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This document is downloaded from DR‑NTU (https://dr.ntu.edu.sg)Nanyang Technological University, Singapore.
Imperfect predictive maintenance model formulti‑state systems with multiple failure modesand element failure dependency
Tan, Cher Ming; Raghavan, Nagarajan
2010
Tan, C. M., & Raghavan, N. (2010). Imperfect predictive maintenance model for multi‑statesystems with multiple failure modes and element failure dependency. Prognostics andSystem Health Management Conference (pp. 1‑12) Macau.
https://hdl.handle.net/10356/93527
https://doi.org/10.1109/PHM.2010.5414594
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Imperfect Predictive Maintenance Model for Multi-State Systems
withMultiple Failure Modes and Element Failure Dependency
Cher Ming Tan I,2, *and Nagarajan Raghavarr''Division of
Circuits & Systems, School ofElectrical & Electronic
Engineering, Nanyang Technological University.
2Singapore Institute of Manufacturing Technology, A*STAR,
Singapore - 638075.3Division of Microelectronics, School
ofElectrical & Electronic Engineering, Nanyang Technological
University.
I,3BlockS2, Nanyang Avenue, Singapore - 639798.*Email :
[email protected], Ph : (+65) 6790 4567, Fax: (+65) 6792 0415
Abstract - The objective of this study is to develop a
practicalstatistical model for imperfect predictive
maintenancebased scheduling of multi-state systems (MSS)
withreliability dependent elements and multiple failure modes.The
system is modeled using a Markov state diagram andreliability
analysis is performed using the UniversalGenerating Function (UGF)
technique. The model issimulated for a case study of a power
generation -transmission system. The various factors influencing
thepredictive maintenance (PdM) policy such as maintenancequality
and user threshold demand are examined and theimpact of the
variation of these factors on systemperformance is quantitatively
studied. The model is foundto be useful in determining downtime
schedules andestimating times to replacement of an MSS under the
PdMpolicy. The maintenance schedules are devised based on
a"system-perspective" where failure times are estimated byanalyzing
the overall performance distribution of thesystem. Simulation
results of the model reveal that a slightimprovement in the
"maintenance quality" can postponethe system replacement time by
manifold. The consistencyin the quality of maintenance work with
minimal varianceis also identified as a very important factor that
enhancesthe system's future operational and downtime
eventpredictability. Moreover, the studies reveal that in order
toreduce the frequency of maintenance actions, it isnecessary to
lower the minimum user expectations from thesystem, ensuring at the
same time that the system stillperforms its intended function
effectively. The modelproposed can be utilized to implement a PdM
program inthe industry with a few modifications to suit the
individualindustry's needs.
I. INTRODUCTION
Maintenance has evolved from the age-old ad hoc corrective(or
reactive) maintenance [1] (CM) to preventive maintenance(PM) [2]
and then to the presently popular predictivemaintenance (PdM) [3,
4]. However, it is well recognized thatboth the CM and PM are
ineffective. In the case of CM, the"completely failed" system is
highly degraded, makingmaintenance very difficult, time-consuming
and expensive.Also, CM is associated with large and
unpredictabledowntimes resulting in low mean availability,
increased delays,larger inventory storage requirements and
increased forgoneproduction losses. As for PM, the fixed downtime
intervalsimply more-than-necessary repair frequency during the
initialperiods of the system operation that could increase
theprobability of maintenance-induced failures. On the otherhand,
as the system ages and enters into its wear-out period,PM results
in less-than-necessary repair frequency, therebyincreasing the
probability of unanticipated catastrophic failuresand making PM
similar to CM.
In PdM, which is also referred to as condition-based PM [5],the
maintenance schedule and frequency match the age orhealth of the
system at all times, making the schedule nearlyoptimum, prolonging
the time to replacement (TTR) as aconsequence. The expected times
to future failure of a systemare estimated during each operational
period based on thevariation pattern of its physical properties
(conditionmonitoring) that are indicative of its state of
degradation usingimplanted sensors, and the downtime schedule for
eachoperation cycle is determined based on the estimated
futurefailure times. Past research studies show that the
averagesystem reliability (and yield), availability and mean
systemperformance are the highest for PdM and the
incurredmaintenance operation costs are the lowest [6]. The spare
partrequirements and delay times are also reduced due to
reliablepredictions of future downtime events.
However, there are currently two main obstacles to thepractical
implementation of the PdM policy. Firstly, there is nosimple
concrete statistical model that PdM can be based upon.The past
models developed are theoretical in their approachwith idealistic
assumptions and fitting parameters, renderingthem unfit for
practical real-world implementation. Forexample, in [7], it was
proposed that the system being repairedcould be restored to either
the "as-good-as-new" condition orthe "as-bad-as-old" condition with
complementaryprobabilities, failing to account for the possibility
that thesystem's restoration could be somewhere in between these
twopossible extreme cases. Although the virtual age modelproposed
by Kijima et. al. [8] to account for the imperfectrestoration
helped overcome the above-mentioned problem, thedetermination of
the effective age parameter 'a' in theproposed model is not given,
making its implementationvague.
Secondly, the implementation of PdM requires advancedmonitoring
technologies, real-time data acquisition systemswith sophisticated
data storage and speed requirements andsignal processing and
filtering techniques [9], making theimplementation of PdM complex
and expensive. However,with the advances in sensor technologies
today, this difficultyis gradually overcome [10].
In this work, we will focus on the first obstacle which is
todevelop a comprehensive and practical statistical model forPdM.
Imperfect maintenance will be considered in this workfor practical
applications. This imperfect maintenance is a termfrequently used
to refer to maintenance activities in which thefuture reliability
and degradation trend of the system dependson the skill and quality
of the current and previous repairworks performed. In other words,
imperfect maintenanceaccounts for the impact of maintenance quality
on the futurereliability of repairable systems. In reality,
maintenance
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strategies for most systems can be categorized under
imperfectmaintenance because repair / replacement is
typicallyperformed only for some of the components in the
system;while there are other components which are degraded but
notto the extent of needing a repair / replacement. Therefore,
froma "system perspective", repair does not rejuvenate a system
toits original zero degradation state, calling for the need to
useimperfect maintenance models.
The structure of this paper is as follows. Section II gives
abrief review on the various existing models for
imperfectmaintenance. Section III introduces the methodology for
themulti-state system PdM modeling and the description of thesystem
case study. Section IV describes the various resultsfrom the model
simulation and fmally, a short summary of thework done and results
achieved is presented in Section V.
II. IMPERFECT MAINTENANCE
Various models have been proposed for imperfectmaintenance in
the past from different perspectives asreviewed in complete detail
in [11]. Basically, there are fourclasses ofmodels developed so
far.
