In this article, a mathematical model is proposed for the joint planning of maintenance policies and inventory control in a deteriorating production system. A safety stock is maintained to meet the demand during the conduction of maintenance actions and to avoid shortages. The optimal planning of maintenance and inventory improves the productivity of the manufacturing system. In a deteriorating production system, the process has two operational states including in-control and out-of-control states as well as a non-operational state, or failure mode. The time for the transition among the states follows a general continuous distribution. The time duration of maintenance actions is also considered as a random variable. The purpose of this study is to optimize the safety stock level and the time to conduct maintenance actions so that the expected total cost per time unit can be minimized. To verify the efficiency of the model, some numerical examples are solved with a genetic algorithm, and validation is conducted for the solutions. Finally, sensitivity analyses are performed on the critical parameters.
Condition-based maintenance (CBM) has been emerged as a relatively new trend in maintenance management. Instead of conducting preventive maintenance actions in specified time intervals, the CBM program collects information through condition monitoring, then recommends maintenance actions based on the observed data. On the other hand, Bayesian control charts use the posterior probability of being the system in an unhealthy state as the chart statistic. An attribute Bayesian control chart is employed in this study to monitor a deteriorating system and plan CBM actions based on a continuous-time homogeneous Markov chain. The system consists of three states: healthy, unhealthy, and failure states. A partially observable Markov decision process (POMDP) is developed, which optimally determines the sample size, sampling interval, and warning limit to minimize the long-term expected cost per time unit. Numerical examples and sensitivity analyses are conducted to clarify the performance of the proposed attribute control chart. To the best of the authors’ knowledge, this is the first study of the applications of attribute Bayesian control charts in condition-based maintenance.
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