Modeling and Analysis of Complex Equipment Maintenance Dynamics

Intemationsl Joumal of Plant Engineering and ManagementVol.12 No.3Septcmber 2007Modeling and Analysis of Complex EquipmentMaintenance DynamicsYIN Xiao-hu' , LJU Hai-yan2，WEN Xi-sen' , QIAN Yan-ling' , YANG Yong -min'1. Institute of Mechatronic Engineering, School of Mechatronica and Automation,National University of Defense Technology, Changsha 410073, P. R. Cbina2. School of Language and Culture, Nanjing University of InformationScience Technology, Nanjing 210044, P. R. ChinaAbstract: An equipment maintenance system is naturally a complex dynamical system. The ffecive ma-intenance management must be based on the knowledge of the system's intrinsic dynamics. And the strue-ture of the maintenance system determines is beharior. This paper analyzes the basic structures and ele-ments of a maintenance system for complex multi-components equipment. The maintenance system is con-sidered as a dynamic system whose behasior is influenced by is struture's feedback and interaction, andthe system's awvailable resources. Building the dynamical model with Simulink, we show some resultsabou the maintenance system's nonlinear dynamics , which are never given by stochastic process meth-ods. The model can be used for understanding and determining maintenance system behavior, towardswhich operational adjustments of maintenance infrastructure, precise prediction of maintenance require-ments and timely supply of maintenance resources can be made in a more informed way.Key words: modeling and simulation, dynamics, maintenance system , complex equipment1 IntroductionIn the informnation age， precise and eficient maintenance support bas been necessary for eystematiccounterwork. In termns of 8ystem structure, an equipment maintenance system is naturally a multi-scaleaystem. On the scale of a Bystem' evolvement life, the cbange of equipment perfermance is continu-ous, while the maintenance activities are stochastic and discrete. However, wben the system's consti-tution is explored, it may deal with equipment, maintenance workers, maintenance resouree etc. Andon the 8cale of maintenance decision, three levels should be taken into account: the strategic, thetactic, and the organizational. The characteristics on different scales of a maintenance aystem are in-teractive and afected with maintenance informnation, s0 that the system will exhibit complex dymamicalbehavior in the equipment life cycle. In order to manage maintenance activities in a more informedand rational manner, it is very important to understand the inherently complex and dynamics of thesystem, to evaluate the systen's whole performance focusing on the maintenance information flow'I,and to catch the feedback and interaction between different enalee nf tha avstam(2]中国煤化工Tradinally , the stochastic simulation or Markov proceaTYHCN M H cmodel the equipment maintenance system, which considers the system a8 probaD1usuc ana containing several differentRceived 28 March 2007122International Joumal of Plant Engineering and Management Vol.12 No.3September 2007possible states. Based on the reliability of the single component or subsystem and some assumptions ofsystem structure，maintenance effects and equipment faults, various optimal models or statistical mod-els can be built. Although this method is very flexible with the application of various probability distri-butions, the drawback is obvious'?. On one hand, these assumptions have bard and fast precondi-tions; on the other hand, because of many complex feedbacks and delays in the system, the effect ofthe model and the system characters described by it cannot be observed and estimated. As to mainte-nance management, what people care is not the single component's change, but the whole system'schanges, such as maintenance requirement, resource demand ，equipment availability and degrada-tion. It is necessary that we should explore and analyze a maintenance system from a new angle.In system theory, it is the structure that determines the system's behavior. This paper considers thechanges of the whole equipment maintenance system as complex behavior resulting from its intrinsicfeedbacks in order to explore the effects of the feedbacks and the system's dynamics.2 Problem articulations and dynamic hypothesisThis