The first class of models was based on a probabilisticapproach
[12] - [14] where it was assumed that the systemundergoes "perfect
renewal" to "as-good-as-new" conditionwith a constant probability
of p and "minimal repair" to "as-bad-as-old" condition with a
probability of (J-p). Furtherenhancement to this probabilistic
approach was to consider theprobabilities as time-varying
functions, p(t) and [J-p(t)}, toaccount for the change in these
values with the aging system'sdegradation [15, 16]. Makis and
Jardine [17] further accountfor the probability that the repair is
unsuccessful and causes acatastrophic complete system failure and
the p(t) function wasmodified to p(n ,t) to describe the
probability accounting forthe number of previous failures, n,
undergone by the systemprior to the current one.
The second class of models was based on the improvementfactor
method where the system was analyzed by looking atthe failure rate.
Certain models were proposed to reflect thereduction in failure
rate after repair [18, 19]. The degree ofimprovement in the failure
rate was called improvement factorand "failure rate" was used as
the threshold reliability index.
The third class of models was based on the age of thesystem. The
most popular model in this class is known as thevirtual age model
proposed by Kijima et al, [8, 20]. The virtualage of the system
after the nth repair (Vn) is expressed as:V
n=V
n-
l+a- X; where Xn is nth failure time, Vn-J is the virtual
age after (n-I)" repair and "a" is the virtual age parameter (0
:Sa s 1). However, the method of estimating the parameter "a" isnot
mentioned in the literatures. Another age-based modelcalled the
proportional age setback model was proposed in[21] which is very
similar to the virtual age model, except thatthe effects of
equipment working conditions and surveillanceeffectiveness on
imperfect maintenance andcorresponding age reduction are accounted
for in addition tothe maintenance work quality.
The fourth class of models was based on the systemdegradation
where the system is considered to suffer randomshocks at variable
intervals of time causing it to undergoprogressive increments of
damage [22, 23]. When a threshold
cumulative damage level is reached, the system is interpretedto
have failed. The effect of the imperfect maintenance actionsis
described by the degree of reduction of the cumulativesystem damage
after repair as compared to that before repair.Wang et al. [24] -
[27] treated imperfect maintenance bymodeling the decrease in
system lifetime with the increase inthe number of repairs. They
also modeled the time betweenmaintenance actions using a
quasi-renewal process [26].
There are other models to account for imperfectmaintenance, and
readers may refer to references [14] and [28]for detailed
information. However, all the above-mentionedmodels are focused on
a binary system where the systemoperates in only two discrete
performance states, viz."functional" or "non-functional". Also,
most of the modelsassume a "single unit" system with negligible
maintenanceduration and the impact of maintenance quality on the
systemreliability is not included. For practical applications,
multi-state systems should be considered [29, 30], and the study
ofthe impact of maintenance quality is especially useful as
itdirectly impacts the time to replacement of the system. It iswith
the motivation to enable PdM model to be applicable in apractical
environment that this work is produced.
In this work, we analyze the system from a
multi-stateperspective for a generic complex n-component system
withany system structure (series, parallel, k-out-of-n
structuresetc... ). Imperfect PdM is modeled by considering the
effect ofthe mean and variance in the quality of maintenance
workseparately. The impact of the skill of maintenance work andthe
spare part product quality on the future reliability of asystem is
modeled by a parameter called the RestorationFactor (RF) which
describes the percentage recovery in thesystem performance for the
new operation cycle, aftermaintenance, relative to the previous
operation cycle of thesystem. Being a quality index, RF is assumed
to have a normaldistribution with its mean (PRF) and standard
deviation (aRF)giving a clear indication of the skill and
consistency ofmaintenance work performed respectively. The
modeldeveloped here is widely applicable to most industrial
systemsand its application to a dependent multi-state system
(MSS)with multiple failure modes is illustrated in this work.
Although an imperfect maintenance policy for multi-statesystems
(MSS) has been proposed earlier in [31] based on theproportional
age setback model [21], the maintenance durationis assumed to be
negligible, and the user threshold demand isassumed to be constant.
Furthermore, no method for thedetermination of the time to
replacement (TTR) of the systemis discussed. For practical
applications, the model proposed inthis work considers the fmite
maintenance duration and itsvariability, and the system replacement
time is determinedusing a simple approach.
The novelty of the work lies in characterizing the
systemperformance variation in dependent and multiple failure
modeMSS for different maintenance work quality standardsrepresented
by the restoration factor (RF) distribution anddifferent user
threshold demands (W). In other words, thesystem's performance
capability is being examined from theuser's perspective. The system
is modeled using a MarkovState Diagram in this work, which is found
to be a good choicefor modeling complex systems [32]. Readers may
refer to [33]for the earlier study of PdM applied to the simplest
case of an
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Fig. 2. Markov State Diagramfor the 3-elementpower
generatorsystem.
For example, if n observations on n different identicalsystems
are made from their historical maintenance records
.........•
ELEMENT 3
)..13(3)
r······· 'ELEMENT 2
.......•
;......•
The system in this study is modeled such that Element 2
isdependent on Element 1 and Element 3 is influenced by twofailure
modes (FM). The symbol p in Table I denotes theconditional
probability of occurrence of FM B given that FMA has occurred. In
other words, FM A is assumed to be thefailure mode which will
defmitely occur while FM B istriggered depending on FM A.
Each performance rate in Table I corresponds to a discreteamount
of power processing capacity that every element of thegenerator
system can process. For example, Element 3 has 3discrete states of
performance. It could be processing power atits maximum capacity
(performance) of g31 = 10 MW orintermediate capacity of g32 = 5 MW
or at g33 = 0 MWimplying complete non-functional failure. Elements
1, 2 and 3each have 3 discrete states of performance, thus making
up atotal of 3 x 3 x 3 = 27 discrete system performance rates.
Under some reasonably general conditions, the failures of
acomplex system can be shown to follow the exponentialdistribution
even though the individual components in thesystem may follow other
failure distributions [32]. Thus, if thepower generator system in
Fig 2 is assumed to be complex, itwill follow the exponential
failure distribution pattern, therebyjustifying the use of a Markov
State Diagram, in which thedegradation rates are all
time-independent constants.
During the operation of the system, the elements transit fromone
state of performance to another in a period of time. Usingthe
concept of hazard rate, the inter-state transitions can bedescribed
using the degradation rate, which is expressed as thenumber of such
state transitions per year (unit time). Thehypothetical values
assumed for the degradation rates of eachelement are shown in Table
I. The values of these parametersin Table I for various state
transitions may be extracted frompast maintenance data records and
condition monitoring dataof previously operated similar systems
using the standardMaximum Likelihood Estimate (MLE) procedure for
theexponential distribution [34].
