Opportunistic Actions for Subassemblies of a Reciprocating Compressor: An LCC Based Approach

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1 Iteratioal Joural of Performability Egieerig, Vol. 9, No. 3, May 2013, pp RAMS Cosultats Prited i Idia Opportuistic Actios for Subassemblies of a Reciprocatig Compressor: A LCC Based Approach MOHAMMAD ASJAD 1 *, SATISH MOHITE 2, MAKARAND S. KULKARNI 2, ad O.P. GANDHI 1 1 ITMMEC, IIT Delhi, INDIA 2 Departmet of Mechaical Egieerig, IIT Delhi, INDIA (Received o May 14, 2012, revised o August 10, 2012) Abstract: I this paper, a opportuistic maiteace approach has bee studied o a reciprocatig compressor, which cosists of series coected structure. Whe the system is dow, either uder corrective or prevetive maiteace, the opportuity to replace eve prevetive o-failed subassemblies is cosidered. The optimizatio of opportuistic actio depeds upo the failure cost, which agai depeds upo the miimum cost of opportuistic actio. The impact of opportuistic maiteace o the Life Cycle Cost (LCC) of a reciprocatig compressor has bee simulated. The case study result shows the reductio of INR 12,541,750 i LCC of a reciprocatig compressor ad esures the required level of operatioal availability, whe the opportuistic maiteace is icorporated i its traditioal maiteace approach. Keywords: Opportuistic maiteace, mechaical system, LCC, availability 1. Itroductio Mechaical systems (like machie tool, egie, compressors, etc.) start deterioratig, i geeral, with the passage of time; to upkeep them i the operatioal state, appropriate maiteace actios are required. Maiteace improves the system performace by reducig the umber of catastrophic failures. The aim of maiteace is to sustai the system performace over ad above the desired level but at miimum possible cost, so as to achieve the operatioal objective(s) of the maiteace, i geeral, ad of the system i particular. Maiteace for a mechaical system comprises of actios like ispectio, corrective, prevetive ad overhaul icludig opportuity maiteace that was first coied by Rader ad Jorgeso [1] ad McCall [2]. Opportuistic maiteace refers to a kid of prevetive actio, i which the ecessary maiteace actio for o-failed compoets/subassemblies is carried out at opportuities whe the system is dow, either correctively or prevetively. Thus, wheever a system is take for maiteace of ay kid, there may be a opportuity to do maiteace of its other compoets, which have ot failed, but their scheduled maiteace is due shortly. It ca ehace the system performace through prevetig radom breakdows by availig the opportuities of maitaiig the o-failed compoet, durig plaed ad/or uplaed maiteace activity. The opportuistic maiteace decisios deped upo the maitaiability, the available time, failure cost ad maiteace cost, etc. The maiteace cost ca be estimated from the cost icurred i differet activities like corrective, prevetive, overhauls ad opportuistic; that do cotribute i systems Life Cycle Cost (LCC). The maiteace cost may get affected by failures which ca be reduced by icorporatig the opportuistic actios durig plaed ad uplaed maiteace activities. However, the executio of opportuistic actio o o-failed compoet(s) may be carried out, whe its executio time is less tha or equal to the available dowtime. Therefore a trade-off Commuicatig author s asjad_alig@rediffmail.com 273

2 274 Mohammad Asjad, Satish Mohite, Makarad S. Kulkari ad O.P. Gadhi betwee maiteace activities ad operatioal objectives is required to have a miimum LCC with a assured level of system performace. The objective of this paper is to icorporate the opportuistic maiteace actio i a particular schedule of prevetive actio for a multi-subassemblies system subjected to high dowtime losses ad ecoomic depedece. I this work, a attempt has bee made to study the effect of opportuistic maiteace o the LCC of a reciprocatig compressor that cosists of 19 subassemblies; coected i series ad are subjected to radom failures over their operatig spa. The subassemblies are replaced/repaired o failure, ad at the same time, the opportuities for prevetive maiteace o other subassemblies that are due are also udertake. The LCC model for the reciprocatig compressor is developed, ad miimized o the basis of optimized opportuistic maiteace actio while esurig the required level of operatioal availability. Oe of the three alteratives of opportuistic actios i.e. Do Nothig (N), Repair (r) ad Replacemet (R) are chose to study their effect o the LCC. The optimizatio of opportuistic actio for a particular subassembly is based o its criticality of failure; which further depeds upo the miimal cost of the opportuistic alteratives amog the possible oes. I the ext sectio, the relevat literature, particularly dealig with opportuistic maiteace is preseted. Sectio 3 presets the mathematical models for LCC ad availability of the system. I Sectio 4, the proposed approach is illustrated by a case study, which explais the formulatio ad verifies the covergece of the solutio procedure. Sectio 5 cocludes the work ad suggests the future scope of research. Notatio a Restoratio factor A Operatioal Availability C aqi Acquisitio cost of i th subassembly i the system C fix Fixed