A Bayesian model and numerical algorithm for CBM availability maximization

• Published in: Annals of operations research Vol. 196; no. 1; pp. 333 - 348
• Main Authors: Jiang, Rui, Kim, Michael Jong, Makis, Viliam
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.07.2012; Springer Science + Business Media; Springer; Springer Nature B.V
• Subjects: Algorithms; Analysis; Availability; Bayesian analysis; Bayesian statistical decision theory; Business and Management; Combinatorics; Control charts; Decision making; Failure; Linear equations; Linear programming; Markov analysis; Markov processes; Mathematical models; Maximization; Operations research; Operations Research/Decision Theory; Policies; Preventive maintenance; Scheduling (Management); Studies; Theory of Computation; Canada; Iran; Hidden Markov model; Multivariate Bayesian control chart; Semi-Markov decision process; Availability maximization; Condition-based maintenance
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-011-1013-1

In this paper, we consider an availability maximization problem for a partially observable system subject to random failure. System deterioration is described by a hidden, continuous-time homogeneous Markov process. While the system is operational, multivariate observations that are stochastically related to the system state are sampled through condition monitoring at discrete time points. The objective is to design an optimal multivariate Bayesian control chart that maximizes the long-run expected average availability per unit time. We have developed an efficient computational algorithm in the semi-Markov decision process (SMDP) framework and showed that the availability maximization problem is equivalent to solving a parameterized system of linear equations. A numerical example is presented to illustrate the effectiveness of our approach, and a comparison with the traditional age-based replacement policy is also provided.