cognitive map-based system modeling for identifying interaction failure modes
TRANSCRIPT
ORIGINAL PAPER
Cognitive map-based system modeling for identifying interactionfailure modes
Manu Augustine • Om Prakash Yadav •
Rakesh Jain • Ajay Rathore
Received: 23 March 2010 / Revised: 24 June 2011 / Accepted: 22 July 2011 / Published online: 12 August 2011
� Springer-Verlag London Limited 2011
Abstract Past few decades have seen an upsurge in
failure analysis techniques capable of dealing with reli-
ability issues up front in the early stages of the product
development process. Most of these approaches are cen-
tered on component-specific failures. However, with the
advent of highly complex systems that derive functional-
ities from multiple physical phenomena domains, more
emphasis is required on identifying failures arising due to
various system interactions, which is largely absent in
existing failure analysis approaches. Owing to the causal
nature of system interaction failures, the use of cognitive
maps in system modeling and simulation for failure anal-
ysis is highly suitable. This paper proposes a structured
framework for the development and use of cognitive map-
based system models capable of capturing all types of
failure modes, including interaction failures. The applica-
bility of the proposed framework is demonstrated with the
example of an electric water heater.
Keywords Failure analysis � Failure modes �System interaction failures � Cognitive map �System modeling � Simulation
1 Introduction
One of the main metrics of performance of a product in the
market is the total amount of warranty cost associated with
its failures during customer ownership. The basic reason
behind failure-prone products reaching the hands of cus-
tomers is a lack of in-depth understanding of the failure
propagation mechanisms on the part of product developers.
Failure analysis (FA) plays a very vital role in the identi-
fication and elimination of potential failure modes in order
to design a reliable or a failure-free product. It gives
valuable insights into the causes of system failures and
provides input for further improvement in product design.
Some of the well-known FA techniques that have been
commonly used for identifying and eliminating failures
include failure modes and effects analysis (FMEA) (MLT-
STD-1629 1980), fault tree analysis (FTA) (Vesely et al.
1981), event tree analysis (ETA) (Papazolglou 1998), root
cause analysis (RCA) (Mobley 1999). However, these
traditional approaches contribute to system improvement
mostly by considering past failure data. Due to this fact,
these approaches are not very effective in their original
form in the early stages of new product development
(NPD), since historical data are unavailable for new
products and technologies.
In the past few decades, intense global competition,
coupled with the onset of the First Product Correct (FPC)
paradigm (Yadav and Singh 2008), has driven the efforts
toward minimizing product failures to undergo a shift of
focus from the traditional ‘‘make and test’’ approach, to a
more proactive ‘‘anticipate and prevent’’ approach. In the
field of FA, this has led to an emergence of approaches
applicable at the design stage of the product development
process. These are basically proactive approaches used for
acquiring knowledge of various mechanisms through
M. Augustine � R. Jain � A. Rathore
Department of Mechanical Engineering,
Malaviya National Institute of Technology,
Jaipur, India
O. P. Yadav (&)
Department of Industrial and
Manufacturing Engineering,
North Dakota State University,
Fargo, ND 58108, USA
e-mail: [email protected]
123
Res Eng Design (2012) 23:105–124
DOI 10.1007/s00163-011-0117-6
which failures can occur (generally even before the system
is materialized). Hence, these approaches are more suitable
for application in an NPD environment.
One underlying feature that can be commonly identified
in most of these approaches is their orientation toward
component-specific failures. However, in the present sce-
nario of technological advancements, failure analysis from
a simplistic viewpoint of physical failures of individual
components is not sufficient. As an example, Brombacher
et al. (2005) report increasing percentage of ‘‘No Fault
Found’’ (failures where cause of failure could not be
determined) at a major manufacturer of high tech, high-
volume consumer electronics, and other complex products
over the last two decades. For an FA technique to com-
prehensively capture all modes of system failures, it is
necessary to incorporate failure reasoning at the structural,
functional, and system interaction levels simultaneously.
1.1 Motivation and outline of proposed work
Mechanisms through which failures occur in any given
system are many. While identification of component-
specific failures may suffice for simple systems, it hardly
covers any ground in the case of complex systems that
derive functionalities from multiple disciplines of science
and engineering. For such systems, owing to their
complexity, there occur a myriad of unintended inter-
component, inter-functional, as well as other environ-
mental interferences that can give rise to unpredictable
behaviors. Such behaviors constitute a major source of
failures for any given system (hereafter in this paper,
these failures will be referred to as system interaction
failures). One typical example of a system interaction
failure is carburetor icing in IC engines, which results
due to the freezing of air moisture during the suction of
highly humid air through the carburetor. The rigor of
physics of failure-like approaches is required to gain an
understanding of such failure mechanisms. However, the
feasibility of such approaches in early stages of product
development is limited due to the general non-availability
of hard numerical data and representative mathematical
relationships. As a matter of fact, there exist very few FA
techniques that support effective identification of system
interaction failures at the design stage and help generate
an understanding of their mechanisms.
Since system interactions of any kind are basically
cause-and-effect propagations within the system, cognitive
maps present quite an appealing modeling platform for
identifying interaction failure modes (Augustine et al.
2009). Although cognitive maps can effectively represent
the causal flows that exist within a system, the responsi-
bility for its efficacy primarily depends on the system
expert who constructs the map. Even after three decades of
significant research contribution, the literature still lacks
work directed toward automation and standardization in the
construction of cognitive maps (Schneider et al. 1998).
Motivated by the above-mentioned facts, this paper
proposes a cognitive map-based system representation
schema for facilitating the identification of a wide variety
of failure modes including system interaction failures in
physical systems. Further, the paper also proposes the
development of an expert system-based framework for
semiautomatic construction of these cognitive maps.
A structured procedure is outlined to first convert ini-
tially available raw data (CAD model, bill of materials)
depending on the level of abstraction at which modeling is
done in the design stage) into an appropriate functional
model. The functional model is then systematically con-
verted into a cognitive map representation of the entire
physical system under consideration. Nodes interconnected
through causal arcs in the resulting cognitive map are
variables, which are representative of the system’s com-
ponents, interfaces, and the general environment with
which the system interacts. Cognitive map simulation is
performed to identify failed nodes within the causal net,
which are then mapped back to the functional model of the
system. The set of functional descriptors thus identified are
interpreted as functional failure modes that also include
those arising due to system interactions. The main advan-
tage of using the proposed approach of knowledge repre-
sentation lies in the fact that complete knowledge regarding
the structure, functionality as well as causality of a system
can be incorporated into a single model. Moreover, the
reusability of the knowledge fragments being used as
modeling constructs is also high.
The rest of the paper is organized as follows: In Sect. 2, a
review of relevant literature is given. Apart from a discus-
sion on existing FA approaches that are applicable in the
early stages of product development, an introduction to
cognitive maps is also given. In Sect. 3, the guidelines for
developing the proposed expert system-based framework
are detailed. A typical electric water heater is taken as an
example to clarify the steps involved in the framework that
ultimately results in the generation of a cognitive map rep-
resentation of the system. Section 4 demonstrates the pro-
cess of identification of failure modes of the electric water
heater through cognitive map simulation. Finally, in Sect. 5,
conclusions along with future research directions are given.
2 Related work and prior research
2.1 FA in early stages of product development
A majority of researchers all over the world consider
FMEA as the most widely accepted FA approach till date.
106 Res Eng Design (2012) 23:105–124
123
A generic classification of this popular approach is often
done into design FMEA and Process FMEA, with the
former being more popular of the two (Bhamare et al.
