Abstract
In this paper, we propose a new model for availability maximization under partial observations for maintenance applications. Compared with the widely studied cost minimization models, few structural results are known about the form of the optimal control policy for availability maximization models. We consider a failing system with unobservable operational states. Only the failure state is observable. System deterioration is driven by an unobservable, continuous-time homogeneous Markov process. Multivariate condition monitoring data which is stochastically related to the unobservable state of the system is collected at equidistant sampling epochs and is used to update the posterior state distribution for decision making. Preventive maintenance can be carried out at any sampling epoch, and corrective maintenance is carried out upon system failure. The objective is to determine the form of the optimal control policy that maximizes the long-run expected average availability per unit time. We formulate the problem as an optimal stopping problem with partial information. Under standard assumptions, we prove that a control limit policy is optimal. A computational algorithm is developed, illustrated by numerical results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aven T, Bergman B (1986) Optimal replacement times: a general set-up. J Appl Probab 23: 432–442
Barlow R, Hunter L (1960) Optimum preventive maintenance policies. Oper Res 8: 90–100
Bertsekas DP, Shreve SE (1978) Stochastic optimal control: the discrete time case. Academic, New York
Cox DR (1972) Regression models and life tables. J Roy Stat Soc 34: 187–220
Cui LR, Xie M (2001) Availability analysis of periodically inspected systems with random walk model. J Appl Probab 38: 860–871
Dalpiaz G, Rivola A, Rubini R (2000) Effectiveness and sensitivity of vibration processing techniques for local fault detection in gears. Mech Syst Signal Process 3: 387–412
Davis MHA (1993) Markov models and optimization. Chapman & Hall, London
Dayanik S, Gurler U (2002) An adaptive Bayesian replacement policy with minimal repair. Operat Res 50: 552–558
Edgar JF, Bendell T (1986) The robustness of Markov reliability models. Qual Reliab Eng Int 2: 117–125
Hatoyama Y (1979) Reliability analysis of 3-state systems. IEEE Trans Reliab 28: 386–393
Jin L, Mashita T, Suzuki K (2005) An optimal policy for partially observable Markov decision processes with non-independent monitors. J Qual Maint Eng 11: 228–238
Khan NM, Gupta A (1985) Availability analysis of 3-state systems. IEEE Trans Reliab 34: 86–87
Kharoufeh JP, Finkelstein DE, Mixon DG (2006) Availability of periodically inspected systems with Markovian wear and shocks. J Appl Probab 43: 303–317
Kiessler PC, Klutke GA, Yang Y (2002) Availability of periodically inspected systems subject to Markovian degradation. J Appl Probab 39: 700–711
Kim MJ, Jiang R, Makis V, Lee CG (2011) Optimal Bayesian fault prediction scheme for a partially observable system subject to random failure. Eur J Operat Res 214: 331–339
Liao H, Zhao W, Guo H (2006) Predicting remaining useful life of an individual unit using proportional hazards model and logistic regression model. Annual reliability and maintainability symposium. pp 127–132
Lin DM, Makis V (2004) On-line parameter estimation for a failure-prone system subject to condition monitoring. J Appl Probab 41: 211–220
Lin DM, Makis V (2004) Filters and parameter estimation for a partially observable system subject to random failure with continuous-range observations. Adv Appl Probab 36: 1212–1230
Littlewood B (1975) A reliability model for systems with Markov structure. J Roy Stat Soc 24: 172–177
Maillart LM (2006) Maintenance policies for systems with condition monitoring and obvious failures. IIE Trans 38: 463–475
Makis V (2009) Multivariate Bayesian process control for a finite production run. Eur J Operat Res 194: 795–806
Makis V, Jiang X (2003) Optimal replacement under partial observations. Math Operat Res 28: 382–394
Ohnishi M, Kawai H, Mine H (1986) An optimal inspection and replacement policy under incomplete state information. Eur J Operat Res 27: 117–128
Pike MC (1966) A method of analysis of a certain class of experiments in carcinogenesis. Biometrics 22: 142–161
Rahim MA, Raouf A, Lashkari RS (1985) A three-state Markovian model for predicting human reliability. Kybernetes 12: 87–91
Smallwood RD, Sondik EJ (1973) The optimal control of partially observable Markov decision processes over a finite horizon. Operat Res 21: 1071–1088
Sondik EJ (1978) The optimal control of partially observable Markov processes over the infinite horizon: discounted cost. Oper Res 26: 282–304
Stachowiak GW, Batcherlor AW, Stachowiak GB (2004) Experimental methods in tribology. Elsevier Science, UK
Tijms HC (1994) Stochastic models: an algorithmic approach. Wiley, USA
Wang HZ, Pham H (2006) Availability and maintenance of series systems subject to imperfect repair and correlated failure and repair. Eur J Operat Res 174: 1706–1722
Wang WJ, Mcfadden PD (1996) Application of wavelets to gearbox vibration signals for fault detection. J Sound Vib 192: 109–132
Wu JM, Makis V (2008) Economic and economic-statistical design of a chi-square chart for CBM. Eur J Operat Res 188: 516–529
Yang M, Makis V (2010) ARX model-based gearbox fault detection and localization under varying load conditions. J Sound Vib 329: 5209–5221
Ye MH (1990) Optimal replacement policy with stochastic maintenance and operation costs. Eur J Operat Res 44: 84–94
Zhu Y, Elsayed EA, Liao H, Chan LY (2010) Availability optimization of systems subject to competing risk. Eur J Operat Res 202: 781–788
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jiang, R., Kim, M.J. & Makis, V. Availability maximization under partial observations. OR Spectrum 35, 691–710 (2013). https://doi.org/10.1007/s00291-012-0294-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00291-012-0294-3