cost to carryig out each maiteace actio, which icludes the costs of material required like lubricatig oil, etc. C Ci Cost of i th subassembly withi the system d Discout rate per aum, ad assumed to be costat throughout the life of the system dt Time differece betwee the plaed maiteace ad the opportuity E[C CA ] Expected cost of corrective actio durig ivestigatio period for a system E[C OM ] Expected cost of opportuistic actios durig ivestigatio period for a system E[C ORi ] Expected cost of replacemet of i th subassembly of the system durig opportuistic actio E[C Ori ] Expected cost of repair of i th subassembly i the system durig opportuistic actio E[C PA ] Expected cost of prevetive actio durig ivestigatio period for a system E N CM i Expected umber of failure of ith subassembly of the system E N PM i Expected umber of prevetive maiteace schedule of ith subassembly i the system E N Ori Expected umber of opportuistic repair of i th subassembly i the system E N ORi Expected umber of opportuistic replacemet of i th subassembly i the system

3 Opportuistic Actios for Subassemblies of a Reciprocatig Compressor: A LCC Based Approach 275 E[TDT] Expected dowtime for which the system is ot available INR Idia Currecy L Expected life of the system L C labour cost per uit time MTTCM i Mea time required to perform the corrective actio of i th subassembly i the system MTTPM i Mea time to perform the prevetive maiteace of i th subassembly i the system MTTRA i Mea time to replacemet of i th subassembly of the system durig opportuistic actio Number of subassemblies i the system N Do Nothig; opportuistic actio N(t/V) Coditioal umber of failure PVc Preset value of LCC r Repair; opportuistic actio R Replacemet; opportuistic actio R CA Reveue lost due to failure/breakdow R PA Reveue lost due to scheduled maiteace T Plaed operatig period T opr Actual operatig time t pm Schedule maiteace iterval t O Time at which the opportuity arises V Virtual age of the compoet V Virtual age of the uit at the time of the th repair completio V (-1)i Virtual age of the compoet before carryig out a particular maiteace actio X Prevetive maiteace iterval β Shape factor, defies the shape of distributio i Weibull η Scale parameter, defies where the bulk of the distributio lies i Weibull 2. Literature Review Opportuistic Maiteace was first itroduced by Rader ad Jorgeso [1] ad McCall [2]. Sice its itroductio, it has bee widely implemeted ad reported i the literature, which shows its effectiveess i differet segmets of egieerig. Literature pertaiig to opportuistic maiteace has bee reviewed ad described i this sectio. Zheg ad Fard [3] studied a opportuistic situatio with a maiteace policy based o failure rate tolerace for a system havig k differet types of uits. A uit is replaced either whe the hazard rate reaches a particular value ad/or at failure i a particular time iterval. Pham ad Wag [4] proposed two opportuistic maiteace policies for k-out of- system. The miimal repairs are performed o the failed subassembly before time s (a decisio variable) while corrective maiteace of all failed subassemblies is combied with prevetive maiteace of all operatig uits after time s. Dagpuar [5] proposed a maiteace policy, where replacemet of a subassembly withi the system is carried out at a opportuity, which arises whe some other part of the system fails ad eeds to be replaced. Laggoue et al. [6] studied a prevetive maiteace approach for a hydroge compressor istalled at oil refiery, by availig the opportuities to replace prevetively o-failed compoet that miimizes the productio losses. While they further studied the

4 276 Mohammad Asjad, Satish Mohite, Makarad S. Kulkari ad O.P. Gadhi opportuistic replacemet policy for the same equipmet uder the ucertaity associated i failure data that miimizes the expected cost per uit time while cosiderig the geeral lifetime distributio [7]. Samrout et al. [8] preseted a method to miimize the prevetive maiteace cost of series-parallel systems usig At coloy optimizatio. Duarte et al [9] proposed a algorithm for maiteace maagemet optimizatio of a series system based o prevetive maiteace, with all the subassemblies assumed to exhibit liearly icreasig hazard rate ad costat repair rate. Besard et al. [10] studied a opportuistic maiteace optimizatio model for offshore wid power system. The results showed 43% of cost savig i scheduled maiteace. Besard et al. [11] preseted a stochastic optimizatio model for opportuistic maiteace of offshore wid farms. They forecasted the opportuities at corrective maiteace activities that miimize up to 32% of the total cost. The effect of opportuistic maiteace will be immese, if it ca correlate with system LCC, which may be oe of the criterios for equipmet purchase [12]. I aother study, Lad ad Kulkari [13] proposed a cost based Failure Modes ad Effects Aalysis (FMEA) by idetifyig critical failure evet based o actual cost of failure to the user s, which ca be helpful i estimatig the system s LCC. LCC geerally refers to all the costs associated with a product throughout its operatig spa that icludes cost related to coceptual desig, detailed desig ad developmet, productio, product use ad support, ad phase