A POMDP Framework to Find Optimal Inspection and Maintenance Policies via Availability and Profit Maximization for Manufacturing Systems


Department of Industrial Engineering, Yazd University, Yazd, Iran


Maintenance can be the factor of either increasing or decreasing system's availability, so it is valuable work to evaluate a maintenance policy from cost and availability point of view, simultaneously and according to decision maker's priorities. This study proposes a Partially Observable Markov Decision Process (POMDP) framework for a partially observable and stochastically deteriorating system in which inspection and maintenance optimal policies of Condition Based Maintenance (CBM) must be determined to maximize the average profit and availability of the system simultaneously. A recent exact method named Accelerated Vector Pruning method (AVP) and some other popular estimating and exact methods are applied and compared in solving such problems.


1.     Ahmad, R., and Kamaruddin, S., “An overview of time-based and condition-based maintenance in industrial application“, Computers & Industrial Engineering, Vol.63, No. 1, (2012), 135-149.
2.     Rasay, H., FallahNezhad, M. S., and ZareMehrjardi, Y., “Application of the multivariate control charts for condition based maintenance“, International Journal of Engineering, Vol. 31, No. 4, (2018), 204-211.
3.     Rahimi Komijani, H., Shahin, M., and Jabbarzadeh, A., “Optimal policy of condition-based maintenance considering probabilistic logistic times and the environmental contamination issues“, International Journal of Engineering, Vol. 31, No. 2, (2018), 357-364.
4.     Jiang, R., Kim, M.J., and Makis, V., “Availability maximization under partial observations“, OR Spectrum, Vol. 35, No. 3, (2013), 691-710.
5.     Keizer, M. C. O., Flapper, S. D. P., and Teunter, R. H., “Condition-based maintenance policies for systems with multiple dependent components: A review“, European Journal of Operational Research, Vol. 261, No. 2, (2017), 405-420.‏
6.     Ruschel, E., Santos, E. A. P., and Loures, E. D. F. R., “Industrial maintenance decision-making: A systematic literature review“, Journal of Manufacturing Systems, Vol. 45, (2017), 180-194.‏
7.     Bousdekis, A., Magoutas, B., Apostolou, D., and Mentzas, G., “Review, analysis and synthesis of prognostic-based decision support methods for condition based maintenance“, Journal of Intelligent Manufacturing, (2015), 1-14.‏
8.     Ghorbani, S., “Reliability analysis for systems subject to degradation and shocks“, PhD diss., Rutgers University-Graduate School-New Brunswick, (2014).
9.     Ferreira, R.J., de Almeida, A.T., and Cavalcante C.A., “A multi-criteria decision model to determine inspection intervals of condition monitoring based on delay time analysis“, Reliability Engineering & System Safety, Vol. 94, No. 5,(2009), 905-912.
10.   Martorell, S., Carlos, S., Villanueva, J. F., Sanchez, A. I., Galván, B., Salazar, D., and Cepin, M., “Use of multiple objective evolutionary algorithms in optimizing surveillance requirements“, Reliability Engineering & System Safety, Vol. 91, No.9, (2006), 1027-1038.
11.   Zio, E., and Viadana, G., “Optimization of the inspection intervals of a safety system in a nuclear power plant by Multi-Objective Differential Evolution (MODE)“, Reliability Engineering & System Safety, Vol. 96, (2011) 1552-1563.
12.   Caballé, N. C., and Castro, I. T., “Assessment of the maintenance cost and analysis of availability measures in a finite life cycle for a system subject to competing failures“, OR Spectrum, (2018), 1-36.‏
13.   Kumar, G., Jain, V., and Gandhi, O. P., “Availability analysis of mechanical systems with condition-based maintenance using semi-Markov and evaluation of optimal condition monitoring interval“, Journal of Industrial Engineering International, Vol. 14, No. 1, (2018), 119-131.‏
14.   Qiu, Q., Cui, L., and Shen, J., “Availability analysis and maintenance modelling for inspected Markov systems with down time threshold“, Quality Technology & Quantitative Management, (2018), 1-18.‏
15.   Qiu, Q., Cui, L., and Gao, H., “Availability and maintenance modelling for systems subject to multiple failure modes“, Computers & Industrial Engineering, Vol. 108, (2017) 192-198.‏
16.   Alaswad, S., and Xiang, Y., “A review on condition-based maintenance optimization models for stochastically deteriorating system“, Reliability Engineering & System Safety, Vol. 157, (2017), 54-63.
17.   Pak, P. K., Kim, D. W., and Jeong, B. H.,“Machine Maintenance Policy Using Partially Observable Markov Decision Process“, Journal of the KSQC, Vol. 16, (1988).
18.   Kaelbling, L. P., Littman, M. L., and Cassandra, A. R., “Planning and acting in partially observable stochastic domains“, Artificial Intelligence, Vol. 101, (1998), 99-134.
19.   Jin, L., Mashita, T., and Suzuki, K., “An optimal policy for partially observable Markov decision processes with non-independent monitors“, Journal of Quality in Maintenance Engineering, Vol. 11, No. 3, (2005), 228-238.
20.   Papakonstantinou, K. G., and Shinozuka, M., “Planning structural inspection and maintenance policies via dynamic programming and Markov processes. Part I: Theory“, Reliability Engineering & System Safety, Vol. 130, (2014), 202-213.
21.   Kumar A., and Meenakshi, N., “Marketing management“, Vikas Publishing House, (2011).
22.   Ahmadi-Javid, A., and Ghandali, R., “An efficient optimization procedure for designing a capacitated distribution network with price-sensitive demand“, Optimization and Engineering, Vol. 15, No. 3, (2014), 801-817.
23.   Spaan, M. T., and Vlassis, N., “Perseus: Randomized point-based value iteration for POMDPs“, Journal of Artificial Intelligence Research, Vol. 24, (2005), 195-220.
24.   Qian, W., Liu, Q., Zhang, Z., Pan, Z., and Zhong, S., “Policy graph pruning and optimization in Monte Carlo Value Iteration for continuous-state POMDPs“, In Computational Intelligence (SSCI), 2016 IEEE Symposium Series on IEEE, (2016), 1-8.
25.   Walraven, E., and Spaan, M. T. “Accelerated Vector Pruning for Optimal POMDP Solvers“, In AAAI, (2017), 3672-3678.
26.   Ahuja. D., www.codeproject.com/Articles/9898/Heap-Walker, (2005).
27.   Agrawal, R., Realff, M. J., and Lee, J. H., “MILP based value backups in partially observed Markov decision processes (POMDPs) with very large or continuous action and observation spaces“, Computers & Chemical Engineering, Vol. 56, (2013), 101-113.
28.   Smallwood, R. D., and Sondik, E. J.,“The optimal control of partially observable Markov processes over a finite horizon“, Operations Research, Vol.21, No. 5, (1973), 1071-1088.
29.   Özgen, S., and Demirekler, M., “A Fast Elimination Method for Pruning in POMDPs“, In Joint German/Austrian Conference on Artificial Intelligence, (2016), 56-68, Springer International Publishing.
30.   Cassandra, A., Littman, M. L., and Zhang, N. L., “Incremental pruning: A simple, fast, exact method for partially observable Markov decision processes“, In Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence(1997), 54-61,Morgan Kaufmann Publishers Inc.
31.   White, C. C., “A survey of solution techniques for the partially observed Markov decision process“, Annals of Operations Research, Vol. 32, No. 1, (1991), 215-230.
32.   Littman, M. L., “The witness algorithm: Solving partially observable Markov decision processes“, Brown University, Providence, RI, (1994).