4.2 Quantitative framework
In this framework first the Petrinet model of the system is obtained from its equivalent
fault tree (Figure 7(a) and 7(b)) and then the system behavior is analyzed using fuzzy
synthesizes of information based on the steps (shown in Figure 8) discussed as follows.
Step 1. Under the information extraction phase, the data related to failure rate [
l
i]
and repair time [
t
i] of the components Where, i¼1[ Head box]; i¼2 [wire mat], i¼3
[suction box]; i¼4,5,6 [roller bearing, roller bending and roller rubber wear]; i¼7
[press felt]; i¼8,9,10 for upper roll and i¼11,12,13 for bottom roll [roller bearing,
roller bending and roller rubber wear]; i¼14 [Dryer felt]; i¼15,16 for upper roll and
i¼17,18 for bottom roll [roller bearing, and roller bending] is collected from
present/historical records of a paper mill and is integrated with expertise of
maintenance personnel (Sharma and Kumar, 2008) as presented in Table IV.
Step 2. To account for imprecision and uncertainties in data, the crisp input data of
l
and
t
is converted to fuzzy numbers using triangular membership function, with
^15 percent spread on crisp value (as shown in the Figure 9 for the first component of
Potential cause of
failure
Traditional RPN
output
Traditional
ranking
Fuzzy RPN
output
Fuzzy
ranking
PC
11
320 1 0.664 1
PC
12
294 2 0.660 2
PC
13
168 5 0.617 4
PC
14
180 4 0.659 3
PC
15
216 3 0.511 6
PC
16
320 1 0.664 1
PC
17
144 6 0.521 5
PC
21
512 2 0.667 3
PC
22
441 4 0.679 2
PC
23
150 9 0.511 9
PC
24
180 8 0.511 9
PC
25
648 1 0.699 1
PC
26
280 5 0.664 4
PC
27
270 6 0.657 6
PC
28
280 5 0.660 5
PC
29
240 7 0.617 7
PC
210
504 3 0.601 8
Table III.
Comparison of traditional
FMEA and fuzzy output
System failure
behavior
77
press unit i.e. press felt). To obtain fuzzy probabilities values, the fuzzy transition
expressions for
l
and
t
are obtained by using the extension principle coupled with an
a
cut and interval arithmetic operations on conventional AND/OR expressions as listed
in Table. For instance, OR transition expressions for
l
and
t
were represented by
Equation (i) and (ii) in the Table V using similar approach AND transition expressions
can be computed.
Step 3. After knowing the input fuzzy triangular numbers for all the components
shown in Petrinet model the corresponding fuzzy values of
l
and
t
for the system at
different confidence levels are determined using fuzzy transition expressions. To
analyze the behavior of system in quantitative terms various parameters of interest
such as system availability, system reliability, expected number of failures, and mean
Figure 7.
(a) Fault tree (b) Petrinet
model
JQME
16,1
78
Forming unit
l
1
¼1£10
24
,
l
2
¼3£10
23
,
l
3
¼
l
4
¼1£10
23
,
l
5
¼1.5 £10
23
,
l
6
¼2£10
23
failures/h
t
1
¼10,
t
2
¼10,
t
3
¼
t
4
¼2,
t
5
¼3,
t
6
¼4hrs respectively
Press unit
l
7
¼1£10
24
,
l
8
¼
l
11
¼1£10
23
,
l
9
¼
l
12
¼1.5 £10
23
,
l
10
¼
l
13
¼2£10
23
failures/h
t
t
¼5,
t
8
¼
t
11
¼2,10,
t
9
¼
t
12
¼3,
t
10
¼
t
13
¼4hrs respectively
Dryer unit
l
14
¼1£10
24
,
l
15
¼
l
17
¼1£10
23
,
l
16
¼
l
18
¼2£10
23
, failures/h
t
14
¼10,
t
15
¼
t
17
¼2,
t
16
¼
t
18
¼4hrs respectively
Table IV.
Input data
Figure 9.
Input fuzzy triangular
number representation
Figure 8.
Procedural steps
System failure
behavior
79
time between failures are computed at different alpha cuts. The summary of the fuzzy
reliability parameters, for each confidence factor i.e.
a
level, ranging from 0 to 1, with
increments of 0.1, is presented in Table VI with left and right spreads. Depending on
the value of
a
, the analyst predicts the measures for the system. The graphical results
(Figure 10) shows that if uncertainty in input data is described by means of triangular
fuzzy numbers, then the possibility distribution of failure rate and repair time is a
distorted triangle because after applying the fuzzy mathematics, the linear sides of
triangle changes to parabolic one (Sittithumwat et al., 2004).
Step 4. In order to make decisions with respect to maintenance actions it is
necessary to convert fuzzy output into a crisp value. By using centroid method
defuzzification is carried out.The defuzzified values for the respective reliability
parameters are calculated at ^15 percent, ^25 percent and ^60 percent spread.
Table VII presents both crisp and defuzzified values for the unit. The crisp value
remains same irrespective of change in spread.