2007). Design FMEA aims at utilizing past knowledge on
failures for improvement in future designs. However,
without a proper way to archive and manage the knowledge
generated through it, the task of performing an FMEA
becomes quite laborious. The WIFA (short form for
‘‘knowledge-based FMEA’’ in German) project (Wirth
et al. 1996) is aimed at providing a solution to the
knowledge management problem for FMEA. It facilitates
past knowledge reuse by populating and managing
knowledge bases to support descriptions of various prod-
ucts and processes. Nevertheless, traditional FMEA and all
its variants are not supported by any basis that can enable
actual reasoning on causes, effects, and propagation of
failures. A firm basis like that is a mandatory requirement
for FA in early stages of new product development where
historical knowledge is hard to come by. Our study of lit-
erature indicates that appropriate functional representations
of target systems have been prominently employed to fulfill
the above requirement.
Functional modeling has been the mainstay in repre-
senting systems for FA in early stages of design, wherein
system failures are identified as failure to achieve one or
more predefined functions. Function may be defined as the
goal of what must be achieved, without specifying how it is
achieved (Eubanks et al. 1996). In this context, a functional
model of a system is simply a graphical representation of
the system functionality (Otto and Wood 2001), irrespec-
tive of any associated structural and behavioral details.
Functional modeling involves the decomposition of the
overall function of the given system into small and easily
solved sub-functions (Tumer and Stone 2003). For doing
this, like in any modeling environment, standardized
modeling constructs are required, which can be effectively
used in representing various functions and sub-functions.
Owing to this fact, a lot of research effort has been directed
toward the development of a generic functional basis for
functional modeling. See for example (Pahl and Beitz
1988; Koch et al. 1994; Otto and Wood 1997; Kirschman
and Fadel 1998; Stone and Wood 2000; Stone et al. 2000;
and Hirtz et al. 2002). A functional basis is a standard set of
functions and flows capable of describing the design space
(Tumer and Stone 2003).
The use of functional modeling in a direct FMEA like
application can be seen in conceptual failure modes anal-
ysis (CFMA) introduced by Hari and Weiss (1999). In
CFMA, the principles of FMEA are modified so as to make
it applicable in the conceptual design stage. Essentially, the
method can be considered as FMEA of system functions
rather than components. This FMEA is conducted on a
function tree representation of the system. Although this
method gives the additional advantage of conducting an
FMEA even in the absence of detailed design knowledge, it
still inherits the weakness of traditional FMEA in working
only with previously known failures.
Among functional modeling approaches that have been
successfully applied in numerous applications are the
‘‘Goal Tree-Success Tree’’ (GTST) modeling (Modarres
and Cadman 1986) and Multilevel Flow Modeling (MFM)
(Lind 1990). GTST is a functional decomposition frame-
work that has been used widely in modeling complex
physical systems. The framework has been successfully
used to model a number of specific physical systems for
various applications. A detailed discussion about this
method and its applications is given in (Modarres 1999).
The MFM is basically functional modeling from a process
point of view. Functions are realized by flow of mass,
energy, and information. The system is described by trac-
ing ‘‘flows’’ within the system. The modeling constructs
used in MFM make it highly suitable for diagnosis algo-
rithms like alarm analysis. Since its introduction in 1990,
Larsson has contributed several new algorithms and
implementations of MFM (Larsson 1992, 1994, 1996).
However, the first successful application of MFM in failure
mode analysis was demonstrated by Ohman (1999). Basi-
cally motivated by the alarm analysis algorithm (Larsson
1992), the author augments various condition relations and
storages in the MFM model with timing information.
Hence, apart from a list of failure modes generated as
output of the model, predicted time to failure values is also
provided. Nevertheless, since the basic modeling theme
still revolves around pre-specified goals and functions, the
capability to capture any type of unexpected system
interaction failure is not present.
Among FA methodologies using functional representa-
tions, the most noted is the function-failure design method
(FFDM) (Stone et al. 2005). It enables identification of
failure modes in the conceptual design stage by using
functional models of product designs. It is based on the
assumption that similar failure modes are manifested in
products having similar functionality. The most promising
feature of FFDM is realized as its capability to guide
designers in making component selections on the basis of
an analysis of potential functional failures. Moreover, the
methodology employs simple matrix manipulations that
can be easily understood and handled. However, the overall
approach is still dependent on the availability of historical
knowledge of past failure modes and there is no mecha-
nism for addressing causality of system interactions.
Apart from those FA approaches that are generically
applicable across all disciplines of engineering, some
domain-specific approaches have also been proposed for
the design stage. For example, the FLAME system
(Hunt et al. 1995; Price 1996) is a notable effort toward
Res Eng Design (2012) 23:105–124 107
123
automating the FMEA process for electrical designs. In
FLAME, standard components from a component database
are embedded into a functional model, which is then sim-
ulated to extract failure modes corresponding to compo-
nents. AutoSteve (Price 1997) is an improvement over the
FLAME system, wherein a software linkup with an
appropriate CAD platform enables easy design and analysis
of electrical circuits. In the mechanical engineering
domain, Hughes et al. (1999) have also attempted the
automation of FMEA for mechanical systems by algorith-
mically developing functional models from the geometry
and assembly information already present in existing CAD/
CAM models. The resulting functional models (which are
basically network-like representations of components) are
simulated to record system response on the failure of one or
more components. It can be observed that the domain-
specific approaches discussed here; apart from having the
drawback of limited applicability, are also constrained to
component-specific failures.
One difficulty that arises in functional modeling is
related to the fact that different functional models exist at
different levels of abstraction (Gietka et al. 2002). In
general, a modeling scenario might require knowledge
representation at multiple levels of abstraction. In such
cases, the use of any one specific functional modeling
technique might be insufficient. Another problem that has
often been associated with functional modeling is the lack
of a generic ontology of functional descriptors. Increasing
complexity of products over the years has introduced
technological blends that derive functionalities from mul-
tiple disciplines of science and engineering. A common
ontology/functional language that can be used to model all
flows and functions related with all fields of science does
not exist as of yet.
To make FA more rigorous in the design stage,
researchers are currently focusing on approaches that are
capable of effectively utilizing every bit of the limited
information available at this stage. According to Eubanks
et al. (1997), behavior modeling provides a more robust
basis for performing FA during early stages of the product
development process. This is because a behavior model
provides more information about the system compared to
its functional model. Moreover, although the physical
elements or components of a given system might change as
the design evolves, the general behaviors remain the same
and can be defined in the early stages itself.
The definition of behavior normally follows the notion
of ‘‘how (an) expected result is attained’’ (Keuneke 1991)
or the ‘‘detailed description of internal physical actions
based on physical principles and phenomena’’ (Welch and
Dixon 1994). Lind (1990) describes function as useful
behavior. However, using these definitions, the distinction
between function and behavior blurs very quickly during
the process of functional analysis (Eubanks et al. 1996).
Researchers have developed more rigorous definitions and
methods for describing the behavior of devices from the
aspect of causal process descriptions of devices (Iwasaki
and Chandrasekaran 1992) and causal ordering based on
process models (Iwasaki and Simon 1994). Eubanks et al.
(1996) define behavior as a sequence of stage changes, a
transition from one state to another, i.e., initial state ?behavior ? final state. According to them, the general
distinction between models for function and behavior is the
latter’s use of pre- and post-conditions, i.e., what condi-
tions must be true in order for the behavior to take place
and what conditions exist given that the behavior has taken
place. In behavior modeling, a device or system is repre-
sented as a behavioral hierarchy by decomposing behavior
into sub-behaviors and so on and behaviors are represented
as sequences of state changes.