paper deals with the maintenance system for multi-components complex equipment. Although theevents in the maintenance systems may be discrete, such 8s sudden unexpected failures, there are lots ofcontinuous and interacting processes, such as degradalion and repairing of machines , changes of mainte-nance requirements and supply of maintenance resources. Therefore ，continuous approximations can beused with dynamical simulation to model and analyze the complex equipment maintenance syetem.If complex equipment consists of many components, each having a different mean life and variancewhich are randomly distributed, then the system malfunction rate becomes esentally constant asfailed parts are replaced4. From a dynamic simulation point of view , the probabilistic nalure of fail-ures is " noise". Compared with the average failure rate, when the nunber of independent componentsin the complex equipment increases, the proportion of noise becomes smaller and smaller. Therefore,the maintenance system is simplified s0 that the stochastic behavior of failures can be considered as thedeteministic function of the average of the components populations. And the failure rate of themulti-components complex equipment could be approximated with an exponential function. Comparedto traditional methods, the fundamental difference is that its concermn is the proportion of broken-downcomponents in the whole, rather than the failure probability of each component.Failures or not depends on the level of equipment degredation and cumulative defects of components.On account of manufacture arts and crafts and wearing in use, there are some inevitable defects inequipment or its components. During the operational cycle, defects are continually stimnulated tomake the equipment degrade continuously. When the degradation level or the number of accumula-tive defects goes beyond a critical value , the failure happens. With the repair of failures or instantmaintenance of defects, the efet of degradation and d中国煤化工md the perform-ance of equipment could be restored.TYHCNMHGAccording to the execution time of maintenance , there are three maintenance policies: preventivemaintenance ( PM) , condition based maintenance ( CBM) and corrective maintenance (CM). PMModeling and Analysis of Complex Equipment Maintenance Dynamics123ig the maintenance work generating on the ground of determinate schedule in an equipment' s opera-tional cycle. PM is often performed within established time after some stated interval period, and isconsidered to be useful to eliminate the defects and restore equipment's performance. However, theoverload of equipment will speed up and exacerbate the degradation with limited PM capabiliy. Ifthe defects could be detected real-time, then CBM will be started. Otherwise, the accumulative de-fects will make failures happen and CM is required. PM and CBM do not require the stoppage of amachine, but CM must be performed when the equipment is stopped. Only after the performance hasbeen restored to a stated level with CM, can the equipment be operated again.With the assumptions mentioned above, 迁the mainte~Detlects ubayslcm e Falurs subystemn tnance resource ia not limited, the whole equipment ma-intenance system can be made up of defects subsystem,CBMfailures subystem, PM subsystem, CBM Bubsystem, CMruhsystemsubaysicmlubaystemsubsystem and performnance subsystem. Their mutual re-lations are described as Figure 1. A number of defectsPerfonance subaysteonare eliminated by PM and CBM, and the rest is accom-Figure 1 The subeystem structure of theplished by failure repairing witb CM. The numbers ofmaintenance syslemaccumulative defects, failures and all the maintenancetasks in the maintenance system determine the whole performance of the equipment. Meanwhile, the per-formnance subsystem interacts with the PM subeystem, CBM subeystem and CM subsystem and changestheir maintenance requirements based on the current equipment performance.CBM capacityPM capacityFailures.Dects(marhours)~Duration of CBM/per limeDuration ofcorrect rate -+ eliminating -PM cycle。 