ELEMENT 1
III. METHODOLOGY & SYSTEM CASE STUDY
r---------------------------------------------,, ,,: ~~~!.......
:. . . ,, . . ,: ~. ~ (3)~:, . . ,, : ':........... ~--+J. ..... ~
· ,: : : :: : ~(2): .:, : :'. . .: ....•,,
,~---------------------------------------------~
independent MSS with no element failure dependency andsingle
failure mode.
In this work, the power generator system is analyzed usingthe
Markov process [29, 30]. Each element has its own markovstate
diagram with different states of performance andcorresponding
degradation rates (conventionally known as"failure rate") as shown
in Fig 2. The parameters gij representthe t" discrete degraded
state of performance of the lh elementin the system. The symbol
liJ(m) is the degradation rate ofelement m where its performance
degrades from the lh state tothe jth state. The operational
lifespan of the system may beclassified into different operation
cycles. The J(h operationcycle is defined as the operating time
interval between the(k_J)th and J(h maintenance actions. Referring
to the MarkovState diagram shown in Fig 2, the numerical values for
thevarious states of performance of each element and thedegradation
rate (l) are given in Table I.
Fig. 1. Power generatorsystemtopologyexaminedin this case
study.
The system examined in this work is a power generatorsystem
which is a flow transmission MSS. The topology of thesystem
consists of 3 generator elements as shown in Fig 1.Elements 1 and 2
are in parallel with each other and they arecollectively in series
with element 3. The performance(degradation) index of the system is
the power processingcapacity of each generator element expressed in
the unit ofmegawatts (MW). In this study, element 2 is considered
to bedependent on element 1 and element 3 degrades under
theinfluence of two failure modes which may be dependent oneach
other.
There are two types of multi-state systems (MSS). One is thejlow
transmission system [29] in which the performance(degradation) of
the system is characterized and measured interms of its
productivity or capacity. Typical examples are (a)hydraulic systems
where performance is measured in terms ofvolume and massjlow rates
(tons/min), (b) power systems withits power generating capacity and
(c) continuous productionsystems with its rate ofproduction.
The other type is the task processing system [30] in
whichperformance is described in terms of processing speed
orresponse time. Typical examples include server, control andother
software systems where the performance index of interestis the
speed of processing data and instructions, expressed inmega bits
per second (mbps). The analysis of these two typesof MSS mentioned
above are different owing to the differentproperties being examined
in them and the different nature oftheir basic functions.
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and the duration (ti) for transition between consecutive
statesof performance gi,j and gi,j+1 is measured, then the
degradationrate ~, j+1 could be estimated using the exponential MLE
as in(1) where t, is the time to degradation (TTD) of the
lhobservation from statej to statej+1.
As mentioned in Table I, the values of Al,2(3) and Al,3(3)
areassumed to depend on the failure modes A and B and
theconditional probability, p. If FM A causes FM B, thenelement 3
is under the influence of two failure modes and it ismost likely to
undergo a catastrophic breakdown from state g31to state g33. The
probability for such a catastrophic failure isthe conditional
probability (P) of FM B occurring given thatFM A is present. In
contrast, when FM B is not triggered byFM A with a corresponding
probability of (1 - p), thenelement 3 degrades gradually from state
g31 to g32 andeventually to g33, since it is under the influence of
only onefailure mode. Based on the above proposition, the
expressionsfor Al,}3) and Al,3(3) in terms of AA' AB and p may be
expressedas in (2) and (3). The terms AA and AB refer to the
degradationrates of element 3 with respect to failure modes A and
Brespectively.
Aj,j+l =
AI,/ 3) = (1- p). AA
AI ,3 (3) = P'(AA +AB )
(1)
(2)
(3)
change according to the particular system. Therefore,
equations(2) and (3) are not standard expressions. Rather, they
aremodels used to describe the nature of failure of the
generatorsystem.
There are two important factors which affect the
predictivemaintenance (PdM) policy. They are the restoration factor
(RF)and the user threshold demand (W). Since the impact of thesetwo
factors on PdM will be investigated in this work, let usnow discuss
these two factors in detail.
A. PdM Model Parameters
1) Restoration Factor (RF)
To study the impact of the quality of a maintenance work
onsystem performance quantitatively under the PdM policy, anew term
called the Restoration Factor (RF) is introduced. Itrepresents the
percentage recovery of the system's meanperformance in the Ith
operation cycle (after the (k-1)thmaintenance action) relative to
its mean performance duringthe previous (k-L)" operation cycle. The
Ith maintenanceaction (cycle) refers to the downtime duration
between thesuccessive Ith and (k+l)th operation cycles. The better
themaintaining quality is, the higher the RF.
Based on the defmition ofRF, the system mean performanceduring
the Ith operation cycle, denoted by Gk(t) , may beexpressed in
terms of the corresponding mean performance inthe (k-I )" operation
cycle, Gk-1(t) using the restoration factor ofthe preceding (k_1)th
maintenance cycle, RF[k-1] as follows:
(4)
TABLEINUMERICAL VALUES OF PERFORMANCE STATES AND TRANSITION
DEGRADATION RATES IN THE MARKOV MODEL
It is to be noted that the model above is based on theobserved
system dynamics of the generator being examined.Different systems
have different natures and modes of failureand in each case, the
model in equations (2) and (3) will
Element(#)
2
3
PerformanceState (MW)
gll = 6.0gI2 = 3.5g13 = 0.0
g2I = 4.0g22 = 2.5g23 = 0.0
g3I = 10.0g32 = 5.0g33 = 0.0
DegradationRates (yr")
Al 2(1) = 0.020A2:3(1) = 0.030
Al 2(2) = 0.035~:3(2) = 0.045
AA = 0.050AB = 0.080A2,3(3) = 0.040
Remarks
Element 1 has 3distinct states ofperformance. It hasonly one
failure modeand it is independentof other elements.
Element 2performancedistribution dependenton Element
1performance state.
Element 3 has twofailure modes {A, B}where failure mode Aalways
exist and theconditional probabilityof occurrence of FM Bgiven that
FM A existsis p. The values ofA {3) and A (3) depend1,2 1,3on AA'
AB andp.
An RF value of 100% represents the system beingmaintained to an
as-good-as-new (renewal process) condition.However, this is
practically unachievable unless the system isreplaced (expensive)
instead of being maintained (repaired)upon failure.
The RF value is not a constant throughout the system lifecycle.