There have been several serious attempts toward the
development of standard frameworks for behavior as well
as functional modeling. Well known among these include
the function–behavior–structure (FBS) framework (Gero
1990) and the FBRL behavior and function representation
language (Sasajima et al. 1996). These approaches have
presented a common platform for the analysis and com-
parison of various knowledge representation models. In
this line of work, the functional representation scheme
developed by Hata et al. (2000) is a commendable effort as
a direct application to product failure reasoning. In the field
of artificial intelligence, qualitative reasoning (refer: De
Kleer and Brown 1984; Forbus 1984) has been the main-
stay in behavioral as well as functional modeling of
physical entities. It essentially employs the knowledge
about the behavior of individual components and structure
(Umeda et al. 1990). Qualitative simulation or QSIM
(Kuipers 1986), which is the seminal work done by
Benjamin Kuipers, is one of the landmark contributions in
this direction. QSIM involves first, the generation of the
model of a given mechanism (which is essentially a qual-
itative abstraction of an ordinary differential equation), and
then the prediction of the possible qualitative behaviors of
the mechanism (Kuipers 1987). Since its inception, QSIM
has been used in a variety of applications. For example,
system monitoring (Dvorak and Kuipers 1991), fault
diagnosis (Umeda et al. 1995), modeling, and simulation
(Franke and Dvorak 1989; Crawford et al. 1990).
Advanced FMEA (AFMEA) (Eubanks et al. 1997) is a
direct application of behavior modeling to FA in design
stage that demonstrates the capability of capturing a
broader set of failures compared to traditional FMEA.
However, AFMEA relies on the personal expertise of
individual designers rather than an expert system (Stone
et al. 2005). Teoh and Case (2005) in their FMEA gener-
ation method (FMAG) combine the principles of behavior
108 Res Eng Design (2012) 23:105–124
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modeling with a simple functional representation of sys-
tems called as functional diagram to enable FMEA gen-
eration in the conceptual design stage. The functional
diagram is a network-like representation of system com-
ponents with interconnecting directed arcs depicting func-
tional flows. The functional diagram is simulated by
affecting changes in component states. In turn, failure
causes and effects are defined by failed component states in
the functional diagram. Although causal reasoning is used
to identify failures, yet, its implementation does not allow
capturing interaction failures. Moreover, failure reasoning
is also component-centric since it is derived from a limited
set of component behavior states.
Among more recent efforts in conceptual stage FA, the
functional failure identification and propagation (FFIP)
analysis (Kurtoglu and Tumer 2008) merits special atten-
tion. It employs a combination of functional, structural, as
well as behavioral modeling. Failure reasoning is done
using function-failure logic (FFL) reasoner, which is a
rule-based algorithm that checks the status of system
functions (whether fully functional, degraded, or com-
pletely lost) at each time step when it is provided with an
input comprising of the physical state of the system. The
FFIP enables capturing of system interaction failure modes
through a mapping between components and functions
based on mode transitions and behavioral changes that
occur due to failures. Hence, it provides the additional
advantage of identifying functional failures that do not
result from direct component failures. The FFIP framework
is further extended by Jensen et al. (2009) to incorporate
the failure mechanisms arising due to unanticipated
energy–material–signal flows within the system through
the introduction of a Flow State Logic (FSL). Kurtoglu
et al. (2010) further enhanced the role of the function-
failure logic (FFL) module of the FFIP framework by
incorporating the impact of functional failures on the
overall system. An impact rating obtained as the output of
this module is then used to obtain an assessment of risk
reduction by evaluating alternative system architectures.
Another recent contribution to the field of design stage
failure analysis is the work done by Henning and Paasch
(2010). Although their framework does not directly address
the extraction of various types of possible failure modes
from an early design stage system model, it is a significant
addition in the field of fault diagnosis. Specifically, their
work emphasizes on measuring system diagnosability in
early design stage.
Among the FA techniques applicable in early design
stages reviewed by us, large scope for improvement was
found toward the development of a common basis for
reasoning at component, functional, as well as interaction
failure levels simultaneously. Therefore, in order to
incorporate better capability in capturing system inter-
action failures, a cognitive map-based approach is pro-
posed in this paper that shows significant deviation from
existing approaches. Since system interaction failures
arise due to causal interactions of components, interfaces,
and the environment in general, a cognitive map-like
causal reasoning approach is deemed suitable for devel-
oping a framework for comprehensively capturing all
types of failures in the design stage itself. To facilitate
better understanding of the proposed framework, a brief
overview of cognitive maps is presented in the next
subsection.
2.2 Cognitive maps: a brief overview
Cognitive maps were introduced by the political scientist
Robert Axelrod (1976) in the 1970s as a means of mod-
eling decision making in social and political systems
(Pelaez and Bowles 1996). A cognitive map is essentially a
signed digraph consisting of nodes (representing concept
variables) and directed arcs (representing causal relation-
ships). In its simplest form as introduced by Axelrod, it
consists of concept variables interconnected with causal
arcs labeled with either a ‘‘?’’ or a ‘‘-’’ sign. Figure 1
shows an example of such a cognitive map that models the
relationship between working conditions in a factory and
the profits accrued.
The ‘‘?’’ or ‘‘-’’ sign on an arc connecting two concept
variables indicates positive or negative correlation between
them, respectively. However, due to the simplistic nature of
the type of cognitive map mentioned above, apart from
giving a graphic representation of causality, it is of not
Quality of working conditions
+ +
+
+-
-Job Satisfaction
Sincerity of workers
Job quality
Wastage
Profits
Fig. 1 Example of a simple
cognitive map
Res Eng Design (2012) 23:105–124 109
123
much use in modeling real-world scenarios. Moreover, due
to lack of any form of quantification, it is difficult to derive
any useful inference.
The first appearance of an appropriate quantification in
cognitive maps was through fuzzy cognitive maps (FCMs)
proposed by Bart Kosko (1986). Apart from having a ‘‘?’’
or ‘‘-’’ sign showing the type of causality, the arcs in
Kosko’s FCMs also carry weights (usually in the interval
[0, 1]) expressing the strength of causality. A numerical
quantity is associated with each node in an FCM, repre-
senting the state/level of that node. Interestingly, quite
contrary to what the term ‘‘Fuzzy,’’ in the name ‘‘Fuzzy
cognitive map’’ suggests, an FCM has no relationship with
fuzziness or fuzzy logic in the traditional sense.
An FCM is simulated in discrete/continuous time (as the
case may be), during which the weights on the arcs remain
constant, but the concept values change. During simulation,
the updated value of any given concept is evaluated by
passing the weighted sum of all concept values that are
input to the given concept node, through an appropriate
threshold function. For more clarity, let us take an example
of a concept node (of a discrete time FCM) with value (Cj)t
at time step t with n number of input nodes having values
(Ci)t (where i = 1 to n). Let wij be the respective weights on
the arcs. Then, at the end of time step t, the updated value
of the jth node will be given by Eq. 1.
ðCjÞtþ1 ¼ TXn
i¼1
ðCiÞt � wij
� � !
ð1Þ
Here, T �ð Þ is an appropriate threshold function. The
purpose of a threshold function is to constrain the values of
concept nodes within a certain interval (usually [0, 1] or
[-1, ?1]). Equation 1 represents the traditional node
updating process in FCMs. Stylios et al. (1997) use a
modified node updating process for cognitive maps in
modeling systems. This modification, as given in Eq. 2,
updates each node by including their previous value too.
ðCjÞtþ1 ¼ TXn
i¼1
ðCiÞt � wij
� �þ ðCjÞt
!ð2Þ
Hence, FCMs using Eq. 2 for updating nodes have one
time-step memory capability.
FCM simulation can be depicted using simple matrix
multiplications as given by Eq. 3.
Ctþ1 ¼ T ½ðCt � EÞ þ Ct� ð3Þ
Here, Ct is a 1 9 n matrix containing the node values
(Ci)t at any given time step t; E is an n 9 n matrix (called
the adjacency or connection matrix) that contains all the
weights stored in the arcs of a cognitive map having
n number of nodes, and T ½�� is the threshold operation on
matrices.
FCMs that were initially in common use were either
bivalent or trivalent in nature. An FCM is called bivalent if
the concept nodes take values from the set {0, 1} and
trivalent if concepts take values from the set {-1, 0, ?1}.