per timeC8MRequired CBMFailurcs-complcte rate,CMAverige CBMs complelecomptcte Required PMsubsystemnfor climiraiunn rate /CBMprate complete ratecapacityfper defect“(subsystemAccumulative.AccumulativefailuresAveranc defects 过\ AccumulalivePMs (marhours)APM interval period, WorkloaddefectsCBMs(marthours)Duration of t CMconrectedrequired byCM cycleby per CMper failureDefectsI subsystem generatesubsystcmPM schedulequalityderradation\The ffect of_CBM qualitysubsysterFailureleveltdegradation on thegeneration of PMgenerateRequired CMTrateThe effect of ~The effect ofrate M AccumulativereDderet-gencratccumulative PMs dcefects onCMs(manhours) >-gencralcZ The ffectof ratevon degridation deyradationdegradation onCM generate ratedefects gencratingAverage CBMsMaximum defectPerfomanceMapousletets Defect/(manhours) forper coorponentsubsystemdetectionper defectsAverage CMs required bycovcrageEquipmentper failure (manhours)state(operatdional time)avilbilityFigure 2 The model strueture and their relatioas中国煤化工3 The dynamical model and its componentsMYHCNMHGIn Figure 1, there are six subsysterms involved in the whole structure representing diferent functions.Mapping these subsystems and depicting their relationships diagrammatically is important to gain a124International Joumal of Plant Engineering and ManagementVol.12 No.3 September 2007broad overview of the model. Figure 1 also conveys information on the boundary and level of aggre-gation in the model; then the components of each subsystem and their inter-feedback relation can bedepicted as Figure 2.3.1 PM subsystemA8 the most often used maintenance policy, PM is the scheduled maintenance tasks with specifiedtime intervals during the equipment's operational life. Normally, the scheduled maintenance tasksper unit time and the time intervals determine the workload of PM. This work is used to prevent theequipment's degradation. But if the workload of PM cannot be completed in time, it will exacerbatethe degradation to require more PMs. Moreover, the more abominable the operational environmentis, the more rapidly the equipment degrades. Thus, the PM task generation rate depends on thescheduled PMs, PM interval, equipment's degradation and working strength. And if there are muchmore real data, the parameters of such factors will be identified. For example, in Reference [1],the funetion of PMe' generation rate and equipment's degradation can be approximated with an expo-nential function. In Figure 1, the symbols " +" and " - " reflect the effect of such factors on PMs'generation rate, completion rate and accumulative amount. So is the same symbols' effect in the fol-lowing sections.3.2 Defects subsystemThe generation of defects is dependent on the equipment's degradation, failures, accumulative CBMsand CMs6s]. When the degradation adds up to some theshold, defects will generate. At the samnetime, due to the maintenance quality, CBMs and CMs may ereate defects. Furthermore , failuresmay cause cascade fault and defects. Witb the data from the Reference [1]，we find that the rela-tion of equipment degradation and defects generation rate can be ftted well with a Gauss function, inwhich the defects generationtate can be described with the proportion between the defects caused bydegradation at present and tbe rest as a whole. Defects can be eliminated by CBM and CM. If thedefects can be detected instantly, CBM will start. If not, failures will bappen and CM is required.When CBM or CM is completed, the defects will be cleared,3.3 CBM subsystemBecause CBM is triggered by the defect detection, the generation rate of CBM is relevant to the de-fects generation rate, detection coverage, and maintenance time required per defect. Maintenancetime usually falll into the fllowing three probability distibution forms: normnal distribution, suitablefor mechanical or electromechanical equipment; exponential distribution, suitable for electronicequipment with built-in test capability; and log normal distribution, suitable for electronic equip-ment without built-in test capabilityfol. In the fllowing sections, we assume that the maintenancetime probability distribution of CBM and CM both fllw a nomal distibution, and the real comple-tion rate of CBM depends on the CBM capability ( man hours) available in unit time.3.4 Failures subsystem中国煤化工If the defects cannot be detected instantly, then the acc.MYHCNMHGin failure. Sothe generation rate of failures is relevant to the defects generation rate, dection coverage and themaximum possible defects per component. CM is required