It is a random variable that can vary during everymaintenance
action because it is influenced by various factorssuch as the
concentration and attentiveness of the maintenancepersonnel (state
of mind), the ability to accurately locate thepoint of defect due
to the complexity of the failure, availabilityof appropriate spare
parts and maintenance tools etc. Also, thesame system might be
maintained by different personnelduring different downtimes having
different capabilities inperforming the same maintenance work.
Moreover, at thesystem-level, not all the components undergo a
repair /replacement during the maintenance task. This variability
inthe quality of maintenance work and confmement of repair
tocertain critical components of the system renders RF to
beconsidered as a random variable.
The RF parameter is modeled as a random variablefollowing a
Normal Distribution as given by (5) in this work.As RF is always
positive, it should be modeled by a statisticaldistribution with a
positive valued random variable. However,the ensemble of the many
RF values over a period of operationtime and a large number of
equipment maintenance actionsjustify its representation by a normal
distribution with largemean value and moderately low standard
deviation, such thatthe probability of having negative value is
negligible, as thetail of the normal p.d.f narrows down around RF =
0, making
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the probability, Pr(RF < 0) very small (rare event). In (5),
PRFis the mean value of the RF distribution and aRF is
thecorresponding standard deviation.
As most industries are adopting the conventional CM policy,past
maintenance history of downtime events for previouslyfailed systems
could be used to estimate RF values and thenuse them to predict the
parameters of the RF distribution. TheRF estimate for a particular
Jth maintenance action, denoted byRFk, can be calculated using (6)
where Tk+1 and T, representthe durations of the (k+l)th and Jth
operation cyclesrespectively. Quantities ti;1 and tk refer to the
absolute timeinstance of the (k+1)th and Jth failures respectively,
relative tothe initial time of system operation (t =0); ik and ik-l
are thedowntime durations for the Jth and (k-I)" repair
actionsrespectively. Similar values of RF can be estimated for
allpossible k values and for many such identical systems.
Theobtained RF data set could then be used to compute PRF and
aRFparameters for the RF distribution using the standard
statisticalmean and variance expressions. Based on the estimated
valuesofPRF and aRF from past maintenance records, the
performancetrends for future operation cycles of new similar
systems canbe modeled based on Eq. (4) where RF[k-l] is a
randomnumber representing the expected maintenance quality for
the(k-I)" maintenance action, which is generated from the
normaldistribution with parameters PRF and aRF using the
randomnumber generator function.
(7)
2) User Threshold Demand (W)
In this study, the system's performance is analyzed from
theuser's perspective. The user of the system sets a
minimumexpectation from the system, called the user threshold
demand,represented as W. During each operation cycle, as the
system'smean performance G(t) drops below the user set demand of
W,the system is "interpreted" to have ''failed'' from the
user'sperspective even though the system might not have
physicallyfailed in reality, i.e, the user's "dissatisfaction" is
considered as"system failure" in this case. The higher the user
thresholddemand (W), the sooner will be the time to failure (TTF)
andreplacement (TTR) of the system as seen in Fig 3. The time
tofailure for a system during the r operation cycle is estimatedby
solving (7).
B. Markov Chain Diagram
Having described the parameters RF and W, we nowdevelop and
analyze the Markov model for the system. Fromthe Markov State
diagram for each element shown in Fig 2, theset of simultaneous
differential equations describing the stateprobability expressions
may be extracted. They are listed inequations (8) - (16) below.
Every state is described by itscorresponding differential equation.
In Fig 2, since eachelement has 3 states, there are a total of 3 +
3 + 3 = 9dependent differential equations to be solved
simultaneously,with the following initial conditions: Pl1(O) =
P2I(O) = P3I(O) =1, P12(O) = P13(O) = P22(O) = P23(O) = P32(O) =
P33(O) = O. Theseinitial conditions correspond to the probability
of the system'selements in their most efficient states of
performance {glh g2hg31} being equal 100% at time t = O.
(5)
(6)
This approach of computing the RF distribution parametersfrom
past CM maintenance records is based on the assumptionthat the
quality ofmaintenance in both CM and PdM policies issimilar because
the nature of the maintenance work isessentially the same. Note
that only hands-on field repair onthe system is termed as
"maintenance" in this work. Minorcontrol signal adjustments to the
automated system'sparameters is not considered as a "maintenance"
activity as itdoes not involve or require any hands-on
maintenancepersonnel skills.
Time to Ftlil.re (lTF) - User De mtliN! d
............................
. .···········r···············r···············
t
Fig. 3. Schematicillustrationof the relationship betweentime to
failure (TTF)and user demand(W).
PH"(t) =-~ 2(I) • PH(t) (8)
"( ) ~ (I) A (I)P12 1 = + ,2 • PH (1)- 2,3 • P12 (1) (9)
P13"(t) = +..1,2,/1) • Pl2(t) (10)
P2:(t) =-~,2 (2) • P 21(t) (11)
"( ) ~ (2) A (2)P22 1 = + ,2 • P21 (1)- 2,3 • P22 (1) (12)
P2:(t) =+..1,2,/2) · P22(t) (13)
P3:(t) =-(~,2 (3) + ~,3 (3) ). P31
(t) (14)
•( ) A (3) A (3)P32 1 = + 1,2 • P31(1)- 2,3 • P32(1) (15)
"( ) A (3) ~ (3)P33 1 = + 2,3 • P32(1) + ,3 • P31(1) (16)
The terms Pi,j(t) in the above equations denote the
probabilitythat element i is in statej at any arbitrary time t ~
o.
C. Universal Generating Function (UGF)
The UGF methodology [30, 35] is an essential tool to obtainthe
performance distribution of the overall system from theperformance
distribution of the individual elements of thesystem. A performance
distribution is a probability distributiontable listing the various
states of performance of theelement/system and their corresponding
time-varying state
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probability expressions. The element performance
distributionsfor all the 3 elements of the generator system are
described inTable II based on the Markov analysis results in the
previoussection.
The system performance distribution needs to be obtainedfrom the
individual element performance distributions in orderto
characterize the system's reliability and performancevariation
denoted by R(t) and G(t) respectively, which is ourfmal objective.
This is made possible using the UniversalGenerating Function (UGF)
represented as U(z), which is a z-transform based approach first
proposed by Ushakov (1987)[36]. The UGF is an efficient tool for
complex multi-statesystems (MSS) reliability assessment as it
greatly reduces theproblem complexity and computational intensity
bymodularizing a system into its components and analyzing
eachcomponent of the system individually, thereby enabling acomplex
problem to be broken into sub-problems each ofwhich can be solved
separately, with ease.
For the generator system in this work, the UGF methodreduces the
total number of differential equations to only 3 + 3+ 3 = 9 in (8)
- (16) as compared to using a single "overall-system" markov
analysis which would have required amaximum of 3 x 3 x 3 = 27
differential equations,corresponding to the 27 discrete and
distinct system states.
