Review of Simulation Approaches in Reliability and Availability Modeling

Transcription

1 Internatinal Jurnal f Perfrmability Engineering, Vl. 12, N. 4, July 2016, pp Ttem Publisher, Inc., 4625 Stargazer Dr., Plan, Texas 75024, U.S.A Review f Simulatin Appraches in Reliability and Availability Mdeling MEESALA SRINIVASA RAO 1* and VALLAYIL N A NAIKAN 2 1 GMR Institute f Technlgy, Andra Pradesh, India 2 Reliability Engineering Center, IIT Kharagpur, India (Received n February 27, 2016, revised n June 13, 2016) Abstract: Simulatin, r mre specifically numerical simulatin, is a very pwerful tl fr mdeling f engineering, scial, business, life science and ther systems where the traditinal analytical r graphical techniques becme very cmplex, especially if sme f the system variables have stchastic nature. Simulatin has been applied fr slving prblems in reliability engineering als. In this paper a literature review n the applicatin f simulatin techniques fr mdeling and analysis f prblems in reliability engineering is presented. Varius simulatin methdlgies such as Mnte Carl simulatin, Discrete event (DE) simulatin, Subset simulatin, Hybrid subset simulatin, Simulated annealing, Stchastic simulatin, Digital simulatin, and Markv System Dynamics (MSD) simulatin are discussed in details. Applicatins f these techniques in reliability engineering, their advantages and limitatins are als presented. It is als fund that the full ptential f simulatin as a system mdeling and analysis apprach has nt been explred till date in the field f reliability engineering. Since several variables in reliability engineering field such as time t failure, time between failures, time t repair, dwn time, and thers have stchastic nature, simulatin apprach is very apprpriate. It appears that mdeling f multi-state devices, degradatin and wear ut phenmena, statespace apprach, pint and steady state availability f cmplex systems can be simplified by simulatin techniques. Therefre, this paper als has suggested that mre research in these areas is needed. Keywrds: Reliability, Availability, MSD, Simulatin 1. Intrductin Simulatin is the imitatin f the peratin f a real wrld prcess r system ver time. Whether dne by hand r n a cmputer, simulatin invlves the generatin f an artificial histry f a system, and the bservatin f that artificial histry t draw inferences cncerning the perating characteristics f the real system. In the simplest frm f the basic simulatin, each randm variable in a prblem is sampled several times t represent its real distributin accrding t its prbabilistic characteristics. Cnsidering each realizatin f all the randm variables in the prblem prduces a set f numbers that indicates ne realizatin f the prblem itself. Slving the prblem deterministically fr each realizatin is knwn as a simulatin cycle, trial, r run. Using many simulatin cycles gives the verall prbabilistic characteristics f the prblem, particularly when the number f cycles tends t infinity. The simulatin technique using a cmputer is an inexpensive way (cmpared t labratry testing) t study the uncertainty in the prblem. The behavir f a system as it evlves ver time is studied by develping a simulatin mdel. This mdel usually takes the frm f a set f assumptins cncerning * Crrespnding authr s srinivas.m@gmrit.rg 369

2 370 Meesala Srinivasa Ra and Vallayil N A Naikan the peratin f the system. These assumptins are expressed in mathematical, lgical, and symblic relatinships between the entities, r bjects f interest, f the system. Once develped and validated, a mdel can be used t investigate a wide variety f what if questins abut the real wrld system. Ptential changes t the system can first be simulated in rder t predict their impact n system perfrmance. Simulatin can als be used t study systems in the design stage, befre such systems are built. Thus simulatin mdeling can be used bth as an analysis tl fr predicting the effect f changes t existing systems, and as a design tl t predict the perfrmance f new systems under varying sets f circumstances. With a simple simulatin technique, it is pssible t calculate the prbability f failure fr bth the explicit r implicit limit state functins withut knwing the analytical techniques and with nly a little backgrund in prbability and statistics. The availability f persnnel cmputers and sftware makes the prcess very simple. Applicatins f Simulatin Simulatin can be used as a pedaggical device t reinfrce analytic slutin methdlgies. Simulatin enables the study f, and experimentatin with, the internal interactins f a cmplex system, r f a subsystem within a cmplex system. The knwledge gained in designing a simulatin mdel may be f great value twards suggesting imprvement in the system under investigatin. By changing simulatin inputs and bserving the resulting utputs, valuable insight may be btained int which variables are mst imprtant and hw variables interact. Simulatin can be used t experiment with new designs r plicies prir t implementatin, s as t prepare fr what may happen. Infrmatinal, rganizatinal, and envirnmental changes can be simulated, and the effect f these alteratins n the mdel s behavir can be bserved. By simulating different capabilities fr a machine, requirements can be determined. Simulatin mdels designed fr training allw learning withut the cst and disruptin f n the jb learning. Animatin shws a system in simulated peratin s that the plan can be visualized. The mdern system (factry, wafer fabricatin plant, service rganizatin, etc.) is s cmplex that the interactins can be treated nly thrugh simulatin. Simulatin can be used t verify analytic slutins. Advantages f Simulatin: Simulatin has many advantages. These are listed by Pegden et al., The advantages are as fllws. Insight can be btained abut the imprtance f variables t the perfrmance f the system..