out [14]. Asied ad Gu [15] preseted a review o the issues of LCC aalysis that have bee developed to provide egieers cost iformatio that helped them i addressig at the desig stage. Korpi ad Ala-Risku [16] reviewed the case studies pertaiig to the applicatio of LCC i various sectors. Samarakoo et al. [17] studied that LCC aalysis may be a helpful tool i makig decisios at iitial phase of a project regardig the best available ad qualified techique cosiderig ecoomic aspects. The itegratio of opportuistic maiteace with coditio based moitorig has bee studied by Koochaki et al. [18]. The authors examied the impact of opportuistic maiteace o the effectiveess of coditio based maiteace (CBM), ad results idicated that a opportuistic maiteace strategy ehaced the effectiveess of CBM. From the literature review, it is cocluded that the maiteace cost ca be reduced by icorporatig the opportuistic maiteace throughout the systems operatig spa; as the cost of simultaeous maiteace actios o various subassemblies ad/or compoets is less tha the total cost of idividual maiteace actios, ad thereby, affects at the LCC of the system. A lot of research o opportuistic maiteace has bee reported i a literature, but there seems to be paucity i its itegratio with LCC ad system availability. The proposed work i this paper is a step i this directio, which would be helpful for the cost reductio by icorporatig the opportuistic maiteace while maitaiig the required availability. The ext sectio deals with the mathematical modelig ad problem formulatio 3. Mathematical Modelig Actually, LCC is the summatio of cost estimates, from iceptio to disposal of the system [14]. From mechaical systems users poit of view, the LCC icludes acquisitio cost, operatig cost, maiteace cost, failure costs, etc. But this may differ from case to case. For example, some users may wat to evaluate the LCC i terms of maiteace cost. I this case, it comprises of maiteace cost oly. I this work, the authors have studied the effect of opportuistic actios o the LCC of the system ad cosidered

5 Opportuistic Actios for Subassemblies of a Reciprocatig Compressor: A LCC Based Approach 277 acquisitio cost, corrective maiteace cost ad prevetive maiteace cost for each sub-assembly uder this. The acquisitio cost is the fixed amout that the customer pays for the purchase of system at the iitial stage. The corrective maiteace cost depeds upo the umber of failures or corrective actios. Corrective actios are the appropriate maiteace/repair actios that are take to remove/repair ad/or replace the failed subassembly. The corrective actio cost comprises the labour cost, compoet cost, fixed cost of carryig out the maiteace actio ad associated loss of reveue. Thus, expected cost of corrective actio durig ivestigatio period E[C CA ] for a system is give below; E[C CA ] = i=1 (MTTCM i (R CA + L c ) + C Ci + C Fix ) E N CMi (1) where, MTTCM i is the mea time required to perform the corrective actio of a particular compoet/subassembly withi the system. C fix is the fixed cost to perform the corrective actio, which icludes the costs of material required like lubricatig oil, etc. C Ci is the cost of i th subassembly withi the system. L C is the labour cost per uit time. E N CM is the expected umber of failure for a particular i compoet/subassembly of the system. R CA is the reveue lost due to sudde failure ad/or breakdow. Prevetive maiteace is a scheduled maiteace actios aimed at the prevetio of failures, i geeral, ad accidets i particular. Prevetive maiteace activities iclude equipmet checks at specified periods so they replace or repair wor parts before they cause system failure. The model for calculatig the expected cost of prevetive actio durig ivestigatio period E[C PA ] for a system is give below; E[C PA ] = i=1 (MTTPM i (R PA + L C ) + C fix ) E N PM i (2) where, MTTPM i is the mea time to perform prevetive maiteace actio of a particular compoet/subassembly i the system. C fix is the fixed cost to perform prevetive actio, which icludes the costs of material required like lubricatig oil, etc. L C is the labour cost per uit time. E N PM is the expected umber of prevetive maiteace actios for each i compoet/subassembly of the system. R PA is the reveue lost due to scheduled maiteace. The maiteace of o-failed compoets either with scheduled or corrective maiteace of failed compoet is kow as opportuistic maiteace. Wheever a system is grouded for maiteace work, there may be a opportuity to do maiteace of other compoets which have ot yet failed, but have reached their threshold limit or eed maiteace work i the immediate future. The threshold limit ca be defied by the user ad/or maufacturer, based o their time to failure, residual life, reliability threshold or failure cost. The decisio for opportuistic alteratives for compoet repair/replacemet depeds upo the miimum cost of the opportuistic actio. However, i this work, the opportuistic maiteace decisios are based o failure cost (threshold limit) for each module. The three opportuistic actios i.e. Do Nothig (N), Repair (r) ad Replacemet (R) are to be executed. The expected cost uder N will be zero as this decisio implies o maiteace actio to be performed.