As mentioned earlier, element 2 of the generator system
isdependent on element 1. This dependency can be modeled insuch a
way that the performance distribution of element 2depends on the
performance state ofelement 1.
TABLEIIPERFORMANCE DISTRIBUTION OF THE THREE ELEMENTS OF THE
GENERATOR SYSTEM
Equations (17) - (19) describe the conditional probabilitytheory
used to determine the resultant state probabilityexpressions
P21(t), P22(t) and P23(t) for dependent element 2.
Using the UGF approach, the z-polynomial u-functions, u(z)for
individual elements 1, 2 and 3 of the system may now beexpressed as
follows,
u l (z) = PH (t)zgll + P12 (t) zgI2
+ P13 (t) zg
13 (20)
u2(z) = P21 (t) zg21
+ P22 (t) zg22
+ P23 (t) zg23
(21)
u3(z) = P31 (t) zg31
+ P32 (t) zg32
+ P33 (t) zg33 (22)
To formulate the system's overall performance distributionin
terms of the individual element performances, a systemstructure
function [30], qJ, is constructed. This qJ functiondepends on the
system topology (series - parallel architecture)and also the type
ofMSS being analyzed (flow transmission ortask processing). The
system topology of the generator systemin Fig 2 consists of
elements 1 and 2 in parallel to each otherand the parallel
combination in tum in series with element 3.
The net useful power output of the system (performance),Gs, will
be the minimum of the total amount of powerprocessed by the
parallel combination of elements {I ,2} givenby (G1 + G2) and the
serially connected element 3 having apower processing capacity
represented by the random variable,G3• Based on this configuration,
the system structure function,qJ, for the flow transmission power
generator system in Fig 2 isgiven by (23), where Gs denotes the
overall systemperformance (output power) random variable.
Representing the discrete random variable for performanceof
elements 1 and 2 as G1 and G2, if we assume the followingdependency
condition given in Table III, we have thefollowing equations:
TABLEIIICONDITIONAL PERFORMANCE DISTRIBUTION FOR ELEMENT 2 OF
THE
GENERATOR SYSTEMc=3 b=3 a=3
=LLLPla(t)P2b(t)P3c(t)*z
-
same system performance rate values, in which case,
theassociated state probabilities are summed up.
Representing {gsJ, gs2" ..., gs27} and (PsIt), Ps2(t), ...,
Ps27(t)} asthe set of system performance states and their
probabilities, asimplified form of (24) is:
The performance variation of the system for a general
k"operation cycle, Gk(t), may now be described in terms of GI(t)by
(28) based on the earlier expressions in (4) and (27). Theestimated
time to failure (TTF) for every operation cycle, k, isfound by
solving (7) numerically, where Gk(t) is described by(28).
(25)
E. Modeling ofMaintenance Cycle
The duration for different maintenance actions
(downtimeduration) in any maintenance policy is always a variable
due tomany factors. For example, the root cause of each failure
couldbe different; the degree of the damages caused by the
failurescan be different on different occasions too. Some of the
failuresites might be externally accessible and maintenance could
beperformed without dismantling the system, thus requiring
lessrepair time; whereas some others could be situated deep
insidethe system that requires the system to be opened out for
failureanalysis and restoration work which could end up to be
verytime-consuming. As a result of all these variations,
themaintenance duration needs to be modeled by a randomvariable
with a stochastic distribution. The Weibull andGamma distributions
are commonly used for downtime orrepair distributions [37]. Here,
we use the Weibull distributionfor downtime event modeling. The
shape factor ~ is assumed tobe 1 to reflect the age-independent
randomness in themaintenance durations. The value for the scale
factor, 11 is setto 0.02 years according to maintenance duration
records forpower generators, as revealed in [38].
As the system continues to age, the degree of failure andextent
of damage of the to-be-maintained system becomesmore pronounced and
severe even under the PdM policy, dueto the effect of irreparable
wear-and-tear effects. Thus, thelater stages of system failures are
more difficult and time-consuming to maintain and restore as
compared to the initialfailures. Therefore, it would be appropriate
to model the scalefactor, 1], of the downtime distribution as an
arbitraryincreasing function of the operation cycle, k, to
represent theincreased downtime periods during subsequent repair
actions,as the system's rate of degradation increases with time
forimperfect maintenance.
With the mathematical model developed, we can nowsimulate the
model using Matlab and study the effect of thevarious factors
described, on the system reliability andperformance characteristics
for the MSS PdM policy. Due tothe unavailability of real industrial
data, the numerical valuesof the Markov degradation rates in this
power system casestudy are hypothetically assumed for the sake of
illustration;hence, the magnitudes of the computation results may
notreflect the reality. In other words, the results described in
thefollowing sections serve only to show the practical
usefulnessand applicability of the model.
IV. RESULTS AND DISCUSSION
A. Impact ofThreshold Demand (W)
Figures 4(a) - 4(c) show the system mean performancecurves for
three threshold demand (W) values of9 MW, 8 MWand 7 MW respectively
at a given RF distribution withparameters PRF = 95% and (jRF = 0%.
One can see from these
27
Us(z) = LPSi(t).zgsii=l
The relationship between the state probabilities for eachelement
is: PII(t) + PI2(t) +PI3(t) = 1; P2I(t) + P22(t) + P23(t) =1;
P3I(t) +P32(t) +P33(t) = 1 tj t.
27
For the system, L Psi (t) = 1 tj t ·i=l
From Table IV, the power capacity of gl = 10 MWcorresponds to
the maximum performance rate of the ''fullyfunctional" system. On
the other hand, the power capacity ofg27 = 0 MW represents the
total failure event where the powersystem is "completely
non-functional" i.e, not able to processany power at all. The power
processing capacities of 8.5 MW,7.5 MW, 6 MW etc ... correspond to
the intermediate degradedstates where the system is only
''partially functional andefficient" in its performance.
TABLEIVSYSTEM PERFORMANCE DISTRIBUTION TABLE OBTAINED USING
THE
UGF APPROACH
Systemperformance state 10 8.5 7.5 0
- Gs/MW
State probability -Psl(t) Ps2(t) Ps3(t) Ps27(t)Ps(t)
D. System Reliability & Performance
From the system performance distribution, the
Reliability(Survival) Function of the system, RI(t) for the 1st
operationcycle, can be defmed as the probability that the
system'sperformance (Gs) is above the minimum user-set
thresholddemand value, W. This is consistent with our earlier
defmitionoifailure in Section IIIA.2 where the system is considered
tohave failed from the user's perspective once its meanperformance,
G(t), drops below the threshold user demand(W). Therefore, RI(t) is
expressed as follows:
RI(t) = no, ~ W) = {fpAt) Is, ~ W} (26)1=1
where W is the minimum threshold demand settingrepresenting the
minimum user expectation from the system.