Behavior analysis
The crisp and defuzzified values of reliability parameters at ^15 percent, ^25 percent,
and ^60 percent spread are calculated and are tabulated in Table VII. From the table,
it is evident that defuzzified value changes with change in percentage-spread. For
(a) Conventional expressions
Type of gate
l
AND
t
AND
l
OR
t
OR
Expressions
Y
n
i¼1
l
iX
n
j¼1Y
n
i¼1
i#j
t
i
2
6
6
6
6
6
6
6
4
3
7
7
7
7
7
7
7
5Y
n
i¼1
t
i,X
n
j¼1Y
n
i¼1;
i#j
t
i
2
6
6
6
6
6
6
6
4
3
7
7
7
7
7
7
7
5X
n
j¼1
l
jX
n
j¼1
l
j
t
j,X
n
j¼1
l
j
(b) Fuzzy expressions, or
l
ð
a
Þ¼ X
n
i¼1
{ð
l
i22
l
i1Þ
a
þ
l
i1};X
n
i¼1
{2ð
l
i32
l
i2Þ
a
þ
l
i3}
"#
ðiÞ
t
ð
a
Þ¼ X
n
i¼1
{ð
l
i22
l
i1Þ
a
þ
l
i1}:{ð
t
i22
t
i1Þ
a
þ
t
i1}
X
n
i¼1
{2ð
l
i32
l
i2Þ
a
þ
l
i3}
;
2
6
6
6
6
4
X
n
i¼1
{2ð
l
i32
l
i2Þ
a
þ
l
i3}:{ð
t
i32
t
i2Þ
a
þ
t
i3}
X
n
i¼1
{ð
l
i22
l
i1Þ
a
þ
l
i1}
3
7
7
7
7
5
ðiiÞ
Table V.
(a) Conventional (b)
Fuzzy expressions for
l
and
t
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16,1
80
DOMF Repair hr Failure hr X 10
-3
Availability Reliability MTBF X 10
2
hr ENOF
L.S R.S L.S R.S L.S R.S L.S R.S L.S R.S L.S R.S
1 4.1080 4.1080 23.800 23.800 0.9182 0.9182 0.7882 0.7882 46.124 46.124 1.1831 1.1831
0.9 4.0405 4.1940 23.680 23.925 0.9164 0.9196 0.7872 0.7895 45.992 46.270 1.1771 1.1884
0.8 3.9730 4.2805 23.560 24.050 0.9146 0.9211 0.7862 0.7908 45.860 46.417 1.1712 1.1938
0.7 3.9195 4.3890 23.445 24.183 0.9124 0.9223 0.7852 0.7914 45.741 46.573 1.1148 1.2004
0.6 3.8660 4.4975 23.330 24.316 0.9102 0.9235 0.7841 0.7921 45.622 46.722 1.0585 1.2070
0.5 3.8327 4.6340 23.225 24.454 0.9076 0.9245 0.7830 0.7928 45.524 46.885 1.0529 1.2140
0.4 3.7995 4.7705 23.115 24.596 0.9049 0.9256 0.7819 0.7936 45.427 47.041 1.0478 1.2210
0.3 3.7560 4.9425 23.013 24.742 0.9014 0.9264 0.7802 0.7944 45.359 47.199 1.0424 1.2283
0.2 3.7125 5.1145 22.912 24.889 0.8985 0.9273 0.7796 0.7952 45.292 47.357 1.0378 1.2356
0.1 3.6850 5.3321 22.809 25.043 0.8946 0.9280 0.7784 0.7960 45.263 47.527 1.0324 1.2433
0 3.6575 5.5502 22.706 25.198 0.8907 0.9287 0.7772 0.7968 45.235 47.697 1.0272 1.2511
Table VI.
Computed parameters
(with left and right
spread values)
System failure
behavior
81
instance, repair time first increases by 2.25 percent when spread changes from ^15
percent to ^25 percent and further by 8.82 percent when spread changes from ^25
percent to ^60 percent. Similarly, for failure rate and expected number of failures, with
increase in spread, increase in defuzzified values, is observed. On the other hand, at the
same time for mean time between failures a decrease of 0.17 percent when spread
changes from ^15 percent to ^25 percent and further by 2.40 percent when spread
from changes from ^25 percent to ^60 percent is observed. Similarly for availability
and. reliability decrease in defuzzified values with increase in spread is observed.
Thus, from above discussions it is inferred that the maintenance action for the system
should be based on defuzzified MTBF rather than on crisp value because with the
reduced MTBF values a safe interval between maintenance actions can be established
and inspections (continuous or periodic) can be conducted to monitor the condition or
status of various equipments constituting the system before it reaches the crisp value.
It can also be observed that with increase in repair time (2.25 percent to 8.82 percent)
availability goes on decreasing (0.203 percent to 0.915 percent). Hence, the need to
Figure 10.