The type of values taken by concepts in an FCM is dictated
by the threshold function used. Equations 4 and 5 give the
threshold functions that result in the formation of bivalent
and trivalent FCMs, respectively.
TðxÞ ¼ 0 if x� s1 if x [ s
� �ð4Þ
TðxÞ ¼�1 if x� s1
0 if s1\x\s2
1 if x� s2
8<
:
9=
; ð5Þ
where s, s1, and s2 are pre-specified threshold values.
Bivalent and trivalent FCMs have the limitation that
they can be used to represent an increase or decrease in
concept values (also a stable or neutral condition in the
case of trivalent FCMs). They cannot represent the degree
of an increase or decrease that has occurred. For a more
realistic representation of real-world applications involving
non-linearity, the more recent, continuous FCMs are better.
These FCMs make use of continuous non-linear transfor-
mation/threshold functions, thus enabling the concepts to
take values from a real interval (usually [0, 1] or [-1, ?1]).
Most commonly used among these are the sigmoid
(logistic) and tanh (hyperbolic tangent) threshold functions
that are given in Eqs. 6 and 7, respectively.
TðxÞ ¼ 1
1þ e�axð Þ ð6Þ
TðxÞ ¼ ex � e�xð Þex þ e�xð Þ ð7Þ
2.2.1 Final inference in cognitive maps
The inference procedure of a cognitive map is the meth-
odology or algorithm applied to it in order to derive a
meaningful inference through simulation. The inference
procedure details out, or in other words, sets the rules of
interaction among the nodes and arcs. However, the final
inference for cognitive maps is obtained in the form of one
of the following conditions:
1. A unique solution This is a condition where the states
of all concept variables remain unchanged for succes-
sive iterations. In the absence of any feedback loop in
the cognitive map, the simulation terminates after the
first iteration. In such cases, the cognitive map is said
to be trivial (Miao and Liu 2000).
2. A limit cycle In this condition, a particular set of
concept states’ configuration keeps on repeating
indefinitely with successive iterations.
110 Res Eng Design (2012) 23:105–124
123
3. Chaos In this condition, the iterations will go on
indefinitely, giving neither a final terminating solution
nor any repeating configuration of concept states. The
subsequent result of iterations is always a different set
of values for the concepts.
In the present section, only the traditional cognitive
maps and their inferencing mechanisms were discussed.
However, since their introduction in the 1970s, there have
been a lot of new developments in cognitive maps to
address its various shortcomings in modeling real-world
systems. For a more detailed discussion on various types of
cognitive maps and their reasoning processes, the reader is
advised to refer (Pena et al. 2008).
2.2.2 Cognitive maps in failure analysis
Since the occurrence of failure in any form is in itself
causal in nature, the application of cognitive maps to
failure analysis seems quite appealing. However, surpris-
ingly, direct applications of cognitive maps in failure
analysis are extremely scarce in the literature. One nota-
ble contribution was made by Pelaez (1994) in system
modeling with FCMs for performing FMEA. The con-
cepts/nodes of FCMs used in this work depict various
failure modes and their effects. The arcs carry three
entities: (i) A sign indicating the direction of causality,
(ii) A linguistic label indicating the confidence level of
causality, and (iii) A numeric weight indicating the
strength of causality. Min–max inference approach is used
to evaluate the net causal effect on any given node.
However, simulating this FCM gives information only on
how much (i.e., of what strength) effect is produced by
the activation of some given failure mode. Moreover,
knowledge of all possible failure modes and their mutual
effects is a prerequisite to begin simulation since the
nodes in the cognitive map are all failure modes
themselves.
3 Framework for cognitive map-based system modeling
for an effective FA
In this section, the guidelines for developing a structured
expert system framework for semiautomatic construction
of cognitive map models of physical systems are given.
The resulting cognitive maps within the proposed
framework are aimed at generating a much broader set of
failure modes in early stages of product development
compared to other existing approaches. However, the
main focus is on enabling a capability to capture inter-
action failure modes.
3.1 Premises of the proposed framework
Before detailing out the framework itself, it is necessary to
understand the premises on which the framework has been
developed. These premises are postulated as follows:
1. For a comprehensive description of any physical
system; structural, functional, and behavioral knowl-
edge regarding the following is sufficient: (a) its
constituent components; (b) the interfaces formed by
those components in assembly with one another; and
(c) the environment within which the system interacts
(including human interaction).
2. All possible system interactions related with its
descriptors (mentioned in the first postulate) can be
represented to any desired degree of detail, in the form
of a cognitive map consisting of a set of methodically
chosen system variables and their causal
interdependencies.
3. It is possible to trace all kinds of failures (including
system interaction failures) through cognitive map
simulation by identifying system variables showing
large excesses or deficiencies and mapping them back
to well-defined system functions and structural
features.
3.2 Constructing a cognitive map model of a physical
system
Based on the premises postulated in the previous section,
the basic aim of the proposed framework is the construc-
tion of cognitive map models of physical systems in such a
way that they embody at any given level of abstraction, all
available information regarding the system’s structure,
functions, and interactions. Figure 2 presents an overview
of the proposed framework that is used for achieving the
above-mentioned aim. Next, in a stepwise manner, the
details of the framework are discussed. An electric water
heater example has been taken to elaborate the complete
procedure involved. A simple diagrammatic depiction of
this common household appliance itself is given in Fig. 3.
However, for reducing complexity in order to enhance
clarity and understandability, only some limited aspects of
the device’s structure and functionality have been
considered.
3.2.1 Constructing a structural model of the physical
system
Depending on the stage of product development at which
FA is done, the type and amount of data and information
Res Eng Design (2012) 23:105–124 111
123
regarding the structure of a physical system varies a lot.
For example, at the conceptual design stage, detailed
information regarding various design parameters and
component geometry is not available. On the other hand, in
the detailed design stage, even completely developed CAD
models or detailed bill of materials with complete speci-
fications of the system might be available. However, in
order to be compatible with the proposed framework, ini-
tially available structural data need to be parsed and reor-
ganized into a simple structural model that simply depicts
the components along with the interfaces they form with
each other. Part details even if available, are not used. The
resulting structural model is a network-like representation
of the system with nodes depicting constituent components
and undirected arcs connecting the nodes with each other
depicting the existence of interfaces. An example of this
type of structural modeling is given in Fig. 4, which
depicts four main components of an electric water heater in
interface with water contained in it.
There exist other well-established techniques for struc-
tural modeling like Configuration Flow Graphs (CFG)
developed by Kurtoglu and Tumer (2008), which repre-
sents the components of the system interconnected with
each other through flows of material, energy, and signals.
Essentially, CFG implements a mapping from a pre-spec-
ified functional model of the system to the structural
domain. However, the main motivation behind adopting a
much simpler modeling scheme in the present work (as
exemplified in Fig. 4) is to enable scope for automatic
model extraction from existing data (CAD models, bill of
materials.), which would clearly prove difficult if more
complex schemes like CFG are used despite their better
representation capabilities.
It is proposed to build a database of standard compo-
nents (as a part of a knowledge repository), which will be
constantly updated with new component terms/names as
and when the expert system is fed with input structural
data. This can even help in the automatic construction of
structural models from CAD data (if available) by devel-
oping and incorporating appropriate CAD model parsing
Structural model
Functional diagram
CMFs CMFdatabase
Function unit database
Standard component database
Final cognitive map
Input structural data
USER
Standard functional basis
Materialclassification tree
Physical phenomena classification tree
Interfaceclassification tree
EXPERT SYSTEMFig. 2 An overview of the
proposed framework
Dip Tube
Shutoff Valve
Cold Water Inlet
Hot Water Outlet
Temperature/Pressure Relief Valve
Anode Rod
Outer CaseThermostat
Electric Heating Elements
Drain Valve
Insulation
Overflow Pipe
Steel Tank
Fig. 3 Schematic diagram of an electric water heater
Steel tank
T/P relief valve
Heating element
Anode rod
Water
Fig. 4 Structural model of electric water heater
112 Res Eng Design (2012) 23:105–124
123
algorithms. Work in this direction already exists; for
example, Hughes et al. (1999) present an algorithm for
automatically extracting a list of components and their
assembly relations from CAD models of mechanical
devices. The input–output interfacing with the expert sys-
tem for the generation of structural models can be observed
from Fig. 2.