3 Review f Simulatin Appraches in Reliability and Availability Mdeling 371 A Simulatin study can help in understanding hw the system perates rather than hw individuals think the system perates. New plicies, perating prcedures, decisin rules, infrmatin flws, rganizatinal prcedures, and s n can be explred withut disrupting nging peratins f the real system. Hyptheses abut hw r why certain phenmena ccur can be tested fr feasibility. What if questins can be answered. This is particularly useful in the design f new systems. Bttleneck analysis can be perfrmed indicating where wrk in prcess, infrmatin, materials, and s n is being excessively delayed. New hardware designs, physical layuts, transprtatin systems, and s n, can be tested withut cmmitting resurces fr their acquisitin. Time can be cmpressed r expanded allwing fr a speedup r slwdwn f the phenmena under investigatin. Insight can be btained abut the interactin f variables. Limitatins: Hwever, there are several limitatins t using simulatin mdels. They typically take much lnger t run than analytic mdels and the results frm a simulatin mdel can be difficult t interpret. Fr these reasns, simulatin can be an expensive ptin. And the expertise is required fr develping credible mdels. Hwever the effect f many f these limitatins can be minimized by using pwerful mdern cmputatinal facilities and sftware. 2. General scenari f simulatin in reliability and availability studies Several wrks have been published n representing the use f simulatin in reliability and availability studies as described belw. Several authrs have used the simulatin apprach fr analysis and evaluatin f reliability and availability parameters f systems. They have fcused n utilizing the simulatin apprach in varius purpses such as understanding the system prcesses, mdel frmulatin activities, estimating the imprtance measures f the cmpnents f systems, estimating the system availability, in systems safety analysis, reengineering activities, early reliability predictin at the cnceptual stage f systems, large scale as well as small t medium scale enterprises. Simulatin prgrams, especially if well structured, are in general very cmprehensive and knwn fr the ease with which mdificatins and additins can be made. Perhaps their main benefit arises frm the fact that it is pssible t analyze utput infrmatin abut subsystems t gain mre understanding f the whle system prcesses [1]. Simulatin methdlgy which is used t cnstruct the mdel includes mdel frmulatin, mdel translatin, verificatin and validatin, experimentatin and reprting f results. Hu [2] used a reliability simulatr knwn as BERT (Berkeley Reliability Tl) t study the physics f failure mdels t simulate the ht-electrn effect, xide time dependant breakdwn, electr migratin, and biplar transistr gain degradatin. These fur tls can be simulated separately r simultaneusly.

4 372 Meesala Srinivasa Ra and Vallayil N A Naikan A survey by Baldwin et al. [3] lked at the perceptins f simulatin usage frm bth academic and industry specialists and their findings indicated that simulatin tls make mdeling easier and faster. Luca pdfillini et al [4] presented a simulatin apprach which allws estimating all f the imprtance measures f the cmpnents at a given perfrmance level in a single simulatin, prvided that the cmpnents are independent. He has als a generalized cncept f imprtance measures fr multi state systems (MSS) cnsidered. The generalized measures allw the quantificatin f the relevance f the fact that a cmpnent achieves a given level f perfrmance with respect t a measure f system perfrmance such as the mean system unavailability. The cmputatin f the imprtance measures assciated with the cmpnents f a system prvides useful infrmatin t system analysts and design engineers. The large scale systems have been analyzed by either apprximate empirical methds r by mathematical reliability/availability analysis, which requires severely limiting assumptins abut cmpnent failure and repair time distributins and abut cmpnent linkages. The simulatin mdeling apprach is very accurate fr determining time between failure and time t repair distributins withut any limiting assumptins. Discrete simulatin mdeling is shwn t be f value in determining the time between failure and time t repair distributins at varius pints in series/parallel and nn-series/parallel, crss linked systems. Mst real wrld systems, such as pwer, telephne, gas, water, and electr/mechanical systems, are extremely large and have crss linked cmpnents that are nt well behaved statistically, which make them impssible t analyze accurately and efficiently using mathematical reliability/availability analysis [5]. During the early stages f cnceptual design, the ability t predict reliability is very limited. Withut a prttype t test in a lab envirnment r field data, cmpnent failure rates and system reliability perfrmance are usually unknwn. A ppular methd fr early reliability predictin is t develp a cmputer mdel fr the system. Hwever, mst f these mdels are extremely specific t an individual system r industry. Stephen W et al [6] prpsed a generic simulatin mdel fr predicting system reliability withut knwing the exact failure rate fr the cmpnents in the system at the cnceptual design f the systems. Klarik et al [7] presented a simulatin mdel, as well as the technique fr its develpment which demnstrates a methd fr studying pssible reliability characteristics f a system in the early design stages. It was cmpatible with methds f sensitivity analysis and prvides life cycle reliability utputs in a distributinal frm. Lambrs et al [8] presented a simulatin methd fr reliability analysis f linear dynamical systems based n simple additive rules f prbability. Landers et al [9] reprted a simulatin mdel fr use in the engineering design prcess. This simulatin mdel facilitates reliability mdeling by design engineers and reliability analysts early in the design prcess. The mdel applied t preliminary feasibility and design tradeff studies. This mdel fcused n applicatins t missin reliability analysis. Rtab Khan [10] perfrmed availability simulatin which is a useful tl nt nly n evaluating plant perfrmances but als in indicating pssible ways f imprving plant perfrmance. Plant availability has estimated using the plant cnfiguratin and actual failure and repair time distributins. Thmas et al [11] described mdeling techniques fr