6 278 Mohammad Asjad, Satish Mohite, Makarad S. Kulkari ad O.P. Gadhi The model for estimatig the expected cost of replacemet ad repair uder opportuistic maiteace is give by: Expected cost of replacemet; E[C ORi ] = i=1 (MTTRA i (R CA + L c ) + C Ci ) E N ORi (3) ad the expected cost of repair; E[C Ori ] = i=1 MTTPM i (R CA + L c ) E N Ori (4) where, E N Ori ad E N ORi are the expected umber of opportuistic repair ad opportuistic replacemet of i th subassembly respectively. The expected cost of opportuistic maiteace depeds o the miimum cost of the three alteratives, which further depeds upo the failure cost associated with a particular compoet ad is estimated as : E[C OM ] = E[C ORi ] + E[C Ori ] (5) Let the expected life of the system be L years ad the cost structure of corrective, prevetive ad opportuistic maiteace remai the same throughout its life. Thus, LCC for the system expressed i terms of the preset value of cost is; L 1 PVc = i=1 C aqi + j=1 { (E[C (1+d) j PA ] + E[C CA ] + E[C OM ] )} (6) The opportuistic actios that are icorporated i the schedule maiteace do ehace system operatio. The maiteace actios are therefore required but eed time ad resources, ad thereby, improve system availability. Therefore, it is required to develop a availability model based o the maiteace actios to meet the objective. The availability is defied as the ratio of actual operatig time to the plaed operatig time. Mathematically, A = Actual Operatig Time Plaed Operatig Time Let the plaed operatig time i ay ivestigatio period be T hours. I ay ivestigatio period, let, E(TDT) be the average time for which the system is ot operatig due to maiteace actio. Thus, actual operatig time, T opr, i ay ivestigatio period ca be calculated as follows; T opr = T E(TDT) (8) Actual Operatig Time A = = T opr = T E(TDT) (9) Plaed Operatig Time T T I the above equatio, E(TDT) icludes total time required for all maiteace actios. I geeral, mechaical systems receive oe or more of the followig kids of maiteace actios (Corrective actios, Prevetive actios, ad opportuistic maiteace) durig their useful life. It is assumed that the system is dow oly due to maiteace actios ad the dowtime due to other reasos is ot cosidered. The, Expected dow time E[TDT] i ay ivestigatio period ca thus be estimated as: E[TDT] = i=1 E N CMi MTTCM i + E N PMi MTTPM i + E N ORi MTTRA i + E N Ori MTTPM i (10) where,e N CMi,E N PMi, E N ORi ad E N Ori are the expected umber of corrective, prevetive, opportuistic replacemet ad opportuistic repair respectively, durig the ivestigatio period, suffix i idicates the i th subassembly i the mechaical system. MTTCM i, MTTPM i ad MTTRA i are the average time for which the compoet is dow i each for the corrective, prevetive ad opportuistic actio respectively. (7)

7 Opportuistic Actios for Subassemblies of a Reciprocatig Compressor: A LCC Based Approach 279 Thus the availability ca ow be expressed as, A = T i=1 E N CM i MTTCM i +E N PM i MTTPM i+ E N ORi MTTRA i + E N Ori MTTPM i (11) T The expected umber of failures, MTTPM i, MTTCM i, MTTRA i depeds o reliability, maitaiability, maiteace schedule ad opportuistic maiteace for a particular compoet of a system. As stated earlier the maiteace actios affect both the cost ad performace of the system, so it is required to obtai the optimum opportuistic actio for each subassembly of a system, so as to esure the required availability at miimum possible cost. Thus, a trade-off betwee the opportuistic alteratives is required to get the desired level of system availability at the lowest possible LCC. I other words, it ca be further stated as optimize opportuistic maiteace for each module-subassembly of a system, whose cost is icluded i the objective fuctio ad the availability of the system, may be cosidered as the costrait. Thus, the problem ca be formulated as: Miimize (LCC) Subject to A Desired level of system availability The above formulated problem has bee implemeted o a real life problem, which is described i the subsequet sectio. 