3.2.2 Conversion of the structural model to a functional
model
The procedure explained in the previous section was
intended at incorporating all available structural data into a
simple structural model. The next step involves the
superimposition of functional relations on to the developed
structural model. This is done by replacing each undirected
arc of the structural model with one or more directed arcs
carrying standard expressions describing the functional
flow/transfer occurring at the respective interfaces. As
already discussed, significant research contribution has
been made toward developing a generic functional basis of
standard functional terms that can be used for expressing
functional flows in functional modeling. However, there
are basically two possible ways of expressing a functional
relationship between any given two components. One way
is to express the function as the design intent being fulfilled
between the two components and the other way is to
express it as the actual physical phenomenon taking place
at the interface. For example, the design intent being ful-
filled by bringing a T/P valve in contact with water in a
water heater is to control the temperature and pressure of
water. Whereas the actual physical phenomenon taking
place at the interface of a T/P valve and water is that water
heats and pressurizes the T/P valve. No matter which way
the functional relationship is expressed, a standard onto-
logical functional basis can be used commonly without any
ambiguity.
Functional modeling in the present work builds and
improves upon functional diagrams used by Teoh and Case
(2005). A functional diagram (as its name might imply) is
not essentially the same as functional models in general. A
functional model in its generic form is a graphical repre-
sentation of product (or component) functionality alone
(Otto and Wood 2001) and does not include any repre-
sentation whatsoever of the product’s (or component’s)
structural aspects. A functional diagram on the other hand
accounts for both functionality as well as the structure of
the concerned product, sub-system or component. A
functional diagram can be considered as being composed
of several interconnected function units. An isolated
function unit as shown in Fig. 5 is an expression of a
standard functional descriptor between two components.
The direction of the arrow is from the function executing
operator to the operand. In any given functional diagram,
the number of function units is equal to the number of arcs.
In the present work, we make provision for expressing a
function in both its aspects (as discussed above) in a
function unit by allowing it to carry two arcs (one dotted
and another solid). The solid arc is used to express function
in its physical phenomenon aspect and the dotted one to
express it in its design intent aspect. A single solid arc is
used in those cases where both physical phenomenon and
design intent are expressible with a single functional term.
As will be explained in the next section, the solid arcs are
the ones that participate in the ultimate generation of the
final cognitive map. The dotted arcs (depicting the design
intent) will be used in failure mode identification and
documentation. In other words, when a failure mode is
reported, it will be reported as a failure to fulfill a particular
design intent. As will be explained later, the use of physical
phenomenon as a basis for cognitive map generation helps
a lot in automating the process. Figure 6 shows the func-
tional diagram built for the structural model of Fig. 4 using
the modified function representation scheme.
Further, it is proposed to maintain a database of standard
function units, wherein each function unit would be char-
acterized using a coding system named as seven part
coding system, whose structure is shown in Fig. 7. Each
block in the coding system derives a unique code from a
knowledge repository depending upon the function unit’s
specification corresponding to that block.
In order to develop a knowledge repository that contains
codes for all these seven specifications used for defining a
function unit, it is proposed to archive information
regarding them in the form of the following databases and
classification trees:
(a) Database-1 A database of standard components. Each
standard component in the database will have a code
that will be used for allocation to the first two places/
blocks of the 7 part function unit code.
(b) Database-2 A generic functional basis containing
standard functional terms. Each functional term in the
functional basis will have a code that will be used for
allocation to the fifth place/block of the 7 part
function unit code.
(c) Classification Tree-1 A detailed classification of
states of matter and materials of components.
Figure 8 gives an example of this type of classifica-
tion. Each node in the tree is proposed to have a code
that will be used for allocation to the third and fourth
places/blocks of the 7 part function unit code.
Function Unit: Operator Operand Function
Fig. 5 A typical function unit
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123
(d) Classification Tree-2 A detailed classification of
known physical phenomena in nature. Figure 9 gives
an example of this type of classification. Each node in
the tree is proposed to have a code that will be used
for allocation to the sixth place/block of the 7 part
function unit code.
(e) Classification Tree-3 A detailed classification of
various types of interfaces formed by physical
Water
T/P relief valve
Steel tank Heating element
Anode rod
1. Heats
2. Dissolves [in]3. Pressu
rizes
4. Heats
3. Controls [pressu
re]4. Contro
ls [temp.]
5. Pressurizes
5. Contains
Fig. 6 Functional diagram for
the water heater example
Operator Name
Operand Name
Operator Material
Operand Material
Function Name
Physical Phenomenon
Interface Type
Fig. 7 Structure of the
proposed 7 part coding system
for function units
Materials
Solids Fluids Gas
Metals
Biomaterials
Semiconductors
Composites
Organic solids
Glass ceramics
Ceramics
Minerals
Wood
Polymer
Water
Oils
Emulsions
Foam
Gel
Mineral oil
Organic oil
Synthetic oil
Hydrogels
Organogels
Xerogels
Etc.
Etc.
Fig. 8 A sample classification
tree of materials/states of matter
Physical phenomena
Heat transfer Magnetism Electricity Etc. Strength of materials
Conduction
Convection
Radiation
Fig. 9 A sample classification tree
of various physical phenomena
114 Res Eng Design (2012) 23:105–124
123
components. Figure 10 gives an example of this type
of classification. Each node in the tree is proposed to
have a code that will be used for allocation to the
seventh place/block of the 7 part function unit code.
Extensive work has been done toward the develop-
ment of knowledge databases for design in the past
couple of decades. The highlight of research in this
direction has been the development of functional basis
for functional modeling (as discussed in Sect. 2.1). More
sophisticated representations, databases, and knowledge
management frameworks that adopt a different perspec-
tive than a purely functional modeling approach have
also been proposed (See for example: Welch and Dixon
1994; Schmidt and Cagan 1995; Campbell et al. 1999;
and Kurtoglu et al. 2005). However, the most com-
mendable research contribution of all times toward the
development of a design repository is the ongoing pro-
ject at the National Institute of Standards and Technol-
ogy (NIST)—USA (Szykman et al. 1999). In contrast
with traditional design databases that merely provide
access to schematics, CAD models, and documentation; a
design repository presents ‘‘an intelligent knowledge-
based design artifact modeling system that can be used to
facilitate the representation, capture, sharing, and reuse
of corporate design knowledge’’ (Szykman et al. 2000).
As a part of future research, it is intended to explore the
feasibility of enabling the extraction of knowledge frag-
ments relevant to the present research (databases and
classification trees discussed above) from a well-estab-
lished design repository.
The proposed expert system would interactively collect
information from the user to codify each function unit in
accordance with the seven part coding scheme. By using
this coding scheme for characterizing function units, we are
essentially associating quite a lot of important information
with each function unit that is stored in the database. This
enhances the uniqueness of each function unit, and as will
be explained in the next section, it also facilitates the
automatic construction of the final cognitive map of the
system from the functional diagram.