5 Review f Simulatin Appraches in Reliability and Availability Mdeling 373 simulating the prductin availability f cntinuus prcess plants based n the cnfiguratin, thrughput capabilities and dwntime distributins f its cmpnent prcess units and the capacities f any intermediate buffer strage between prcess units. Labeau [12] presented a biased simulatin which gives the marginals and cmpares different ways f speeding up the integratin f the equatins f the dynamics and quted that simulatin seems t be the nly practical way f dealing with the size f realistic prblems f prbabilistic dynamics. O Kane [13] shwn that simulatin technlgy can be used t help supprt reengineering activities and the mdeling studies allwed the case study cmpanies t analyze system perfrmance and t ptentially achieve maximum prductivity in a cst effective manner. The use f simulatin methdlgy in the small t medium sized enterprise (SME) sectr is smewhat verlked and mst simulatin studies tend t fcus n larger rganizatins. There is a strng argument t make mre use f simulatin in rganizatins and t maximize the benefits that can be accrued thrugh it use. This is even mre imprtant within the small business sectr as simulatin has nt been widely applied t SME s t enable these types f rganizatins t reap the benefits frm adpting and embracing this technique [14]. The simulatin apprach vercmes the disadvantages f the analytical methd by incrprating and simulating any system characteristic that can be recgnized. It can prvide a wide range f utput parameters including all mments and cmplete prbability density functins. It can handle very cmplex scenaris like nn-cnstant transitin rate, multi state systems and time dependent reliability prblems. Hwever, the slutin time is usually large and there is uncertainty frm ne simulatin t anther. But as indicated by Yanez et al [15] the demerits f simulatin can be easily vercme with few mdificatins in the simulatin. It is t be nted that the experimentatin required is different fr different types f prblems and it is nt pssible t precisely define a general prcedure that is applicable in all circumstances. Hwever, the simulatin technique prvides cnsiderable flexibility in slving any type f cmplex prblems. 2.1 Types f Simulatin methds fr system reliability and availability analysis Fllwing simulatin methdlgies are used fr system reliability and availability analysis. Mnte Carl simulatin Discrete event (DE) simulatin Subset simulatin Hybrid subset simulatin Simulated annealing Stchastic simulatin apprach Digital simulatin methds These are briefly discussed in this sectin Mnte Carl simulatin in Reliability and availability studies Mnte Carl simulatin apprach is bvius chice fr cmplex envirnments as this methd allws cnsidering varius relevant aspects f system peratins which cannt be easily captured by analytical methds. The methd cmmnly used t slve the given prblem deterministically and t btain its verall prbabilistic characteristics and als t study the uncertainty in it is called the Mnte Carl simulatin technique. The name itself

6 374 Meesala Srinivasa Ra and Vallayil N A Naikan has n significance, except that it was used first by Vn Neumann during Wrld War II as a cde wrd fr nuclear weapns wrk at the Ls Alams Natinal Labratry in New Mexic. Mst cmmnly the name Mnte Carl is assciated with a place where gamblers take risks. This technique has evlved as a very pwerful tl fr engineers with nly a basic wrking knwledge f prbability and statistics fr evaluating the risk r reliability f cmplicated engineering systems. The Mnte Carl simulatin technique has six essential elements; defining the prblem in terms f all the randm variables; quantifying the prbabilistic characteristics f all the randm variables in terms f their PDFs f PMFs and the crrespnding parameters; generating the values f these randm variables; evaluating the prblem deterministically fr each set f realizatins; extracting prbabilistic infrmatin frm such realizatins; and determining the accuracy and efficiency f the simulatin. This technique is used fr uncrrelated as well as fr crrelated randm variables. In the reliability cmmunity the tw main categries f evaluatin techniques are analytical and simulatin. Mnte Carl simulatin techniques have been used t evaluate the reliability f real engineering systems [16]. In the Mnte Carl simulatin apprach, system reliability evaluatin is perfrmed by randmly determining the rate f each cmpnent and by the applicatin f an apprpriate evaluatin functin, assessing if the system succeeded r failed. A single simulatin run generates either a system success r failure, and multiple simulatin runs (replicatins) can be used t determine a reliability estimatr [17]. Mnte Carl simulatin is recgnized as a prper evaluatin technique if cmplex perating cnditins are cnsidered r the number f events is relatively large [18]. Mnte Carl simulatin methd has its ability in handling sequential peratins reliability prblems and wide applicatins t human errr analysis [19]. The Mnte Carl simulatin methd can be applied t predict r study the perfrmance and respnse f a large system and t analyze cmplex prbability prblems, that is, its majr usefulness and advantage ver analytical methds wuld be mst apparent in prblems where analytical mdels are mathematically intractable [20]. The Mnte Carl apprach is a natural ne t the prblem f parameter estimatin in the presence f uncertain data, and may be the nly practical frmal apprach when cnsidering many parameters at nce. Applicatins t realistic cmmn cause failures data indicate that this apprach is accurate and quick when advantage can be taken f intermediate analytical results (i.e., when emplying cnjugate prir distributins and likelihd functins), even when analyzing highly redundant systems [21]. Mnte Carl simulatin a technique that repeatedly generates randm values fr uncertain variables t simulate a mdel accunts fr the effects n risk factrs such as vehicle psitin and cnsumptin f prpellants, weather uncertainties, vehicle guidance, and vehicle perfrmance deviatins. Mnte Carl simulatin is als used t determine the launch decisins [22]. Lewis et al. [23] frmulated the evaluatin f fault trees fr the unreliability f repairable systems as a Markv prcess suitable fr effective simulatin by Mnte Carl methds. A variety f variance reductin techniques beynd thse discussed may lead t further imprvements in cmputatinal efficiency; these may include Russian Rulette and splitting, crrelated sampling, and number f imprtance sampling techniques. Lewis et al. [24] demnstrated inhmgeneus Markv Mnte Carl simulatin t treat wear, preventive maintenances and cmbinatins f revealed and unrevealed failures fr multi cmpnent systems. They allw wear and preventive maintenance t be mdeled