4. A Case Study A case study is preseted o the basis of work beig carried out i collaboratio with Burckhardt Compressio, which is oe of the leadig compressors maufacturers i the world. The effect of opportuistic maiteace o a reciprocatig compressor of Burckhardt make which is istalled at a automotive Compressed Natural Gas (CNG) statio i Natioal Capital Regio (NCR) is studied. The compressor is expected to ru 24 hrs. a day ad the dowtime cost is high. The customer expects a high level of availability, of the order of 98%, but at the miimum possible LCC. As for ay other mechaical systems, such high level of availability ca be achieved oly through effective maiteace support. As a part of the purchase deal, the customer wated Burckhardt to take the resposibility of its maiteace support. The required service level demads 98% availability of the compressor durig a moth. For maitaiig such a level of service demad, the Burckhardt has required a efficiet ad effective maiteace support effort, which is cost icurrig. With the experiece gaied over last 10 years, Burckhardt is iclied to provide maiteace support for the whole life. Both Burckhardt ad its customers have aggressive plas of expadig their operatios to ew locatios, thus the issue of maiteace support is of extreme importace i order to achieve their busiess goals. Burckhardt provides maiteace support of corrective maiteace ad scheduled maiteace for the compressor, ad expeds huge costs supportig it. The Burckhardt reciprocatig compressor cosists of 19 subassemblies, modeled as beig i series, subjected to radom failures over its useful life. The failure of ay subassembly leads to the breakdow of the etire system i.e. compressor. Thus, the opportuistic maiteace, wherei prevetive maiteace of a subassemblies is carried out durig opportuities arisig out of the failures of other subassemblies, are more appropriate for the subassemblies of the compressor. It has bee assumed that the reciprocatig compressor operates cotiuously ad fails radomly at ay istat. It has also bee assumed that repair activity ad scheduled

8 280 Mohammad Asjad, Satish Mohite, Makarad S. Kulkari ad O.P. Gadhi prevetive maiteace is iitiated immediately upo shutdow. The sub-assemblies are replaced ad repaired upo failure, ad at the same time, the opportuities for prevetive maiteace o other subassemblies are also udertake. The effective operatig time of the compressor is accumulated betwee the failures outages. The operatig life of the compressor is 12 years which is equal to operatig hours (as the system is o a average ruig 500 hrs. per moth), betwee which the system is prevetively maitaied at a scheduled iterval of hrs., after which, all the subassemblies of the system becomes as good as ew. The data is collected from the Burckhardt compressio for a reciprocatig compressor, which icludes cost, prevetive maiteace schedule, corrective, prevetive ad replacemet time, ad desig characteristic (reliability parameter which follows the Weibull distributio) for each subassemblies, as give i Tables 1 ad 2. Table 1 illustrates the differet costs that are required i estimatig the LCC. Table 2 provides the subassembly/module corrective, prevetive ad replacemet time, ad their reliability characteristics. However the costs of subassemblies are ot provided. The operatig cycle to which the opportuistic maiteace decisios will be icorporated is illustrated with the help of Figure 1. Let a system start degradig with the passage of time, after the operatio of t O hours a opportuity arises t O < t pm the there will still be dt more time remaiig for the scheduled maiteace. The radom failure show i the Figure1 is the cosequece of maiteace decisios take at a opportuity over the processig time i the period dt. The maiteace actios at the opportuity are performed i such a way that total time for maiteace work should be less tha maiteace time of a particular subassembly. Table 1: Cost Data Characteristics Cost i Rupees (INR). Fixed cost of maiteace (INR); C Fix 2500 Labor cost for maiteace (INR /hr); L c 1000 Reveue lost due to failure; R CA 3330 Reveue lost due to schedule maiteace; R PA 900 For a give subassembly, the failures occur accordig to the respective time to failure distributio. I such situatios, a ecessary opportuistic actio o the other subassembly has bee permitted. Prevetive maiteaces for these are due i ear future. Total dowtime affects the system availability; therefore the maiteace decisios take at the opportuity decrease the probability of failure ad thereby maitaiig the system availability. Therefore, the optimizatio of opportuistic actio is eeded to maitai the operatioal objective of the system. The objective of the optimizatio is to geerate a set of maiteace decisios that system esured the required availability at miimum possible LCC.