3.2.3 Construction of cognitive map fragments
Once the functional diagram is ready, each function unit
taken one at a time and a cognitive map fragment (CMF) is
developed for it. Contrary to what the name suggests, a
CMF is in fact a full cognitive map that consists of design/
concept variables and their causal interdependencies in
such a way so as to sufficiently provide information and
reasoning related to its associated function unit. Since a
function unit is composed of two components and a func-
tional term (physical phenomenon), the cognitive map
fragment for it essentially contains design variables related
with those two components and the physical phenomenon
taking place at their interface. The total number of CMFs
required to be developed for the whole functional diagram
of the system is equal to the number of function units,
which in turn is equal to the number of solid arcs in the
functional diagram.
For facilitating standardization and reusability, it is
proposed to express the variables used in the cognitive
maps in a standard format, which can be given as follows:
Attribute__preposition_Target. Each variable would
consist of two parts. The first part being some attribute that
is being described for the second part that is the target. The
two parts are joined by the use of an appropriate preposi-
tion (e.g., OF, AT, BETWEEN.). As an example, one
variable used for the water heater is as follows:
Hardness__OF_Water.
Given a function unit, the first step toward constructing
a CMF is to identify one or more suitable function-quan-
tifiers for the function unit. A function quantifier is a var-
iable that quantifies the quality of the functional interaction
represented by the function unit. For example, one suitable
function quantifier for the first function unit in the func-
tional diagram of Fig. 6 (labeled on the arc as 1) is:
Temperature__OF_Water. The rationale behind using
function quantifiers is that large excesses or deficiencies (as
the case may be) in function quantifiers can be directly
treated as an indication of failure of the associated func-
tion. Moreover, function quantifiers provide a basis for
Type of interface
Static Dynamic Intermittent dynamic
Surface contact
Line contact
No contact (Constant distance)
Etc.
Surface contact
Line contact
No contact (Relative motion)
Etc.
Fig. 10 A sample classification
tree of various types of
interfaces
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123
quantifying and monitoring the degradation of functional
flows in systems.
Once function quantifiers are in place, the next step is to
identify all other variables related with the function unit
that causally affect the function quantifiers. Apart from
these basic guidelines, it is difficult to outline a detailed
methodology for constructing CMFs. This is because
domain-specific expert knowledge has to be used to build
CMFs for different function units, and the opinion and
understanding with regards to a given functional interac-
tion may vary from one expert to another. The CMFs
developed for the five function units from Fig. 6 are given
in Figs. 11, 12, 13, 14, 15 in their respective numerical
order. Inset at the top portion of each of these figures is the
corresponding function unit (shown within a rectangle).
These CMFs were developed after consulting respective
domain experts from the academia as well as industry.
Note that function quantifiers in each CMF are depicted as
shaded nodes.
Although the construction of CMFs requires the inter-
vention of experts, it is possible to develop and maintain a
Temp. OF Water
Heat transfer co-eff. AT Heating element (surface)
Scale thickness ON Heating element
Hardness OF water
Temp. OFHeating element
Water Heating element1. Heats
Fig. 11 CMF for function
unit 1
Hardness OF water
Volume OFMg. anode rod
Water Anode rod2. Dissolves [in]
Fig. 12 CMF for function unit 2
Pressure OF water
Temp. OF Water
Heat transfer co-eff. AT Heating element (surface)
Scale thickness ON Heating element
Hardness OF water
Temp. OFHeating element
Pressure threshold OF T/P valve
Scale thickness ON T/P valve seat
WaterT/P relief valve3. Pressurizes
3. Controls [pressure]
Fig. 13 CMF for function
unit 3
116 Res Eng Design (2012) 23:105–124
123
database of CMFs that have already been generated by
experts. New CMFs as and when generated by the experts
will be added to the database. Each CMF in the database
would be associated with a code number given by the
function unit. When the user finalizes the details of a
function unit, a seven part code would be generated for
that function unit (as explained in the coding scheme for
function units in the previous subsection). The output
would be the autosuggestion of CMFs corresponding to
that code (if there exists any) from the CMF database.
Flexibility to changes, improvements, and new additions
can also be allowed for these CMFs. The user would have
the freedom to edit the CMFs (by adding or deleting
variables). The user can even generate a whole new CMF
for a function unit if the existing CMFs corresponding to it
from the database are found unsatisfactory. New CMFs
generated by the user would also be saved along with the
others in the database for further suggestion/use.
Temp. OF Water
Heat transfer co-eff. AT Heating element (surface)
Scale thickness ON Heating element
Hardness OF water
Temp. OFHeating element
Temp. threshold OF T/P valve
Scale thickness ON Temp. sensor
WaterT/P relief valve4. Heats
4. Controls [temp.]
Fig. 14 CMF for function
unit 4
Pressure OF water
Temp. OF Water
Heat transfer co-eff. AT Heating element (surface)
Scale thickness ON Heating element
Hardness OF water
Temp. OFHeating element
Strength OF Steel tank
Volume OF Steel (uncorroded)
Volume OFMg. anode rod
Water Steel tank5. Contains
5. Pressurizes
Fig. 15 CMF for function unit 5
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123
3.2.4 Semiautomation in the construction of CMFs
Earlier in Sect. 3.2.2, it was mentioned that the function-
ality in a function unit is mainly expressed by the actual
physical phenomenon taking place at the interface and not
the design intent. Hence, the actual physical phenomenon
is expressed on a solid arc and the design intent is
expressed on a dotted arc. During our experiments with
different artifacts found in day-to-day life, it was found that
expressing the functionality as mentioned above provides
an additional benefit toward semiautomation in the con-
struction of CMFs. This semiautomation is achieved by
following a simple thumb rule: ‘‘If the tail end of a function
unit happens to be connected to the head portion of another
function unit in any given functional diagram, then the
CMF of the latter would almost certainly be a part of CMF
of the former.’’ Although this is found to be the case in
most of the instances, it is not necessarily true in every
case. From Fig. 6, it is clear that the following function
unit pairs are candidates for the application of the above
thumb rule: 1–3, 1–4, 1–5, 2–3, 2–4, and 2–5. From
Figs. 11, 12, 13, 14, 15, it is clear that the thumb rule was
followed in the case of the pairs: 1–3, 1–4, 1–5, and 2–5,
but not in the case of 2–3 and 2–4. For example, take the
case of the function unit pair 1–3 in Fig. 6, it can be seen
that the tail end of function unit 3, i.e., the block repre-
senting water, is the same as the head portion of function
unit 1. Now, it can be observed from Figs. 11 and 13 that
the CMF of function unit 1 (Fig. 11) is clearly a part of
CMF of function unit 3 (Fig. 13).
The expert system will always suggest a CMF solution
by following the thumb rule whenever a suitable candidate
pair for its application is identified. The CMF of the trailing
function unit (from among the pair) would automatically be
attached to one of the function quantifiers (preferably the
one with no outgoing arcs) of the leading function unit.
However, if not found suitable, the user can modify the
CMF that is autosuggested by the expert system. The
modification can either be an outright rejection of the CFM
of the trailing function unit or its realignment to some other
variable of the leading function unit.
3.2.5 Aggregating the CMFs into the final cognitive map
Once CMFs are finalized for all the function units of the
functional diagram of a given physical system, they can be
automatically aggregated into the final cognitive map (CM)
structure by using the simple union operation on clearly
specified variables and arcs.
Let CMFm (m = 1 to N) represent a CMF, where N is the
total number of CMFs generated.
Let nm be the number of variables/nodes in the mth
CMF.
Let km be the number of arcs in the mth CMF.
Let Vm = {vi|i = 1 to nm} represent the set of all vari-
ables/nodes (vi) in the mth CMF.
Let Am = {aj|j = 1 to km} represent the set of all arcs (aj)
in the mth CMF.
Then, the final cognitive map structure is given by
Eq. 8.
CM ¼[N
m¼1
Vm
(c) Simulate the FCM with a starting input vector to
identify function quantifiers indicating failures in the
form of large excesses (for smaller the better and
nominal the best types) or deficiencies (for larger the
better and nominal the best types).