7 Review f Simulatin Appraches in Reliability and Availability Mdeling 375 within the simulatin f large systems. Mrever, a limited class f repair mdels can als be included fr bth revealed and unrevealed failures. This methd can be easily extended t accunt fr fixed cmpnent dwntimes fr testing and repair f unrevealed failures as well as fr imperfect repair. Heung et al [25] stated that the Mnte Carl simulatin methd has been widely used fr the analysis f uncertainty prpagatin in fault tree analysis and develped the Mnte Carl methd withut srting by using the segmentatin between the sufficient upper bund and the sufficient lwer bund f the evaluated tp event frequencies int meshes and interplatin within the mesh. Celeux et al [26] prpsed a Bayesian methdlgy which makes use f Markv chain Mnte Carl algrithms which allws the analyst t discard limitatins n the parametric flaw distributin functin, n the flaw prbability f detectin functin, and n the flaw sizing errr distributin functins. Mnte Carl simulatin techniques having intrinsic ptentialities which allw taking int accunt many relevant aspects invlved in a prbabilistic safety assessment (PSA) analysis [27]. The Mnte Carl simulatin technique in which experiments are cnducted n a digital cmputer is a very pwerful technique fr pwer system reliability evaluatin. Mnte Carl simulatin methds estimate the reliability indices by simulating the actual prcess and randm behavir f the system. The methd therefre treats the prblem as a series f real experiments. Mnte Carl simulatin may be preferable if nn expnential time distributins have t be mdeled, the basic characteristics f peaking units have t be cnsidered r the distributins assciated with the utput indices are required. Simulatin methds based n the Mnte Carl technique permit the system reliability t be quantitatively evaluated, even in the mst cmplex cases [28]. Zi [29] utilized the Mnte Carl simulatin methd fr mdeling the multi-state system reliability and fr the estimatin f the imprtance measures f multi state elements which entails evaluating the system utput perfrmance under restrictins n the perfrmance levels f its multi-state elements Discrete event (DE) simulatin in Reliability and availability studies A gd discrete event simulatin mdel can replicate the perfrmance f an existing system very clsely and prvide decisin maker insights int hw that system might perfrm if mdified, r hw a cmpletely new system might perfrm. T achieve this fidelity t the perfrmance f a real wrld prcess, a DES mdel requires accurate data n hw the system perated in the past r accurate estimates n the perating characteristics f a prpsed system. DES mdels can represent a system in a cmputer animatin that can prvide a decisin maker an excellent verview f hw a prcess perates, where backlgs and queues frm, and hw prpsed imprvements t the system might alter the system s perfrmance. DES als gives the decisin maker the capability t mdel and cmpare the perfrmance f a system ver a range f alternatives. DES has capabilities that make it mre apprpriate t the detailed analysis f a specific, well defined system r linear prcess, such as a prductin line r call center. These systems change at specific pints in time: resurces fail, peratrs take breaks, shifts change, and s frth. DES can prvide statistically valid estimates f perfrmance measures assciated with these systems, such

8 376 Meesala Srinivasa Ra and Vallayil N A Naikan as number f entities waiting in a particular queue r the lngest waiting time a particular custmer might experience. DES mdelers ften invest a great deal f effrt analyzing histrical data t capture prcess means, variances, and distributins, but nce entered int the mdel these parameters ften remain fixed. There is less emphasis in DES mdels n identifying events that might trigger changes in the mdel s parameters. Simulatin mdeling in the frm f discrete event (DE) simulatin has been used fr many years t analyze different types f rganizatins and the benefits f adpting simulatin are well knwn. In ne f the leading textbks n discrete event simulatin (DES), Law and Keltn [30] defined a system as a cllectin f entities that interact tgether twards the accmplishment f sme lgical end. DES cncerns the mdeling f a system as it evlves ver time by a representatin in which the state variables change instantaneusly at separate pints in time. DES is used t gain an understanding f hw an existing system behaves, and hw it might behave if changes are made in the system. Warringtn et al [31] described that system reliability can be achieved by a cmbinatin f cmpnent reliability, system architecture and maintenance. DES is an imprtant tl t assess the cmbined influence f these factrs. DES f safety and reliability des nt need t mdel cmpnent reliability, system architecture and maintenance using a single methdlgy. Rather, DES may adpt the mst apprpriate methdlgy fr each. And the authrs prpsed a methd that integrates DES with path sets t allw dynamic system mdeling. Thara Angskun et al [32] analyzed the reliability f a self-healing netwrk fr parallel runtime envirnments using discrete event simulatin. This netwrk is designed t supprt transmissin f messages acrss multiple ndes and at the same time, t prtect against nde and prcess failures. Results demnstrated the flexibility f a discrete event simulatin apprach fr studying the netwrk behavir under failure cnditins and varius prtcl parameters, message types, and ruting algrithms. The authrs studied the influence f varius factrs n the netwrk behavir in failure circumstances. Leemis L M, et al [33] nted that discrete event simulatin (DES) can be treated as a methd t mdel the behavir f a system in respnse t designated events as time prgresses. It ffers an alternative t traditinal analytical mdels as it can capture details f the system and illustrate the influence f varius factrs. Juan et al [34] discussed the cnvenience f predicting, quantitatively, time dependent reliability and availability levels assciated with mst building r civil engineering structures by reviewing different appraches t these prblems and prpsed the use f discrete event simulatin as the mst realistic way t deal with them, especially during the design stage. Kim H L et al [35], prpsed a discrete event simulatin mdel fr the availability analysis f weapn systems by incrprating the missins, peratinal tasks and system reliability structures t analyze the availability f weapn systems. The main drawback f this discrete event simulatin methd is that they are cmputer time intensive Petri nets Based Discrete Event Simulatin Petri nets (PN), develped by Carl Petri and is a useful tl fr analyzing and mdeling the cmplex systems with cncurrent discrete events. First, PN research was mainly