9 Opportuistic Actios for Subassemblies of a Reciprocatig Compressor: A LCC Based Approach 281 Table 2: Reliability Characteristic ad Differet Time of Repair for Differet Subassemblies Module- Subassembly β η MTTPM i MTTCM i (Hrs) (Hrs) # # # # # # # # # # # # # # # # # # # MTTRA i (Hrs) Thus, the problem for the Burckhardt ca be formulated as give below. 1 j=1 )}) L Miimize LCC (PVc = i=1 C aqi + { (E[C (1+d) j PA ] + E[C CA ] + E[C OM ] Subject to A 0.98 T t O dt Start of Life t pm Opportuity Radom Failures Ed of Life Figure 1: Mechaism of Opportuistic Maiteace It is required to estimate the umber of differet maiteace actios; which are the icorporated ito a model to assess the system LCC. The prevetive maiteace is scheduled at a iterval of operatig hrs. which is of imperfect type, thus the system is 4 times prevetively repaired durig its operatig life. The expected umber of failures (corrective maiteaces) eeds to be calculated i each year by cosiderig age at the start of that year ad restoratio achieved after each maiteace actio. The age at the start of the each year depeds o the age at the ed of

10 282 Mohammad Asjad, Satish Mohite, Makarad S. Kulkari ad O.P. Gadhi the previous year ad the degree of restoratio achieved by maiteace actios. Every time whe a corrective, prevetive ad/or opportuistic repair is performed, the age is chaged thereby affectig the umber of failures. Lad ad Kulkari [19] developed the model to calculate the coditioal umber of failures as; β β t + V N ( tv ) = ( V /η) + (12) η where, η is the characteristic parameter of a subassembly i a Weibull distributio. β is scale parameter of a compoet/subassembly/system i a Weibull distributio. V is the virtual age after icorporatig the th maiteace actio. The cocept of virtual age was first itroduced by Kijima [20]. Uder this cocept, a uit accumulates age durig each period of operatio. After each failure of compoet, the maiteace actio, removes some of the accumulated ages. Cosider a uit of equipmet that at ay poit of time, is i either of the two states i.e. fuctioig or repair; assume that the uit is iitially (at time t=0) fuctioig. Let X deote the duratio of the period betwee the ( 1) th repair completio, ad the th repair; let V deote the virtual age of the uit at the time of the th repair completio. Kijima s model of virtual age is give as; V =V 1 + (1 a)x, such that 0 a 1, adv 0 = 0 (13) where, a is some costat, kow as restoratio factor, which captures the degree of equipmet restoratio achieved through repair actio. While usig system improvemet model show i Equatio 13, differet degrees of restoratio are used for ispectio, corrective, prevetive ad overhauls. Thus, the legth of a iterval for which the equipmet fuctios deped o the virtual age of the equipmet at the begiig of the iterval. It is to be oted that perfect repair (a=0), ad miimal repair (a=1) are both special cases of this virtual age model. The virtual age is calculated o the basis of icorporated maiteace actios ad their restoratios, which is put i Equatio No. 12 to estimate the expected umber of failures. A Mote Carlo simulatio model for the reciprocatig compressor has bee developed usig discrete-evet framework i MATLAB (R2010a). The model is simulated ad optimized for the data obtaied from Burckhardt. Optimizatio of the radom search method is used, which is a ituitive method of searchig for a optimal solutio. It is based o geeratig a set of radom decisios. This geerated decisio is evaluated for the feasibility of test ad to meet the costraits required if it meets the requiremets of the correspodig stored LCC ad the ext iteratio is geerated. If the LCC give by the latter iteratio is more tha that of previous oe the the previous LCC is replaced by the ew oe. The optimized results are obtaied after ruig iteratios of the MATLAB code, out of these oly those set of maiteace actios that meet the availability costraits are recorded. The best solutio (miimum LCC) amog them is selected ad the correspodig sets of opportuistic maiteace decisios are proposed. The result gives the optimized opportuistic decisio for each subassembly i betwee the scheduled maiteace, LCC ad availability. Table 3 shows the obtaied result of opportuistic maiteace actio for each subassembly of the compressor. Curretly, Burckhardt compressio provides the maiteace support to their equipmet, for which the LCC is INR 29,400,000. However, after icorporatig opportuistic maiteace, the LCC comes out to be of INR 16,858,250. Thus, there is a reductio of INR 12,541,750 i LCC after icorporatig the opportuistic maiteace i their traditioal approach. The result shows a cosiderable reductio i LCC while assurig the required availability whe compared to traditioal approach; whe a