to repair these failures. The completionModeling and Analyais of Complex Equipment Maintenance Dymamics125rate and quality of CM and average ailures repaired by CM will affect the repair rate of failures.3.5 CM subsystemAfter failure happens, some CM tasks will be needed to be carried out. Its generation rate deals withthe failures generating rate and CM maintenance time required for failures. And the available CMcapability ( man hours) determines the execution rate of CM.3.6 Performance subsystemThe accumulative maintenence taske, failures, defects together with cumulative degradation level de-termine the equipment's availability. Moreover, the degradation is relative to accumulative defectsand PM tasks to be accomplished, and the functions can be identifed with practical data. For exam.ple, in [1], the effect of PM on degradation can be approximated with an exponential function, andthe ffect of defects on degradation can be ftted well with a rational fraction.4 Dynamical behaviors analysisBased on the above- mentioned assumptions and analyais, we construct the dynamics model of anequipment maintenance system with Simulink. Some data required for simulation are from the Refer~ences [1, 3], and the results indicate that the equipment maintenance system is a complex dynami-cal system and has some interesting nonlinear behavior.PM cycle=10 weeks600-PM cycle 20 weeks500-PM cycle=10 weeks20-PM cycle 25 weeks-PM cycle= 20 weeks400 |- PM cycle -25 weeks3001020010020 4050 80 T002040 6080 100r(Weeks)1(Weeks)PM cycle-10 wecks ]9 0.04. PM cycle= =20 weeksPM cycle= 25 weeks-PM cycle= -20 weeks0.5-PM cycle =25 wecks弯0.030.30.02B且0.2导0.010.1L080 TOO1 (Weeks)Figure 3 The periodie behaviors of lhe maintenance system4.1Periodic oscillationsSupposing that the duration of PM is 1 week and the PM^中国煤化工eks, 24 weeks,the simulation of accumulative maintenance tasks (PM ,CTCNMHG5t degradation issimulated shown 8 Figure 3. Because PM is carried out poururcnny, w umuuuiauve growth has atypical periodism. The growth of CBM and CM is similar to the growth of PM , but just the change ofIntemational Joumal of Plant Engineering and ManagementVol.12 No.3September 2007their crest values is on the emall side. Moreover, the periodicity of CBM and CM is not more thanthe PM's, and their frequency-changing increases rapidly when the PM cycle grows. On the groundthat the cumulative PM tasks to be completed are the main factor which determines the equipmentdegradation, the periodism of degradation is well seen and matter-of-course.Obviously, these period-like behaviors stem from the periodicity of a PM cycle. So finding a rationalPM cycle is one of the main research objectives in modeling and analyzing the maintenance system.As shown in Figure 4, we simulate and compare the effects of diferent PM cycles on equipment deg-radation and availability. The result indicates that it is adverse to the system performance when 8 PMcycle is too long or sbort. For example , the longer PM cycle will sharpen the equipment degradationand result in the descent of availability,0.2[PM cycle= 10 weeks0.15-PM cycle- 20 weeksPM cyclc=25 weeks|).1-0.T00200300400 500 600700800 900 10001(Weeks)800-PM cycles 20 wecks|-PM cycle 25 weeks400200-100 200 300 400 50600 700 800 900 1000Figure4 Effet of PM eycle on equipmnent aveilablity4.2 Exponential-like growth and adaptionOn account of the periodic-like behaviors mentioned above, we further analyze the system behaviorsin one PM cycle. We find that, in the PM eycle, the behaviors' growth or decay is similar to expo-nential growth or decay, which is consistent with the Reference [1]. We consider that it is the re~8ult of positive feedback in the maintenance system. For example, in Figure 5, the deterioration ofdegradation will bring on the inerease of maintenance requirements. But the completion of these re-quirements is 8ubject to the constraint of maintenance capability currently, and they will furtherworsen the degradation without immediate accomplishment.But considering the long term behavior of the whole maintenance system, we can see that the periodic-like and exponential-ike behaviors tend to be equilibr中国煤花主empliudes rchanged in a limited small region. It is the negative fenerate these be-TYHCNMH Ghaviors. As shown in Figure 6, taking the defects for