The mean performance of the system for the 1st operationcycle,
GI(t), can be modeled from the system performancedistribution.
Since Table IV is a probability distributionfunction (p.d.t) of a
discrete statistical random variable of thesystem performance, Gs,
the mean or expectation of Gs,denoted by E(Gs) , can therefore be
expressed as follows:
(27)
In (27), GI(t) is the system mean performance for the
l"operation cycle; the summation term is the usual
statisticaldefmition for "expectation ofa random variable".
k-l
Gk(t) =G1(t)· TIRF[r]r=1
(28)
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w= 7M~ uRF =0%, P = 50%
_.- IJ.RF =900k••••• IJ.RF=95°k--IJ.
RF=97.5%
10
9.5£e"
I
G) 9uCft5E(; 8.5'f:G)
Q.
C 8ft5G)
::E
~ 7.5(I)
>.en7
6.50 5
TABLE VITIME TO REPLACEMENT (TTR) VERSUS THRESHOLD DEMAND (W)
TRENDS
Table V shows the computed TTR for different thresholddemand
values when the RF distribution is fixed at JlRF = 95%and (jRF =
0%. From Table V, it can be seen that if thethreshold demand W is
increased from 7 MW to 8 MW, TTRdrops by approximately 57.6%.
Similarly, further increase inthe threshold demand from 8 MW to 9
MW again causes thereplacement time to drop further by around
73.1%. Therefore,it is important for the user not to choose a very
high W valueclose to the maximum performance capability of the
system(10 MW in this case study). Instead, a moderate
thresholddemand under which the system can still function
effectivelyshould be chosen.
B. Impact ofMean Restoration Factor (J.lRF)
Fig 6 shows the typical variation of system meanperformance
curves respectively for various f.lRF values of90%,95% and 97.5%
respectively keeping the parameters (jRF = 0%,p = 50% and W = 7 MW
fixed. The figure shows that thehigher the f.lRF, the higher the
average performance at any pointin time, as expected.
Large values of f.lRF coupled with low (jRF indicate very
highquality ofmaintenance work and imply large restorations in
thesystem performance during every maintenance. As a result,
thesystem's initial performance during the start of every
operationcycle is relatively high and it takes longer time for the
system'sperformance to degrade to below the minimum thresholddemand
(W) in that operation cycle. This implies extendedtimes to failure
(TTF) and hence prolonged time toreplacement (TTR).
Fig. 6. System mean performance variation for various mean
restorationfactors of DRF = 90%, 95% and 97.5%, given W = 7MW, DRF
= 0% and p =50%.
8
2
18
1.8
16
7
1.6
14
6
1.4
5
1.2
4
0.8
3
Index of operation/maintenance cycle = k
0.6
11m: =95%, D"RF =0%, P =500/0
2
4
0.4
2
0.2
10 .-.=-_r----r---_r---_r---_r---_r---_r---_r---_r--------.
9.5
I
~ 0cE10~ 9G)
Q.
Cft5G)
::E 0~
10~-~-....,------r------r--_r__-_r__-_,_-___r"------....,~ 9en
8
7L--_-'--_---L-_--..L-_---'-__.&..--_-I..-_--'--_---L-_-----I
o
~ 9
10__----r---r---_,_--r-------r--_r----~-----,
9
9.5
7
IIUC..I§ 8.5
! B W_+_ ~---II 0 at- Maintenance
per Ion Cycle # 1~ 75 Cyde # 1
I·
IllUSTRATING THE DETERMINATION OF TIME TO REPLACEMENT
Sy!ll:em Opendion Time well'-
6 8 10 12System Operation Time (years)
Fig. 4. System mean performance variation for (a) W = 9MW, (b) W
= 8 MWand (c) W = 7 MW.
figures that the higher the threshold demand (W), the soonerthe
time to failure (TTF) and the higher the mean frequency
ofmaintenance actions to be performed. This is because setting
ahigher threshold demand (W) implies that the system's
meanperformance would degrade below the threshold level in ashorter
span of time as illustrated earlier in Fig 3.
Time to Replacement, represented as TTR, is defmed as theinstant
when the degrading system's mean performance cannever be restored
to above the minimum required threshold(W) anymore in spite of any
further maintenance work. In suchan event, further repair work is
not beneficial because theuser's minimum expectations can no longer
be satisfied, andreplacement of the system is therefore the only
alternativeoption. Fig 5 clearly illustrates the replacement
criteria.
Fig. 5. Determination of time to replacement (TIR) from system
meanperformance curve. Symbol 'k' represents the j(h operation
cycle.
TABLE VTIME TO REPLACEMENT (TTR) VERSUS THRESHOLD DEMAND (W)
TRENDS
Threshold Demand W (MW) Time to Replacement (TTR) / yrs
J.1-RF = 95%; (JRF = 0%; p = 50%.
9.0 1.801
Mean RF (flRF) Time to Replacement (TTR) / yr
W = 7 MW; (JRF = 0%; p = 50%.
97.5% 29.99
95.0% 15.81
92.5% 11.19
90.0% 8.856
85.0% 6.508
8.0 6.704
7.0 15.81Table VI shows that the TTR of the system increases
largely
by 36.1% as the f.lRF is increased from 85% to 90%. Further
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Simulation A (SIMA) 0.984 0.879 0.998 0.964 0.782
Simulation B (SIM B) 0.807 0.842 1.004
increase in f.JRF from 90% to 95% prolongs the TTR valuefurther
by as large as 78.5%. It is therefore necessary for anindustry to
strive to improve its f.JRF to as much as possible. Thecost
incurred in improving the f.JRF must be justified incomparison to
the cost savings in maintenance and prolongedTTR achieved as a
result of the improvement.
TABLEVIIRESTORATION FACTOR FOR DIFFERENT MAINTENANCE ACTIONS
OBTAINED
USING RANDOM NUMBER GENERATION FOR TWO DIFFERENT SIMULATIONS,
SIMA AND SIMB WHERE MEAN RESTORATION FACTOR = 85%.
Maintenance # 2 3 4 5
SIM B as shown in Table VII. Therefore, it is crucial tomaintain
consistency in maintenance quality for a longer lifecycle of the
equipment. Note that maintenance quality includesthe technical
skill and competency of the maintenancepersonnel as well as the
quality of spare parts used duringrepair.
It is therefore clearly evident that keeping the
maintenanceactions as consistent as possible is of paramount
importance inorder to enhance the predictability of future
downtimeschedules, facilitate efficient pre-planning of inventory
stocks,reduce delay times and downtime durations, thereby
increasingthe mean availability and production output of the
system.