9 Review f Simulatin Appraches in Reliability and Availability Mdeling 377 fcused n perfrmance analysis f discrete systems, such as cmmunicatin prtcls, cmputer architecture, hardware and sftware systems, fr example t mdel micrprcessr architecture. Varius PN applicatins in several industrial engineering fields are described in scientific literature, such as Flexible Manufacturing System (FMS) mdeling and just in time systems mdeling [36]. Bertlini et.al [37], develped a new methdlgy fr reliability mdeling able t use the data cllected in an FMECA analysis t simulate the reliability behaviur f a cmplex system and the effects f different maintenance plicies. This methd cmbines the FMECA analysis with the Petri nets, riented graphs able t simulate the behaviur f cmplex systems with cncurrent events. It is nly in the last few years that PN have been intrduced in the field f maintenance and reliability analysis. Mst f this recent research wrk still cncentrated n the reliability analysis f fault tlerant cmputer systems and cmmunicatin netwrks [38]. Au et al [39] described that in the previusly existing stchastic Petri net frmulatins, memry was assciated slely with transitins, which resulted in certain difficulties in mdeling the changes in the system cnfiguratin while preserving the memry and intrduced the cncept f aging tkens and demnstrated that these aging tkens significantly imprve the dependability mdeling flexibility and clarity f stchastic Petri nets. The multitude f existing variatins f Petri net frmalism might have excellent mdeling capabilities, but lack a unified standard; as a result, what is referred t as SPNs can vary drastically frm ne applicatin r paper t anther and indicated that such ambiguity can be quite cnfusing fr reliability practitiners, and by and large SPNs are perceived as a technique that is perhaps pwerful but cumbersme and smewhat arcane. It is quite characteristic that SPNs are ften absent frm the list f cmpared techniques fr system dependability (a measure f system perfrmance that includes reliability, availability, and safety). Similarly, SPNs are nly briefly mentined (if at all) in bks n the subject. Althugh the Petri Nets can theretically mdel the behavir f the systems, the main drawback f the apprach is the distance frm mdelers r user friendly ness : the syntax elements (places, transitins, arcs and tkens) are nt directly representing r d nt have any lgic crrespndence with the part f the system being mdeled. Currently, the majr drawback f Petri Nets is the lack f readily available sftware packages. While Markv Chain analysis appears in mst f the majr reliability sftware tls such as thse frm Relex Sftware, Petri Net sftware applicatins are bscure and difficult t integrate with existing sftware tls. The underlying structure f all Petri Net sftware is a cde-based architecture. Different prgrammers use different languages fr each sftware package and the learning curve assciated with each package can be steep Subset simulatin in Reliability and availability studies Subset simulatin [40] has been recently develped as an efficient simulatin methd fr cmputing small failure prbabilities fr general reliability prblems with n special regard t any characteristics f the system. Its efficiency stems frm the bservatin that a small failure prbability can be expressed as a prduct f larger cnditinal failure prbabilities that can be estimated with much less cmputatinal effrt. By estimating the

10 378 Meesala Srinivasa Ra and Vallayil N A Naikan larger cnditinal failure prbabilities t btain an estimate fr the failure prbability, the prblem f simulating rare events in the riginal prbability space is replaced by a sequence f simulatins f mre frequent events in the cnditinal prbability spaces. Hwever, generating samples in the cnditinal spaces is nt a simple task. Subset simulatin makes use f Markv Chain Mnte Carl (MCMC) simulatin t generate cnditinal samples frm a specially designed Markv chain with limiting statinary distributin equal t the target cnditinal distributin. An essential aspect f the implementatin f subset simulatin is the chice f prpsal distributin, which gverns the generatin f the next sample frm the current ne in the MCMC algrithm and which influences the efficiency f the algrithm. The chice shuld depend n the nature f the uncertain parameters as well as the sensitivity f the failure prbability t each f these parameters [41], requiring the prpsal distributin t be tailred t each particular class f reliability prblems. A new subset simulatin apprach prpsed by Ching et al [42] fr reliability estimatin fr dynamical systems subject t stchastic excitatin and it is applicable t general causal dynamical systems and it is rbust with respect t the dimensin f the uncertain input variables Hybrid subset simulatin in Reliability and availability studies Au et al. [43] prpsed a hybrid subset simulatin methd fr dynamic reliability prblems that cmbines subset simulatin with Markv Chain Mnte Carl algrithm and subset simulatin with splitting and als this hybrid subset simulatin apprach perfrms satisfactrily cmpared with the subset simulatin methds. Mrever, the new apprach is mre rbust in the sense that it is less sensitive t the chices f prpsed prbability density functin fr the Markv Chain Mnte Carl algrithm and t the selectin f the intermediate threshld levels Simulated annealing in Reliability and availability studies Simulated annealing (SA) intrduced by Kirkpatrick et al. and Cerny [44] as an alternative f the lcal search, is a general prbabilistic methd fr slving cmbinatrial ptimizatin prblems. SA is an apprach t search the glbal ptimal slutin that attempts t avid entrapment in pr lcal ptima by allwing an ccasinal uphill mve t inferir slutins. Simulated annealing is a technique, which was develped t help slve large cmbinatrial ptimizatin prblems. It is based n prbabilistic methds that avid being stuck at lcal minima. It has prven t be a simple but pwerful methd fr large scale cmbinatrial ptimizatin. Angus and Ames [45] prpsed a simulated annealing algrithm t find the minimum cst redundancy allcatin subject t meeting a minimal reliability requirement fr a cherent system f cmpnents. It is assumed that cmpnents are independent f ne anther, and that the frm f the nminal system reliability functin is available fr input t the algrithm. In ne f the leading texts n reliability, Ku et al [46] were cncerned with great ptentials fr simulated annealing applicatin in the reliability design prblem. Lash Kari [47] develped a simulated annealing based algrithm t slve the multi bjective, multiple prcess plan mdel and this algrithm slves the multi bjective cellular manufacturing systems design mdel and generates near ptimal slutins fr