(d) Map the failure indicating function quantifiers back to
their parent function units.
(e) Declare the functions expressed by the dotted arcs
(solid if dotted is absent) on the corresponding
function units to have failed in the FMEA report.
4.2 FCM implementation and simulation
The same experts who helped in developing the CMFs
(Figs. 11, 12, 13, 14, 15) were consulted for populating
the arcs of the final cognitive map (Fig. 16) with numer-
ical weights. The Delphi method (Clayton 1997) was used
to reach a final consensus on the weights. Initially, each
expert was given a blank adjacency matrix format to be
filled with the weights that in their opinion best described
the strength of the causal relation corresponding to each
cell. Moreover, each of them was asked to freely comment
on the decisions taken by them. Next, the experts were
given statistical details like mean, median of the out-
comes. Even the filled out adjacency matrix formats as
well as comments made by each of them were made
commonly accessible (although maintaining anonymity of
identity). On the basis of all this information, a second
round of weights assessment was conducted and the
experts were asked to revise their previous assessments of
the weights. The outcomes of the second round indicated
that most of the weights (after revision by the experts) fell
within the interquartile range. This was taken as an indi-
cation of having reached a consensus. The final weights
were taken as the medians of the weight values from the
Pressure OF water
Temp. OF Water
Heat transfer co-eff. AT Heating element (surface)
Scale thickness ON Heating element
Hardness OF water
Temp. OFHeating element
Pressure threshold OF T/P valve
Strength OF Steel tank
Volume OF Steel (uncorroded)
Temp. threshold OF T/P valve
Volume OFMg. anode rod
Scale thickness ON Temp. sensor
Scale thickness ON T/P valve seat
Fig. 16 Final cognitive map for the electric water heater example
Table 1 Classification of the
function quantifiersS. No. Function quantifier Category Failure indication value
1. Volume of Mg. anode rod Larger the better -1
2. Temp. of heating element Nominal the best -1 or ?1
3. Strength of steel tank Larger the better -1
4. Pressure of water Smaller the better ?1
5. Temp. of water Nominal the best -1 or ?1
Res Eng Design (2012) 23:105–124 119
123
second round and were finally arranged in the form of an
adjacency matrix (E) (shown as the dark shaded portion of
Table 2).
It was decided to make use of the real interval [-1, ?1]
for the nodes so as to depict states having large defi-
ciencies with -1 and large excesses with ?1 (both states
being indicative of failure). To incorporate the effect of
degradation, the FCM node updating process with one
time-step memory as given by Eq. 2 was used. When
FCM variables take values from the interval [-1, ?1], it
is common to use the tanh threshold function. However, in
order to overcome the tendency of tanh functions to
reduce the values of the components of a state vector
(Bueno and Salmeron 2009), as well as to force simulation
results toward a limit state consisting of clearly identifi-
able failure states (-1 or ?1), we used a modified
threshold function wherein the tanh function is clamped at
the extremes of the interval [-1, ?1] to the ordinate
values of -1 and ?1, respectively. The modified threshold
function is given in Eq. 9.
TðxÞ ¼
�1 if x\� 1
e2kþ1ð Þe2k�1ð Þ �
ekx�e�kxð Þekxþe�kxð Þ if � 1� x� þ 1
þ1 if x\þ 1
8>><
>>:
9>>=
>>;ð9Þ
Here, k is a constant parameter that determines the
steepness of the tanh function. In the present study, the
value of k was set equal to 1.
Table 1 gives the classification of the function quanti-
fiers that appear in the final cognitive map (Fig. 16).
Simulation of the FCM was started with an input state
vector C0 as given in Table 2. A high value for the vari-
able: Hardness_OF_Water is set as the input scenario in
the configuration of vector C0. The rest of the variables
have been allocated either ideal or normal values. FCM
simulation is brought into effect through iterative matrix
multiplications in accordance with Eq. 3. For example, the
state vector obtained after the first iteration is given by: C1
= T [C0 x E ? C0]. The results of FCM simulation are
given in Table 2 itself. As can be seen, a limit state (unique
Table 2 Adjacency matrix (E) and simulation results
Node No. E 1 2 3 4 5 6 7 8 9 10 11 12 13
Hardness OF Water 1 0 0.8 0.8 0.8 -0.6 0 0 0 0 0 0 0 0
Scale thickness ON T/P valve seat 2 0 0 0 0 0 0.7 0 0 0 0 0 0 0
Scale thickness ON heating element 3 0 0 0 0 0 0 0 0 0 0.5 -1 0 0
Scale thickness ON Temp. sensor 4 0 0 0 0 0 0 0.7 0 0 0 0 0 0
Volume OF Mg. anode rod 5 0 0 0 0 0 0 0 0.4 0 0 0 0 0
Pressure threshold OF T/P valve 6 0 0 0 0 0 0 0 0 0 0 0 0 0.6
Temp. threshold OF T/P valve 7 0 0 0 0 0 0 0 0 0 0 0 0.6 0
Volume OF Steel (uncorroded) 8 0 0 0 0 0 0 0 0 0.4 0 0 0 0
Strength OF Steel tank 9 0 0 0 0 0 0 0 0 0 0 0 0 0.4
Temp. OF Heating element 10 0 0 0 0 0 0 0 0 0 0 0 0.9 0
Heat transfer co-eff. AT Heating element (surface) 11 0 0 0 0 0 0 0 0 0 0 0 0.7 0
Temp. OF Water 12 0 0 0 0 0 0 0 0 0 0 0 0 0.9
Pressure OF Water 13 0 0 0 0 0 0 0 0 0 0 0 0 0
(INPUT VECTOR) C0 0.8 0 0 0 1 0.4 0.4 1 1 0.5 1 0.5 0.5
Iteration No. 1 C1 0.8 0.74 0.74 0.74 0.63 0.5 0.5 1 1 0.61 1 1 1
Iteration No. 2 C2 0.8 1 1 1 0.19 1 1 1 1 0.99 0.59 1 1
Iteration No. 3 C3 0.8 1 1 1 -0.37 1 1 1 1 1 -0.15 1 1
Iteration No. 4 C4 0.8 1 1 1 -0.91 1 1 0.91 1 1 -0.91 1 1
Iteration No. 5 C5 0.8 1 1 1 -1 1 1 0.65 1 1 -1 1 1
Iteration No. 6 C6 0.8 1 1 1 -1 1 1 0.33 1 1 -1 1 1
Iteration No. 7 C7 0.8 1 1 1 -1 1 1 -0.1 1 1 -1 1 1
Iteration No. 8 C8 0.8 1 1 1 -1 1 1 -0.6 0.98 1 -1 1 1
Iteration No. 9 C9 0.8 1 1 1 -1 1 1 -1 0.82 1 -1 1 1
Iteration No. 10 C10 0.8 1 1 1 -1 1 1 -1 0.52 1 -1 1 1
Iteration No. 11 C11 0.8 1 1 1 -1 1 1 -1 0.16 1 -1 1 1
Iteration No. 12 C12 0.8 1 1 1 -1 1 1 -1 -0.3 1 -1 1 1
Iteration No. 13 C13 0.8 1 1 1 -1 1 1 -1 -0.8 1 -1 1 1
Iteration No. 14 C14 0.8 1 1 1 -1 1 1 -1 -1 1 -1 1 1
Iteration No. 15 C15 0.8 1 1 1 -1 1 1 -1 -1 1 -1 1 1
Iteration No. 16 C16 0.8 1 1 1 -1 1 1 -1 -1 1 -1 1 1
120 Res Eng Design (2012) 23:105–124
123
solution) was obtained at the end of fourteen iterations
(time steps), after which the node values did not change.
The progression of values of the function quantifiers
toward the final failure indicating state can be traced along
the light-shaded columns in Table 2.
