Optimally maintaining a multi-state system with limited imperfect preventive repairs

Abstract

In this paper, the optimal maintenance policy for a multi-state system with no observation is considered. Different from most existing works, only a limited number of imperfect preventive maintenance actions can be performed between two successive replacements. Assume that the system's deterioration state cannot be observed during its operation expected after each replacement, and it evolves as a discrete-time Markov chain with a finite state space. After choosing the information state as state variable, the problem is then formulated as a Markov decision process over the infinite time horizon. In order to increase the computational efficiency, several key structural properties are developed by minimising the total expected cost per unit time. The existence of the optimal threshold-type maintenance policy is proved and the monotonicity of the threshold is obtained. Finally, a numerical example is given to illustrate the optimal policy.

An Optimal Imperfect Maintenance Policy for a Partially Observed System With Obvious Failures and Limited Repairs

“…The structural properties were obtained still based on perfect maintenance. Hence, our work can be viewed as an extension of the works of [25], [28].…”

“…The former case can be easily understood and has been studied by many researchers. While the latter case means that a system subject to IM2 becomes more prone to deterioration as the number of performed repair actions increases [22]- [25]. And such case can also be found in many engineering and service applications [11].…”

“…As far as we know, there exist few works on the above-mentioned problem. Fan et al [25] considered the similar problem of optimally maintaining a multi-state system only based on IM2, and no observation was used to make the maintenance decision.…”

“…Chen et al [28] improved the work in [25] through taking IM1 into consideration. However, IM1 was only considered in maintenance modelling.…”

Analysis of k-Out-of-N-Systems with Different Units under Simultaneous Failures: A Matrix-Analytic Approach

“…The analytical structure proposed by the authors is a multivariate Weibull model based on the Marshall-Olkin multivariate exponential distribution. The Markov processes have been an appropriate model in reliability, see [6,7], among many others. A limitation of the Markov processes in modeling systems is that the staying times in states are exponentially distributed, or, equivalently, that the instantaneous transition rates do not depend on the time; they are constant.…”