exanupn, anc giun niu ue increase of de-fects and further result in the inerease of CM maintenance requirements. Under the constraint ofModeling and Analysis of Complex Equipment Maintenence Dynamics127available maintenance capabilty, these CMs are completed gradually. Their completion repairs thefailures and eliminates the defects, which will restrain the equipment degradation.25p r600rPM cycle-40 weeks500PM cycle=40 wecks400300200”100 wwwwwwW.0-5六5202530540方0方20305401(Weeks)t(Weeks)0.0.04r.6A0.035 I PM cyclc=40 weeksPM eycle=40 weeksg 0.50.03-国0.e 0.025-者0.20.02-0.015|0.1(wWWNwwwwM0.010.0055 10520253035400510152025303540Figure 5 Exponential-like behavior of growth ( decay)0pPM cyele=40 weeks20000f1500-1000wWWWWWW0 200 400 600 800 Too200 400~ 600- 800 1000l(Weeks)r(Weeks)百拿25|PM cycle=40 weeks|PM cyele-40 weeks2f酉1.5-0.I|, 0.05-t wu200 400 600 800 10001(Wecks)1 (Weeks)Figure 6 Adoption of the mainlenance ysten4.3 Effect of condition monitoringAs the concept of equipment health management is well known, the effect of condition monitoring isoften mentioned and given great expectations. According中国煤化工n coverage')l ,the proportion of defects detected by condition monitorinMHC N M H Gused to expressthe capability of condition monitoring. We simulate with the possible variations of condition monito-ring capability and maximum CBM capability, and the results are shown in Figure 7.128Intermational Joumnal of Plant Engineering and MnagementVol.12 No.3Septemrber 20073100 200300400600700800 900 1000s(Weeks)0.0250.020.0150.01.05100200400 5008009001000l(Weeks)600p旨畜200500600800 9001 (Weeks)Detection coverage- 0.6.maximum CBM capability-S0 manhoursDetection coverage-0 8 maximum CBM capahihity-Deetion coveraco.maximum CRM eanalitty-HDo manhoursDetection coverage-0.8,maximum CBM capability- 200 manhours0 manhoursFigure 7 Effect of condition moniloringWe find that the enhancement of condition monitoring capability can reduce the required CM taskseffectively, but have litle effect on equipment degradation. Meanwhile, the enhancement of condi-tion monitring capability will increase CBM tasks. So the maintenance aystem must have enoughCBM capability ( more workers and more resources) , which will cause the reapid increase of mainte-nance cost. If not, these maintenance tasks will not be completed instantly, which will bring on thedecrease of equipment availability.4.4 Performance evaluatlonBased on the simulations above, we can derive that maintenance system is a complex dynamical sy8-tem in nature; its performance evolution is contolled by its intrinsic dynamicso. For complex sy8-tem, each exact system state corresponds to an orderly elements structure, and the transition fromone state to another implies the emergence of a new orderly elements structure!"]. According to thedissipative structure theory , the orderly structure is maintained with the flows of materials, informa-tion and control far from equilibrium condition, which is a process of entropy production. And themaxinum entropy principle means that the most steady state or the utmost emerging orderly ayetemtructure is corresponding to the maximum entropy of the system". Tbus we can use the concept ofentropy to calculate and compare the maintenance Byeten中国煤化工For the maintenance system, the occurence of PM, CB;YHCN M H Gnt state of aye-em. With the simuation above, we can approximate the probabilty of system states with the occur-rence frequency of different :naintenance activities. If the occurrence rate of PM, CBM and CM areModeling and Analyais of Complex Equipment Maintenance Dymamica129denoted asfpm, fob. andfe , the maintenance performance entropy can be defined and calculated 88:S =-fp xln(fg) -fobm xln(fobm) -fo_ x In(.a)Witb the simulation, we calculate the performance entropy of maintenance system under different PMstrategies, as Figure 8. These plots show that, at the early stage of simulation, because the equip-ment is a good the new one, there are very few maintenance activities in the aystem. But略thetime increases, the maintenance system is gradually activating with the PM, CBM and CM stimula-ted by the degradationsa or failuree of equipment,0.3rand transits from one state to another coupled0.25with the entropy production. The entropy of the0.2-PM cycle=5 weeksmaintenance system bolds the