D. Effect ofMultiple Failure Modes
1614
REPLACE
P =00/0ITR =15.81 years
4 6 8 10 12System Operation Time (years)
J.1FF =950/0 GFF =00/0THRESHOLD DEMAND =W =8.0 MW
2o
7.8
9.8 ,9.6 ~
a: 9.4 \§ 9.2 \~ 9 ~.e 88 \ II... 1 I , n~ , I , I'e 8.6 t I
'I',J II 'It,
Ill:: 8.4 , I II' ItE 'I 'I 'n! 8.: __l_lt\-__ _ _
I~ REPLACEII P =1000/0\ TTR = 4.226 years
Fig. 8. Impact of the presence of multiple failure modes on the
systemperformancetrends.
E. Determination ofMaintenance Schedule
Based on the simulations of the proposed model, the timesto
failure (TTF) data can be obtained from the numericalsolution of
(7) and an estimate of the maintenance (downtime)
When p = 0%, the element is under the influence of only FMA and
therefore, it has a lower degradation rate as it graduallydegrades
with a stepwise state transition from g31 ~ g32 ~ g33.Therefore,
when p = 0%, the system has a prolonged lifespanand the maintenance
intervals are more spread out. In contrast,when p = 100%, the FM A
is certain to cause FM Bandtherefore the element which is now under
the influence of boththe failure modes has a very high effective
degradation rateand hence, it is most likely to undergo a
catastrophicbreakdown directly from the best state of g31 to the
worst stateof g33. As a result, the lifespan of the system is very
short andthe maintenance frequency is very high. From Fig 8, while
theTTR value for p = 100% is only 4.226 years, the
correspondingvalue for p = 0% is 15.81 years which is about four
timeslarger. This shows the significant effect of the presence
ofmultiple failure modes.
10..-----------r--------r--------r----.---------.---------r---.----------r-----o
In the beginning of Section III, we mentioned that element 3of
the power generator system is under the influence of twofailure
modes where FM B is dependent on FM A with aconditional
probability,p. Fig 8 shows the system performancevariation trends
for the extreme values of p = 0% andp = 100% keeping the other
parameters f.JRF = 95%, l7RF = 0%and W= 8 MW fixed.
25
J.1FF=850/0 oFF=100/0 P =500/0THRESHOLD DEMAND = W = 6.0 MW
10 15 20
System Operation Time (t) I years
5.5 L..--__------L_--'"---_------'-__-------'----------'----
----'--------'o
9
9.5
Fig. 7. Impact of inconsistency in maintenance work quality on
variation insystemperformancetrends.
Observations from Fig 7 and Table VII reveal that if theinitial
maintenance goes bad by chance, then futuremaintenance actions will
not be effective in restoring thesystem to a satisfactory level of
performance regardless of howgood these future maintenance actions
are. A bad repair workduring the initial stages of system operation
causes irreparabledamage to its reliability and this damage cannot
becompensated for by trying to improve the quality of futurerepair
works on the system. The ultimate effect is a drasticreduction in
the time to replacement (TTR). In Fig 7, the RFvalue for the first
maintenance in the case of SIM A and SIM Bare 98.4% and 80.7%
respectively. Due to the low initial RFfor the case of SIM B, the
TTR for SIM B is as low as 11.85years in comparison to the longer
(almost double) TTR valueof23.99 years for SIM A despite the
subsequent higher RF for
C. Impact ofVariation in Restoration Factor (l7RF)
Figure 7 illustrates the large deviation between a
possibleoptimistic-case (SIM A) and pessimistic-case (SIM
B)scenario of a system's performance variation pattern when thel7RF
is as high as 10%. The curves were generated by keepingall the
parameters fixed at f.JRF= 85%, l7RF= 10%, P = 50% andW = 6 MW. The
random number generator in Matlab providestwo entirely different
set of values of RF[k] from the same RFdistribution during the two
separate simulations. The variousRF values at each maintenance
cycle for SIM A and SIM Bareshown in Table VII.
10r-----------r--------r---------r-------r-------r--------r
':t:i'(!8 8.5IiE 8.g8! 7.5i:E 7EI>- 6.5UJ
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It may be noticed that in the case of a dependent system,since
element 2 degrades along with element 1 because of thedependency,
the effective degradation rate of the system ishigher and hence, it
is to be replaced in a shorter period oftime. In contrast, when the
elements are independent of each
A company's long term fmancial position hinges largely onits
ability to reduce plant operational and maintenance costs,which
currently accounts for as much as around 15 - 70% ofits overall
production expenses [1]. The new PdM policyproposed in this study
can defmitely lower the maintenancecost, and hence increase the
company's profitability.
ACKNOWLEDGEMENTS
A statistical model for the PdMpolicy ofMSS based systemshas
been developed by combining the Universal GeneratingFunction (UGF)
and Markov Chain analysis theories.Restoration factor (RF), which
is indicative of maintenancework quality and threshold demand (W),
which represents theminimum user expectations are identified as
important PdMparameters, and their impacts on the system
performance,downtime schedule and replacement time were
quantitativelyexamined.
other, degradation of element 1 does not affect theperformance
of element 2 and as a result, the effectivedegradation rate of the
system is lower resulting in prolongedoperation times and longer
time to replacement. In Fig 9, theTTR value for dependent system
was 6.732 years while for theindependent system, it is 3% larger at
6.942 years.
V. CONCLUSION
REFERENCES
[1] Bevilacqua, M. and Braglia, M, "The analytic
hierarchyprocess applied to maintenance strategy
selection",Reliability Engineering and System Safety, Vol. 70,
Issue1, pp. 71 - 83, (2000).
[2] Zhao, Y.X., "On preventive maintenance policy of acritical
reliability level for system subject to
Using the stochastic model for the restoration factor
(RF),system performance variation for various PRF, (jRF and Wvalues
were simulated and presented graphically. The resultsclearly
indicate the significant impact of PRF, (jRF and W onsystem
reliability. A highly skilled maintenance crew (high)JRF) can help
improve the system reliability and maintainabilityto a large
extent, thus saving costs and reducing wear and tearof the system
and in tum prolonging its useful lifespan.Consistent performance of
maintenance (low (jRF) is also veryessential for more accurate
predictability of future downtimeschedules and times to system
replacement (TTR) which in turnassist the management to precisely
pre-plan the productionactivities so as to meet the timely customer
market demands.