11 Opportuistic Actios for Subassemblies of a Reciprocatig Compressor: A LCC Based Approach 283 opportuistic actio has bee icorporated i the curret practice. The reduced LCC is substatial, as it will ot oly improve the customer satisfactio but also help i beatig the competitio. Therefore, it ca be cocluded that, icorporatio of opportuistic maiteace i the curret maiteace schedule will be helpful i attaiig a efficiet support at the miimum possible cost. Hece, the obtaied opportuistic maiteace for the reciprocatig compressor of Burckhardt compressio has bee recommeded for ehacig their maiteace support. Table 3: Opportuistic Actios for Subassemblies of a Reciprocatig Compressor Subassembly Optimized Opportuistic Actio Durig I PM II PM III PM IV PM # 1 N N N N # 2 N N N N # 3 N N N N # 4 N N N N # 5 r r r r # 6 N N N N # 7 r r r r # 8 r r r r # 9 r r r r # 10 r r r r # 11 N N N N # 12 N N N N # 13 r r r r # 14 r r r r # 15 r r r r # 16 r r r r # 17 r r r r # 18 N N N N # 19 N r N r N-Do Nothig; r-repair ad R-Replacemet 5. Coclusio The proposed work is based upo applicatio of a opportuistic policy for a reciprocatig compressor uder a give maiteace schedule. The model was implemeted by applyig the idustrial data obtaied from a reciprocatig compressor maufacturer. For implemetig the research, a case study was coducted at Burckhardt compressio. After icorporatig the opportuistic maiteace i the scheduled maiteace the LCC has come out to be of INR 16,858,250, as compared to traditioal LCC of INR 29,400,000. Therefore, the opportuity maiteace optimizatio has the potetial for substatially reducig the LCC of the system while assurig the required level of operatioal availability. The study is limited to the applicatio of opportuistic maiteace o mechaical systems i geeral, a reciprocatig compressor i particular. However, fidigs of the research will be useful to OEMs, service providers, customers, academicias, scietists, researchers, maiteace professioals ad other persos cocered or iterested, to

12 284 Mohammad Asjad, Satish Mohite, Makarad S. Kulkari ad O.P. Gadhi uderstad the impact of opportuistic maiteace o LCC of a system uder a desired operatioal objective. Some of the future aspects of research are listed below; which will be helpful for carryig out further research i the field of opportuistic maiteace. Practically, a lot of mechaical systems are multi-uit series systems. Each uit of which has its ow reliability characteristics ad subsequetly may eed differet PM techique. Itegratig multi PM techiques ito this kid of system will provide a potetial area of research. A future research may cosider failure cosequece, based o which the optimizatio of opportuistic actio ca be made. The estimatio of spares, resources, etc., ca be doe after icorporatig the opportuistic actio ad its optimizatio. Ackowledgemet: We are thakful to the M/S Burckhardt Compressio Limited, Pue, Maharashtra (Idia), for agreeig to joitly work with us i this research study. We express our heartfelt appreciatio of Mr. Sajay Pathak, Mr. Viod Sharma ad Mr. R. K. Sachdeva, of Burckhardt Compressio Limited, for sharig their experiece with us. Refereces [1] Rader, R. ad Jorgeso, D.W. Opportuistic Replacemet of a Sigle Part i The Presece of Several Moitored Parts. Maagemet Sciece, 1963; 10: [2] McCall, J.J. Operatig Characteristics of Opportuistic Replacemet ad Ispectio Policies. Maagemet Sciece, 1963; 10: [3] Zheg, X. ad Fard, N. A Maiteace Policy for Repairable Systems Based o Opportuistic Failure Rate Tolerace. IEEE Trasactios o Reliability, 1991; 40: [4] Pham, H. ad Wag, H. Optimal (τ; T) Opportuistic Maiteace of a k-out-of-: G System with Imperfect PM ad Partial Failure. Naval Research Logistics, 2000; 47: [5] Dagpuar, J.S. Maiteace Model with Opportuities ad Iterrupt Replacemet Optios. Joural of the Operatioal Research Society, 1996; 47(11): [6] Laggoue, R., Chateaueuf A. ad Aissai D. Opportuistic Policy for Optimal Prevetive Maiteace of a Multi-Compoet System i Cotiuous Operatig Uits. Computers ad Chemical Egieerig, 2009; 33: [7] Laggoue, R., Chateaueuf A. ad Aissai D. Impact of Few Failure Data o the Opportuistic Replacemet Policy for Multi-Compoet Systems. Reliability Egieerig & System Safety, 2010; 95: [8] Samrout, M., Yalaoui, F., Chatelet, E., ad Chebbo, N. New Method to Miimize the Prevetive Maiteace Cost of Series-Parallel Systems Usig At Coloy Optimizatio. Reliability Egieerig ad System Safety, 2005; 89: [9] Duarte, J.A.C., Craveiro, J.C.T.A., ad Trigo, T.P. Optimizatio of the Prevetive Maiteace Pla of a Series Compoets System. Iteratioal Joural of Pressure Vessels ad Pipig, 2006; 83: [10] Besard, F., Patriksso, M., Stromberg, A.B., Wojciechowski, A. ad Bertlig, L. A Optimizatio Framework for Opportuistic Maiteace of Offshore Wid Power System. I Proc. of IEEE Power Tech Coferece, Bucharest, Romaia, [11] Besard, F., Patriksso, M., Stromberg, A.B., Wojciechowski, A., Katharia, A.F. ad Bertlig, L. A Stochastic Model for Opportuistic Maiteace Plaig of Offshore Wid Farms. I Proc. of IEEE Power Tech Coferece, Trodheim, Norway, 2011.