11 Review f Simulatin Appraches in Reliability and Availability Mdeling 379 medium t large sized prblems. Kim et al [48] prpsed a simulated annealing algrithm t search the ptimal slutin f reliability redundancy allcatin prblems with nnlinear resurce cnstraints and several test prblems are investigated t shw its effectiveness. The applicatin f the simulated annealing is expanded t the reliability redundancy allcatin prblems, which can help reliability engineers design the system reliability Stchastic simulatin in Reliability and availability studies Stchastic simulatin, als knwn as kinetic Mnte Carl, is a numerical prcedure fr determining the dynamics f a cntinuus time Markv prcess. A cntinuus time Markv prcess is a memry less stchastic prcess that is used t describe all srts f systems. The slutin f a Markv prcess includes tw equivalent parts: a time dependent prbability distributin f states in state space r trajectries f the state mving in state space ver time. By cmputing an ensemble f trajectries, ne can generate the distributin. Or, by cmputing the distributin, ne can sample it t btain trajectries. If the state space f the Markv prcess is discrete, it is called a jump Markv prcess and its prbability distributin is gverned by the Master equatin. If the state space is cntinuus, it is called a cntinuus Markv prcess and its distributin is gverned by the Fkker Planck equatin. Fr all but the mst trivial systems, the Master equatin is analytically unslvable. Fr large dimensinal systems (i.e. many chemical species), the Fkker Planck equatin is impractical t slve. Stchastic simulatin is a way t generate trajectries f a Markv prcess and then t cmpute the distributin f all pssible trajectries, effectively sidestepping the prblems with slving either the Master r Fkker Planck equatins. Of curse, fr sme systems, stchastic simulatin can be as impractical, mtivating the usage f hybrid stchastic simulatin methds. Verma et al [49] prpsed a stchastic simulatin apprach applied t availability evaluatin f AC Pwer supply system f Indian Nuclear Pwer Plant (INPP) and emphasizes the imprtance f realistic reliability mdeling in cmplex peratinal scenari with Mnte Carl simulatin apprach and simulatin prcedure fr evaluating the availability/reliability f repairable cmplex engineering systems having stand by tested cmpnents. The same simulatin mdel finds applicatin in imprtance measures calculatin, technical specificatin ptimizatin and uncertainty quantificatin. Arthur et al [50] prpsed a stchastic prductin cst simulatr which gives a methd f simulating the annual peratinal cst f an electrical pwer system. The significant aspects f this simulatin methd are; the methd f simulatin was chrnlgical, the uncertainty f unit availability was mdelled and fuel/emissin cnstraints were adptively met. The purpse f their wrk is t describe a methd f stchastic simulatin. The first part f their wrk is a summary f the methd used fr chrnlgical simulatin, while the last part f the wrk describes a Mnte Carl type f sampling that is applicable fr an annual simulatin. Such a sampling methd is necessary because f the emissin cnstraints and the fuel cnstraints which are adaptively met in actual system peratin. Thus, the annual stchastic prductin cst simulatin shuld reflect the adaptive peratinal decisins Digital simulatin methds in Reliability and availability studies Accrding t Shannn [51] digital cmputer simulatin is the prcess f designing a mdel f a real system and cnducting experiments with this mdel n a digital cmputer fr a specific purpse f experimentatin. Digital simulatin methds, widely used in

12 380 Meesala Srinivasa Ra and Vallayil N A Naikan many fields, can in sme cases be a gd tl t use t avid methdlgical prblems in studies f typical cntrl rm peratins and als fr efficient reliability evaluatin prcesses [52]. As the cmplexity f engineering systems increases and the demands n designers and peratrs t carry ut reliability studies intensify, much attentin is being directed twards the develpment f reliability assessment tls. Recent advances in digital prcessr design, the develpments in simulatin methdlgies and the advances in special purpse simulatin languages have made the technique f system simulatin ne f the mst widely used and accepted tls in the analysis f system perfrmance in general, and reliability assessment in particular [53]. Chenming Hu [54] has described mtivatin and challenges f IC reliability simulatin prcess using BERT simulatr which can be used either SPICE 2 r 3 in circuit analysis by indicating that a reasnable gal is t simulate circuit reliability and failure rate with CPU time twice that f typical SPICE simulatins s that design fr reliability adds nly a mderate effrt t the rutine prcess f design fr perfrmance. And als indicated that the reliability mdels must be simple, yet accurate and general enugh t pin pint majr reliability weak spts in a circuit and t always crrectly predict at least the relative changes in what if design prcedures. Lu et al [55] described that as billins f transistrs are integrated int a high end chip, traditinal circuit simulatrs such as SPICE are inefficient fr VLSI signal analyses wing t its intlerable cmplexity. As a result, a number f methds are prpsed recently fr efficient signal analysis, fr instance the wavelet analysis methd and S dmain circuit reductin simulatin methds Rare event simulatin in system reliability and availability analysis Rare event is an event that is deemed t be rare with very lw prbability and is the ccurrence f large delay dispersins amng the items. Fr example, the simulatin f a netwrk r even a single switch t estimate the prbability f ccurrence f such rare events wuld require a very large simulatin time if accmplished thrugh a traditinal Mnte Carl technique. This has stimulated the applicatin f existing, and the creatin f new, advanced simulatin techniques t estimate these very lw prbabilities t reduce the simulatin time dwn t reasnable values as fllws. Cancela, H et al [56] studied the rbustness measures, the standard nes in the literature being bunded relative errr and bunded nrmal apprximatin. By cnsidering the prblem f estimating the reliability f a static mdel fr which simulatin time per run is the critical issue, in this wrk, it has been defined bunded relative efficiency and generalized bunded nrmal apprximatin prperties f the tw previus measures in rder t encmpass the simulatin time with an illustratin which gives hw a user can have a lk at the cverage f the resulting cnfidence interval by using the s called cverage functin. Altamiran [57] derived efficient imprtance functins fr netwrks with tw stages and different ndes in each stage. Sme apprximatins were used t derive the frmulas. The gdness f such apprximatins was supprted by the simulatin results btained; very lw values f the inefficient factr and thus efficiencies clse t the ptimal REpetitive Simulatin Trials after Reaching Threshlds (RESTART) efficiency were btained with the imprtance functins. This methdlgy can be extended t ther netwrks. Dupuis. P et al [58] discussed the issues