Throughout this study, the model developed and the resultsshown
were all based on the case study of a simple 3-elementpower
generator system MSS. However, it is important to takenote that the
exact same procedure described in this workcould be applied to any
n-element MSS of any type (flowtransmission or task processing)
with any arbitrary topology.The only feature to take note of is the
system structurefunction, Gs =qJ(GI'G2 , ••• ,Gn ) which will vary
for differentsystems depending on its MSS classification and its
topology[30].
The authors would like to thank the Office of Research,Nanyang
Technological University (NTU), Singapore forfunding this research
work and providing the necessarylogistical support.
DEPENDENT SYSTEM
INDEPENDENT SYSTEM
IJ.FF= 95% GFF = OOk P = SOO/o
THRESHOLD DEMAND =W =8.0 MW
COMPARING DEPENDENT vs INDEPENDENT SYSTEMS
DOWNTIME(lIAAlNl'ENANCE) SCHEDULE(allunUsin YEARS,J
(i) (ii) (iii) (iv)
L:'bwntin:leW=8IvIW W=1IvIW W=1IvIW W=8IvIW
# ~u=95%~u= 95% ~u=90% ~u= 95%
C'u=O% C'u=O% C'u=O% C'u=O%p=50% p=50% p=50% p= 100%
REPLACE 6.704- 15.81 8.856 4.226
1 2.419 3.982 3.982 1.556
2 4.384 1.385 6.111 2.162
3 5.129 10.21 8.400 3.601
4 6.498 12.48 REPLACE 4.0955 REPLACE 14.16 REPLACE6 15.21
1 REPLACE
9.6
9.8
e- 9.4(J
I 9.28Ii 9E~ 8.8~e 8.6II~ 8.4
i1 8.2(J)
REPLACE ~7.8 ITR =6.732 years023 456 7 8
System Operation Time (years)
Fig. 9. Comparing the performance variation of a system with
dependent andindependent elements.
schedules can be constructed. Table VIII shows a typicalexample
of a maintenance schedule derived from the model forthe following
four different cases:
TABLE VIIIDETERMINATION OF MAINTENANCE SCHEDULE FROM PDM
MODEL
SIMULATION FOR FOUR DIFFERENT CASES.
(i) PRF = 95%, (jRF = 0%, W =8 MW, P = 50%.(ii) PRF = 95%, (jRF
= 0%, W =7 MW, P = 50%.(iii) PRF = 90%, (jRF = 0%, W =7 MW, P =
50%.(iv)PRF=95%, (jRF=O%, W=8MW,p= 100%.
F. Comparison ofDependent & Independent Systems
In this study, Element 2 is modeled to be dependent onElement 1.
In order to quantitatively examine the impact of thisdependency on
the system lifespan, two simulations areperformed. One of them
models the dependency of element 2according to Table III and
equations (17) - (19), using theconditional probability theory. The
other simulation assumeselement 2 to be independent of element 1.
In both these cases,the values of the degradation rates, A1,2 (2)
and A2,3 (2) are thesame and the values of the other PdM parameters
PRF = 95%,(jRF = 0%, W = 8 MW and p = 50% are all kept fixed. Fig
9illustrates the performance degradation trends for these
twodifferent cases of dependent and independent systems.
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-
degradation", Reliability Engineering and System Safety,Vol. 79,
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Xplore. Restrictions apply.
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BIOGRAPHY
CHER MING TAN was born inSingapore in 1959. He received the
B.Eng.degree (Hons.) in electrical engineeringfrom the National
University of Singaporein 1984, and the M.A.Sc. and Ph.D.degrees in
electrical engineering from theUniversity of Toronto, Toronto,
ON,Canada, in 1988 and 1992, respectively.He joined Nanyang
Technological
University (NTU) as an academic staff in 1997, and he is now
anAssociate Professor in the Division of Circuits & Systems at
theSchool of Electrical and Electronic Engineering (EEE),
NanyangTechnological University (NTU), Singapore. His current
researchareas are reliability data analysis, electromigration
reliabilityphysics and test methodology, physics of failure in
novel lightingdevices and quality engineering such as QFD. He also
works onsilicon-on-insulator structure fabrication technology and
powersemiconductor device physics.
Dr. Tan was the Chair of the IEEE Singapore Section in 2006.
Heis also the course-coordinator of the Certified Reliability
Engineerprogram in Singapore Quality Institute, and Committee
member ofthe Strategy and Planning Committee of the Singapore
QualityInstitute. He was elected to be an IEEE Distinguished
Lecturer ofthe Electron Devices Society (EDS) on Reliability in
2007. He isalso the Faculty Associate of Institute of
Microelectronics (IME)and Senior Scientist of Singapore Institute
of ManufacturingTechnology (SIMTech). He was also elected to the
ResearchBoard of Advisors of the American Biographical Institute
andnominated to be the International Educator ofthe Year 2003 by
theInternational Biographical Center, Cambridge, U.K. He is
nowappointed as a Fellow ofthe Singapore Quality Institute
(SQI).
He is currently listed in Who's Who in Science and Engineering
aswell as Who's Who in the World due to his achievements inscience
and engineering.
NAGARAJAN RAGHAVAN was bornin Bangalore, India in 1985. He
receivedhis B.Eng (Hons.) from the School ofElectrical and
Electronic Engineering(EEE), Nanyang Technological University(NTU),
Singapore. He then completed aDual Master degree (M.Sc,
M.Eng)majoring in Materials Science at theNational University of
Singapore (NUS)
and Massachusetts Institute of Technology (MIT), Boston underthe
Singapore-MIT Alliance (SMA) program in the field ofAdvanced
Materials for Micro & Nano Systems (AMM&NS).
He was the recipient of the prestigious Nanyang Scholarship,NTU
President Research Scholar and Singapore-MIT Alliance(SMA) Graduate
Fellowship awards. He was one of the fiverecipients to be bestowed
with the IEEE Reliability SocietyGraduate Scholarship award in 2008
for his researchaccomplishments in reliability and its application
to the field ofmicro and nano-electronics. He is currently pursuing
his PhD at theDivision of Microelectronics, EEE, NTU focusing on
reliabilitymodeling and characterization of high-x dielectric
materials innanodevices. His research interests include
electromigration, high-K and low-x dielectric breakdown, wafer
bonding, reliabilitystatistics and maintenance modeling.
To date, he has authored / co-authored more than 18
internationalpeer-reviewed publications and serves on the review
committee formany journals. He is currently a Student Member of
IEEE and theMaterials Research Society (MRS), in the US.
978-1-4244-4758-9/10/$26.00 e 2010 IEEE MU3006 2010
Prognostics& SystemHealthManagement Conference(PHM2010
Macau)
Authorized licensed use limited to: Nanyang Technological
University. Downloaded on March 02,2010 at 03:30:58 EST from IEEE
Xplore. Restrictions apply.