13 Opportuistic Actios for Subassemblies of a Reciprocatig Compressor: A LCC Based Approach 285 [12] Lad, B K. ad M.S. Kulkari. Itegrated reliability ad Optimal Maiteace Schedule Desig: A Life Cycle Cost Based Approach. Iteratioal Joural of Product Life Cycle Maagemet, 2008; 3(1): [13] Lad, B.K., ad M.S. Kulkari. A Expert Based Methodology for Cost Orieted Aalysis of Machie Tool Reliability. Iteratioal Joural of Performability Egieerig, 2010; 6(2): [14] Fabrycky, W. ad Blachard, B. Life Cycle Cost ad Ecoomic Aalysis. Pretice, New Jersey, 1991 [15] Asiedu, Y., ad Gu, P. Product Life Cycle Cost Aalysis: State of the Art Review, Iteratioal Joural of Productio Research,1998;36(4): [16] Korpi, E., ad T. Ala-Risku. Life Cycle Costig: a Review of Published Case Studies, Maagerial Auditig Joural, 2008; 23(3): [17] Samarakoo, S.M.K., T. Markeset, ad O.T. Gudmestad. Life Cycle Costig as a Tool for Selectig the Best Available ad Qualified Techique for Maagig Physical Assets. Iteratioal Joural of Performability Egieerig, 2012; 8(3): [18] Koochaki, J., J.A.C. Bokhorst, Wortma, H. ad Kligeberg, W. Coditio Based Maiteace i the Cotext of Opportuistic Maiteace. Iteratioal Joural of Productio Research, 2012; 50(23): [19] Lad, B.K., ad M.S. Kulkari. Optimal Maiteace Schedule Decisios for Machie Tools Cosiderig the User's Cost Structure. Iteratioal Joural of Productio Research, 2012; 50(20): [20] Kijima, M. Some Results for Repairable Systems with Geeral Repair. Joural of Applied Probability, 1989; 26: Mohammad Asjad is a Research Scholar at the Idia Istitute of Techology, Delhi. He did his M.Tech. i Idustrial Egieerig from Z.H. College of Egieerig ad Techology, Aligarh, Idia. He is presetly workig i the field of Supportability, Reliability, Maiteace, ad Life cycle egieerig. Satish Mohite is a M.Tech. studet i the Departmet of Mechaical Egieerig at Idia Istitute of Techology, Delhi. He is curretly workig i the area of Maiteace ad Reliability egieerig. Makarad S. Kulkari is workig as a Associate Professor at the Idia Istitute of Techology Delhi i the Departmet of Mechaical Egieerig. He received his Ph.D. from the Idia Istitute of Techology Bombay, Idia. His research iterest icludes Quality, Reliability ad Maiteace egieerig ad their itegratio with operatios plaig. O. P. Gadhi is a Professor ad Head, Idustrial Tribology, Machie Dyamics ad Maiteace Egieerig Cetre (ITMMEC) at the Idia Istitute of Techology Delhi. He received his Ph.D. from Idia Istitute of Techology, Delhi. He has published more tha 100 papers i Iteratioal/Natioal Jourals/Cofereces. He is o the editorial board of several iteratioal jourals. He has vast experiece i teachig, research ad cosultacy spaig more tha 30 years. His curret research iterests are Maiteace, Reliability, Risk ad Safety Aalysis.