13 Review f Simulatin Appraches in Reliability and Availability Mdeling 381 like hw sub slutins f the HJB equatins assciated with a variety f rare event prblems culd be used t cnstruct and rigrusly analyze efficient imprtance sampling schemes, the characterizatin via sub slutins f a PDE fr the purpses f practical cnstructin f imprtance functins. Several authrs have applied the rare event simulatin technique in evaluating and analysis f reliability parameters f systems. They have fcused n utilizing this simulatin apprach in varius purpses like in apprximating the cntinuus time mdel by a discrete parameter semi Markv prcess fr a reliability mdel f a tw unit parallel system; in the estimatin f prbabilities f rare but ptentially damaging events in Markvian systems; in the ptimizatin invlving rare events n discrete event simulatin systems based n likelihd rati and imprtance sampling methds; in the cntext f the estimatin f rare events in Asynchrnus Transfer Mde (ATM) netwrks; in develping a splitting based imprtance sampling technique fr a very general class f mdels including reliability mdels with general repair plicies. The literature analysis n varius types f simulatin methds in reliability studies shws that by using simulatin methdlgies, varius types f reliability prblems can be slved very easily when cmpared with cmplex analytical methds. But s far, the simulatin methdlgies are nly used t speed up the slutin prcesses r used partly in the ttal analysis f reliability studies f systems. The kinetic Mnte Carl simulatin methd used as a numerical prcedure fr determining the dynamics f a cntinuus time Markv prcess, a simulated annealing algrithm used t search the ptimal slutin f reliability redundancy allcatin prblems, subset simulatin used fr cmputing small failure prbabilities fr general reliability prblems and t generate cnditinal samples frm a specially designed Markv chain with limiting statinary distributin equal t the target cnditinal distributin, and Mnte Carl simulatin used t generate randm values fr uncertain variables are sme f the examples fr this. Xia Feng et.al. [59] have prpsed a cmbined dynamic fault tree (DFT) and numerical simulatin based n the minimal sequence cut set (MSCS) methd t evaluate reliability f fault tlerant system with repairable cmpnents as an alternative t the Markv apprach. Apart frm cnstant failure rate cases (expnential distributin), their methd can be used fr any type f failure time distributin. Even thugh the simulatin methdlgy is a pwerful tl, s far it was used in limited areas and fr limited purpses in the reliability and availability mdeling and analysis f systems. Therefre the authrs feel that there is still a lt f scpe fr tapping the full ptential f simulatin methdlgy in reliability and availability mdeling and analysis f engineering systems. The authrs prpsed System Dynamics Simulatin in Reliability and Availability mdeling and analysis f systems. 3. System Dynamics Simulatin in Reliability and Availability mdeling Ra and Naikan [60] have identified sme limitatins f the state space apprach based n the available literature. The state space apprach fr reliability and availability studies f nn-repairable as well as repairable systems requires slutin f large number f cmplicated Chapman Klmgrv system f differential equatins. This is generally perfrmed by traditinal appraches like Laplace transfrms methd r Lagrange s methd, supplementary variable techniques, matrix methds and apprximate numerical appraches. Mrever, in many situatins these techniques becme extremely cmplex

14 382 Meesala Srinivasa Ra and Vallayil N A Naikan and difficult r impssible t apply. Mst published literature are fcused n evaluatin f steady state availability assuming that this ccurs at time equals t infinity. Hwever, in practical systems this is nt realistic. In practice, the system reaches steady state after a certain initial perid f time. The time taken fr a system t reach steady state, and the steady state availability are imprtant system parameters f repairable systems. The literatures d nt address this prblem. There have been attempts in the literature t evlve mre realistic techniques including simulatin apprach fr reliability and availability analysis f systems. These limitatins have been addressed by Ra and Naikan [61-63] by mdeling the systems using basic principles f system dynamics simulatin in cnjunctin with the well-knwn Markv apprach. The authrs call this a hybrid Markv system dynamics (MSD) apprach. This apprach des nt require tedius mathematical treatment f cmplex differential equatins fr time dependent as well as steady state availability and reliability analysis. The authrs have als prpsed MSD apprach fr reliability and availability mdeling f different cnfiguratins including multi stage degraded systems analysis and serial prcesses in prcess industries. The results f Markv System Dynamics (MSD) simulatin apprach are validated with cnventinal state space apprach. The prpsed apprach has simplified the state space apprach by eliminating rigrus mathematical treatment f the prblem. The MSD simulatin apprach is als capable f identifying the steady state pint at which a system reaches its steady state. Fr details, readers may refer Ra and Naikan [64-65]. Ra and Naikan [66-68] have als used this methd fr sensitivity analysis f system reliability and availability. The prpsed apprach can cmpletely eliminate the tedium f rigrus mathematical slutin prcedures f cmplex cnventinal methds. Ra and Naikan [69] perfrmed Reliability Analysis f Repairable systems using System Dynamics Mdeling and simulatin. In this wrk the authrs prpsed a framewrk which was illustrated fr a standby system with repair. The results f the simulatin when cmpared with that btained by traditinal Markv analysis clearly validate the MSD apprach as an alternative apprach fr repairable systems reliability analysis. The prpsed methdlgy is applicable fr all types f failure rates and repair rates and it is much simpler cmpared t traditinal appraches. Ra and Naikan [70] prpsed a hybrid apprach called as Markv System Dynamics apprach fr availability mdeling and t study the dynamic behavir f systems. The prpsed framewrk has illustrated fr a single unit repairable system with a numerical example. The results f the simulatin when cmpared with that btained by traditinal Markv analysis clearly validate the Markv System Dynamics apprach as an alternative apprach fr availability analysis. The prcedure fr the develpment f the MSD apprach fr this system was explained and the mdel was run t bserve all f its states. It has als shwn that the MSD apprach clearly indicates the time at which the system reaches its steady state. It is wrth mentining here that finding the steady state cnditin is extremely difficult r impssible using traditinal appraches. Mrever, the MSD mdel develped in this wrk can calculate the pint, interval availabilities with time varying failure and repair rates r which are user defined distributins. Ra and Naikan [71] presented a System Dynamic mdel fr transient availability mdeling f repairable redundant Systems. In this wrk, the prpsed framewrk has