4.3 Result interpretation and failure report generation
Simulation results as obtained in the previous section are
merely numerical entities (either -1 or ?1) indicated
against function quantifiers of the FCM. In this section, the
procedure for interpreting the simulation results for gen-
erating a meaningful failure report in the form of identified
failure modes is described.
As already discussed, a function quantifier is a numer-
ical representation of its associated function unit’s quality.
Hence, it is appropriate to map the failure indicated against
function quantifiers (through simulation) to their associated
function units. Therefore, a failure indicated against a
function quantifier essentially means the failure of the
associated function unit in appropriately achieving its sta-
ted functionality. Owing to the typical configuration of a
function unit (Fig. 5), it is easy to express it in the form of
a function statement. For example, the third function unit
from Fig. 6 can be expressed in words as: T/P valve con-
trols [pressure] or Water pressurizes T/P valve. In the
present work, a failure mapped to a function unit from its
function quantifier is reported as a negation of the function
statement corresponding to the function appearing on the
dotted arc of the function unit. This can be done by adding
the extension: ‘‘_failed’’ in front of the function statement.
Following the above-mentioned procedure, Table 3 gives
the final failure mode analysis report for the failure modes
interpreted from the mapping of failures indicated for
function quantifiers to their respective function units.
However, it must be noted that standalone expressions
of failure modes as discussed above can sometimes be
misleading. For example, consider the fifth function
quantifier and its associated function unit 1 (refer Fig. 6)
from Table 3. The final node value for the quantifier:
Temp. OF Water is ?1. This indicates that water temper-
ature has highly exceeded its desired value. However, the
corresponding failure mode is expressed as: Heating ele-
ment heats water_failed. This is a self-contradictory sce-
nario, wherein despite the heating element failing to heat
water, there is excess temperature of water. Thus, it
becomes necessary to further elaborate failure modes using
some extra reasoning. This reasoning can be derived from
the association of failure modes with the function quanti-
fiers and their final node values. Hence, the failure mode:
Heating element heats water_failed can be more appro-
priately described by adding the information that the failure
is actually in the form of overachievement of functionality
(final node value of the associated quantifier being ?1, i.e.,
excess). This extra information that completes the charac-
terization of failure modes is given in brackets along with
the failure mode expressions (see Table 3). The added
information can also be an expert’s opinion or interpreta-
tion of the identified failure modes.
5 Concluding discussions and scope for future work
In this paper, detailed guidelines were given for creating an
expert system that facilitates cognitive map modeling of
physical systems for the purpose of FA. The main aim of
Table 3 Failure mode analysis report
S.
No.
Function quantifier Final node
value
Affected function
units
Failure mode (added information)
1. Volume of Mg. anode
rod
-1 Function unit 2 Anode rod dissolves [in] water_failed (electrolysis stopped/anode rod
fully consumed)
Function unit 5 Tank contains water_failed (leaking due to corrosion of tank)
2. Temp. of heating
element
?1 Function unit 1 Heating element heats water_failed (coil burnout due to excess temp.)
Function unit 3 T/P valve controls [pressure]_failed (excess pressure)
Function unit 4 T/P valve controls [temperature]_failed (excess temp.)
Function unit 5 Tank contains water_failed (explosion)
3. Strength of steel tank -1 Function unit 5 Tank contains water_failed (explosion)
4. Pressure of water ?1 Function unit 3 T/P valve controls [pressure]_failed (excess pressure)
Function unit 5 Tank contains water_failed (explosion)
5. Temp. of water ?1 Function unit 1 Heating element heats water_failed (superheating)
Function unit 3 T/P valve controls [pressure]_failed (excess pressure)
Function unit 4 T/P valve controls [temperature]_failed (excess temp.)
Function unit 5 Tank contains water_failed (explosion)
Res Eng Design (2012) 23:105–124 121
123
this research effort was to enable model-based identifica-
tion of system interaction failure modes that are usually
missed by other existing approaches. The motivation for
this work came from the fact that cognitive maps present an
excellent modeling platform for capturing causal interac-
tions among the modeling constructs. Graphical approa-
ches bearing close resemblance to cognitive maps have
been frequently used by researchers for enhancing the
lucidity of model representations in a variety of applica-
tions. An interesting example of such an application can be
found in the work done by Reich and Fenves (1995) toward
the automation of the preliminary stage of design of cable-
stayed bridges. They employ a network of causal influences
for performing bridge redesign after detecting deficiencies
in the bridge analysis. However, the superiority of cogni-
tive map modeling over other similar graphical approaches
is revealed in its adaptability to a variety of cognitive
inference procedures that can be used to simulate and
derive useful results from the model.
The final cognitive map model of a physical system was
obtained by following a procedure that incorporates in a
stepwise manner, all structural, functional, and causal
aspects of the system into one single representation.
Domestic hot water heater was taken as an example to
demonstrate the proposed framework. Standard fuzzy
cognitive map inferencing was used for model simulation,
and results were obtained in the form of a failure mode
analysis report as shown in Table 3.
Heating of water is a very common task. It is already
known that whenever water is heated, scale formation
takes place and it affects the heat transfer process. In
common FA approaches, this kind of interaction/inter-
ference is not considered. Such interaction mechanisms
are understood only after an actual failure experience has
taken place. In the case example of the water heater, the
input scenario presented to the model for simulation was
excessive hardness of water. All other parameters were
either ideal or within normal ranges. It can be observed
from the results shown in Table 3 that failure modes
ranging in severity from as severe as the heater explod-
ing, to merely failing to heat water sufficiently have all
been generated through simulation. Moreover, the cause
of all these failures is scale formation due to excessive
hardness of water. This demonstrates the capability of the
proposed framework in capturing and understanding the
nature of system interaction failures that can result even
if all constituent components of the system are in working
condition.
Other advantages of the proposed modeling framework
of FA include the following:
• The type of modeling undertaken conveniently allows
working at mixed (or multiple) levels of abstraction,
since the modeling constructs are system variables
instead of system elements.
• Graphic representation of the modeling constructs used
in cognitive maps enhances comprehensibility.
• Since the variables considered for constructing cogni-
tive maps are mostly design variables, the failure
modes can be directly mapped to respective design
parameters and inference on what changes in design
have to be made can be easily reached.
One of the drawbacks in the proposed framework lies in
the fact that it relies heavily on the judgment and discretion
of the experts. Although the cognitive map architecture
provides a good platform for capturing a myriad of system
interactions, there is a fair chance of omitting information
due to ignorance of the modeling expert leading to the
development of an inferior model. In order to obtain a good
cognitive map model of a given system, it is imperative that
a good knowledge regarding various underlying physical
phenomena be possessed by the experts involved in its
development. Moreover, there are always some interactions
that give rise to emergent behaviors in complex systems that
are previously unheard of. Such interactions are highly
prone to be left out even by experienced hands.
Another drawback of the proposed methodology is in its
use of traditional fuzzy cognitive map inferencing for
simulation. This type of inferencing is capable of dealing
with monotonous relations only, which often is not the case
in real-world applications. Moreover, apart from getting a
list of possible modes of failures, it is difficult to discern the
sequence in which the failures occur. To overcome these
shortcomings and to further enhance the efficacy of FA, our
current research efforts are focused on the development of a
new inference procedure for cognitive maps that would
enable dynamic failure mode generation/identification from
a cognitive map model of a given physical system. The
conceptual framework of this proposed work has already
been developed by us (Augustine et al. 2009). We also aim
to incorporate root cause analysis like features compatible
with cognitive map representations of physical systems. It is
intended to couple the present work with these future ven-
tures to develop a comprehensive tool that would facilitate
the identification of all modes of failures for physical sys-
tems in early stages of product development.
Acknowledgments Authors would like to sincerely thank editor and
both anonymous reviewers for their very constructive and valuable
comments and suggestion for improving the quality of the paper.
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