line until the 8ys-- PM cycle=l0 weekstem achieves its equilibrium. This doe8 not mean0.15- PM cycle=-20 weeks-PM cycle=40 weeksthe system is absolutely resting. However, the0.equilibrium is maintained by frequently PM,CBM, CM with the flows of materials, informa-tion and controls.04008001200 1600 20000n the foundation of minimum relative entropy1 (Weeks)principle, we can compare and as8esB differentFigure 8 The maintenance perlormance entropyPM strategies. Shown 88 Figure 8, at early stage,under diferent PM Bslralegiesthe maintenance performance under longer PMinterval is better than that under shorter PM interval. But a8 time increases, tbe performance is onthe contrary. This means that the traditional fixed maintenance patterm cannot meet the requirementsof maintenance support of complex equipment in information age, the optimum maintenance patternshould deal with the dynamical evolution of the performance of whole maintenance aystem.5 ConclusionsAcquiring equipment's maintenance requirement well and truly is the premise and basis of the sccom-plishmnent of smart and efficient maintenance. As a complex dynamical eystem , catching the complexfeedbacks in a maintenance Bysterm and the nonlinear dynamics caused by them is the only way to ob-tain and predict equipment maintenance requirements. This paper analyzes the structure of compo-nents and the relation of their constraints and feedback8 in a maintenance system and builds the sye-tem dynamics model based on Simulink. The simulation results explore the dynamice of a maintenancesystem , which was never given by a classical stochastic process method. These beneficial conclusionsestablish the foundations for understanding the essence of maintenance infomation, and bring fortbnew challenges for analyzing and studying the effective control of maintenance aystem.References中国煤化工[1] K. Vishal, Assment of dynamic maintenance mar.MYHC N M H Gf Industrial andSytem Engineering Master of Science, Virginia Polytechnic Institute and Stato University:Virginia. pp. 137, 2004130Intermational Journal of Plant Engincring and ManegerentVol.12 No.3September 2007[2] E. D. Adamides, Y. A. Stamboulis and A. G. Varelis, Model-based ssessment of military air-craft engine maintenance systems. Joumal of the Operational Reearcb Society, Vol.55, PP.957 ~967, 2004[3] Tuomo Honk anen, Modeling industrial maintenance systems and the efcts of outomatic condi-tion monitoring. In: Dissertation of Automation and Systems Technology, Doctor of Science inTechnology. Helsinki University of Technology: Helsinki. pp. 118, 2004[4] X. C. Chen, Modern maintenance theory. Beijing: National Defense Industry Press, 2003 (InChinese)[5}Winston J. Ledet and Winston P. Ledet, Dynamic benchmarking: experiencing the best prac-tices of others in your plant. 2002 , pp. 23, Available from http://www. manufacturing game.com/ docs/ dynamic benchmarking. pdf[6] B. Blanchard, D. Verma and E. Perterson, Maintainaility: a key to efective serviceability andmaintenance management. New York: John Wiley & Sons, 1995[7] Tom Carter, Entropy, power laws and economics. Math Club Lecture, Turlock , 2006Brief BiographiesYIN Xiao-hu is a Ph. D candidate in the School of Mechatronics and Automation of National Univer-sity of Defense Technology. His research interests are in modeling and analysis of maintenance By8-tem dynamics，multi-agent system, and nonlinear system control.LIU Hai-yan is a lecturer in the School of Language and Culture of Nanjing University of Informa-tion Science and Technology. Her research interests are in computational linguisitics and foreign lan-guage teaching.WEN Xi-sen is currently the president of National University of Defense Technology. As a doctoraladvisor and founder of Institute of Mechatronic Engineering. Hia research interests are in conditionmonitoring and fault diagnosis, photonic ceryetal, and maintenance informatization.QIAN Yan-ling is an associate professor in the School of Mechatronice and Automation, NationalUniversity of Defense Technology. His research interests are in fault diagnosis and maintenance in-formatization.YANG Yong-min is a profssor in the School of Mechatronice and Automation, National University ofDefense Technology. His research interests include fault diagnosis and maintenance informatization.中国煤化工MYHCNMHG