15 Review f Simulatin Appraches in Reliability and Availability Mdeling 383 illustrated fr a tw cmpnent active redundant system with repair with cnstant failure and repair rates. Thereafter, transient availability mdeling with time varying failure and repair rates was perfrmed fr the same system.. The results f MSD simulatin are cmpared with that btained by traditinal Markv methd fr validatin. This has shwn that MSD simulatin is a gd alternative t the traditinal mathematically intensive methds. Ra and Naikan [72] develped a nvel Markv system dynamics (MSD) simulatin framewrk fr the reliability mdeling and analysis f a repairable system. The prpsed framewrk has illustrated fr a repairable tw cmpnent system. The results f the simulatin btained in this wrk when cmpared with that btained by traditinal Markv analysis clearly validate that this nvel MSD apprach is an alternative apprach fr reliability mdeling and analysis. The prcedure fr the develpment f the MSD apprach fr this system was explained and the mdel has run t bserve all f its states. Frm the abve wrks f the authrs, it is clear that the MSD simulatin mdels can be run very easily using a digital cmputer with any cmmnly available system dynamics sftware. Anther imprtant aspect f this apprach is that it is capable f incrprating any type f failure and repair rates such as cnstant, increasing, decreasing and user defined failure and repair rates. Mrever, it is pwerful t give time dependent reliability and availability f the system at any given time withut any additinal effrt. This methd is capable f mdeling and simulatin f any level f cmplex systems. Only limitatin culd be cnstructing the state transitin diagram and therefre the cmprehensive Markv system dynamic diagram fr a given system. Hwever, with basic knwledge f reliability and system dynamics this will nt be an issue. It is wrth mentining here that the Markv system dynamics mdeling is much easier cmpared t the traditinal appraches. It is expected that a paradigm shift frm cnventinal methds t Markv system dynamics simulatin seems t be the mst prmising reliability and availability mdeling and analysis strategy fr systems. Mre research wrk in this area is expected frm reliability engineering researchers acrss the wrld. 4. Critical bservatins frm the abve literature survey The fllwing bservatins can be made frm the literature survey cvered in the earlier sectins. * As the systems becme mre cmplex, the analytical techniques becme mre difficult t apply. * Simulatin techniques can be used t perfrm the reliability and availability analysis f systems. * Simulatin apprach vercmes certain disadvantages f the analytical methd by incrprating and simulating any system characteristic that can be recgnized. * Simulatin can prvide a wide range f utput parameters including all mments and cmplete prbability density functins. * Simulatin can handle very cmplex scenaris like nn-cnstant transitin rate, multi state systems and time dependent reliability prblems. * The simulatin techniques are cnceptually simpler fr calculating the reliability measures but cnsume cnsiderable cmputer time, especially when perfrming sensitivity studies.

16 384 Meesala Srinivasa Ra and Vallayil N A Naikan * Smetimes it may be pssible t apply a hybrid apprach, that is, part slutin by analytical methds and part by simulatin. Fr example, the system base prbabilities may be calculated by analytical mdels and the prbabilities f delays by specific system deficiencies calculated by simulatin and the tw results cmbined t yield demand based measures. * Simulatin has been used as a pwerful tl fr mdeling and analysis f system reliability and availability. It is used t represent the dynamic behavir f systems in the mst realistic sense. * There is a need fr further develpment f the analytical and simulatin methds fr applicatin t mre cmplex systems in deriving suitable measures f reliability and availability mdeling and analysis. 5. Cnclusins Simulatin apprach have been successfully applied fr system mdeling and prblem slving in varius areas such as manufacturing prcess, lgistics, transprtatin, business, engineering, science, agriculture, scial as well as in business systems. It is well knwn that simulatin is the best apprach when the systems are cmplex with several subsystems and cmpnents having cmplex interrelatinships. Simulatin can handle such cmplexities and the presence f stchastic variables leading t uncertainties very easily cmpared t analytical appraches. Therefre simulatin is a very pwerful tl fr studying and artificially running the system in digital cmputers and bserving the system perfrmance. It can als handle with ease any type f sensitivity analysis easily and cst effectively. Several attempts have been made fr applying simulatin in the field f reliability engineering. Varius simulatin techniques have been used in the literature as an alternative t analytical methds fr mdeling and slving cmplex reliability prblems. Imprtant simulatin methdlgies used fr system reliability and availability analysis include: Mnte Carl simulatin, discrete event (DE) simulatin, subset simulatin, hybrid subset simulatin, simulated annealing, stchastic simulatin apprach, digital simulatin methds and in the recent times the Markv system dynamic (MSD) simulatin. All these methds reduce the tedium f frmulating and slving mathematical equatins, stchastic variables and differential equatins in the analytical apprach f reliability mdeling. With the applicatin f simulatin, state space mdeling has been simplified with additinal features f incrprating nn-cnstant transitin rates between system states. Evaluatin f pint availability (as a functin f time), steady state availability, time taken fr a system fr reaching the steady state f repairable systems can nw be carried ut with the pwerful MSD apprach. Mdeling f degraded systems (Markv chains), systems having increasing and decreasing failure and repair rates (nn Markvian systems), and any ther type r cmbinatin f transitin rates can be incrprated in such simulatin. There is ample scpe fr further research in the applicatin f simulatin in reliability prblems. Simulatin apprach can be tried fr reliability mdeling f system design, allcatin, netwrks, life testing and data analysis. Simulatin is a very pwerful tl and it is nt yet explred t its full ptential fr reliability mdeling and analysis. It is expected that mre researchers will wrk in this area and the traditinal mathematically intensive reliability mdeling appraches will be simplified.