Fuzzy graph
representations of system
parameters
JQME
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82
System parameters Crisp values Defuzzified value (^15% spread) Defuzzified value (^25% spread) Defuzzified value (^60% spread)
Failure rate (h
21
) 23.800 £10
23
23.889 £10
23
23.990 £10
23
24.86 £10
23
Repair time (h) 4.1080 4.2110 4.306 4.686
MTBF (h) 4.6124 £10
2
4.6069 £10
2
4.5990 £10
2
4.4881 £10
2
ENOF 0.11831 £10
21
0.11877 £10
21
0.119285 £10
21
0.12373 £10
21
A
sys.
9.18204 £10
21
9.1624 £10
21
9.1438 £10
21
9.0601 £10
21
R
sys.
7.8820 £10
21
7.8740 £10
21
7.8670 £10
21
7.7989 £10
21
Table VII.
Crisp and defuzzified
values
System failure
behavior
83
enhance maintainability requirements for the system is felt. A condition monitoring
maintenance planning system describing monitoring methods and frequency of
monitoring (Table VIII) is made which could help the organization in effective
maintenance planning.
5. Conclusion
The analysis of system reliability often requires the use of subjective judgments,
uncertain data and approximate system models. Owing to its sound logic, effectiveness
in quantifying the vagueness and imprecision in human judgment, the study has
successfully incorporated a unified (both qualitative and quantitative) approach to
evaluate and assess system failure behavior. The comprehensive classification of
causes using RCA to diagnose the unreliable aspects of system helps to create a
knowledge base for conducting FMEA. The proposed FDMS based on fuzzy principles
not only addresses the seriously debated disadvantages associated with traditional
procedure for conducting FMEA but also integrates expert judgment, experience and
expertise in more flexible and realistic manner. Further, the estimation of various
system parameters in terms of fuzzy, defuzzified and crisp results not only helps the
maintenance managers to understand the behavioral dynamics of the respective units
but also depending on the value of confidence factor (alpha), the analysts can predict
Lubricant monitoring Vibration monitoring
Thermal monitoring
Components which are
lubricated
Components that moves
Components monitored Heat generating devices
i.e.
Condition of bearings
(bearing housing)
Bearings Rollers (belt, chain or
gear drive)
Hydraulic pumps (gear
case)
Transmission
components (gears,
cams etc.)
Surfaces between
components with
relative motion
Electrical components
(motors)
Monitoring equipment Fluid or bimetallic
thermo meters
Magnetic plugs for
visual examination of
debris using microscope
Accelerometer with
electronic display unit
Thermocouples Spectroscope analysis
On-load removable
filters
Frequency filters and
recorders
Resistance
thermometers
Optical pyrometers
Faults detected Failure of drives Leakage Wear or failure of
bearingsBlockage of ducts Contaminants
MisalignmentLoss of cooling Wear or deterioration of
any component Loosening or
deterioration
Fouling of tubes
Imbalance (rotating or
reciprocating)
Over-use
Mechanical looseness
Monitoring frequency Continuous or periodic Periodic Continuous or periodic
Table VIII.
Condition monitoring
maintenance planning
system
JQME
16,1
84
the reliability measure for the system(s) and take necessary steps to improve system
performance. For instance, According to the crisp value (as depicted in Table VII), the
system failure rate is 23.800 £10
23
but if uncertainty in information regarding the
input failure data is introduced and is synthesized using fuzzy methodology then the
results so obtained at different spreads on crisp value prove beneficial to the
maintenance experts /managers to understand the behavioral dynamics of the system
in more realistic manner as shown in Table VII that with increase in spread as the
failure rate of system increases, the repair time also increases which results in decrease
of both availability and reliability of the system and hence enhancing maintainability
requirements.
6. Managerial implications
The application of proposed framework as discussed in the study will help the
reliability/maintenance engineers/ analysts/managers:
.To model, analyze and predict the behavior of industrial systems in more
realistic manner.
.To manage the dilemma of direct (quantitative) evaluation of intangible
(qualitative O
f
,S and O
d
) criterions used in FMEA with the help of well defined
membership functions to synthesize fuzzy information.
.To plan suitable maintenance practices /strategies for improving system
performance (Jardine, 1991; Sherwin, 2000; Sharma et al. 2005b, c; Pintelon et al.,
2006).
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Zimmermann, H. (1996), Fuzzy Set Theory and its Applications, 3rd ed., Kluwer Academic
Publishers, London.
Further reading
Chen, G. (2000), Introduction to Fuzzy Sets Fuzzy Logic and Fuzzy Control Systems, CRC Press,
Boca Raton, FL.
Dekker, R. (1996), “Application of maintenance optimization models: a review and analysis”,
Reliability Engineering and System Safety, Vol. 51, pp. 225-40.
Sarker, R. and Haque, A.L. (2000), “Optimization of maintenance and spare provisioning policy
using simulation”, Applied Mathematical Modeling, Vol. 24 No. 10, pp. 751-60.
Corresponding author
Rajiv Kumar Sharma can be contacted at: rksnithmr@gmail.com
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