Optimal Stategies for non-costly and costly observations in Condition Based Maintenance

This paper introduces a model for finding the optimal replacement policy for Condition Based Maintenance (CBM) of a system when the information obtained from the gathered data does not reveal the system's exact degradation state, and the process of collecting data is costly or non-costly. The proposed model uses the Proportional Hazards Model (PHM) introduced by D. R. Cox to represent the system's failure rate. The PHM takes into consideration the system's degradation state as well as its age. Since the acquired information is imperfect, the degradation state of the system is not precisely known. Bayes' rule is used to estimate the probability of being in any of the possible states. The system's degradation process follows a Hidden Markov Model (HMM). By using dynamic programming, the system's optimal replacement policy and its long-run average operating cost are found. Based on the total long-run average cost, the optimal interval between data collection, and the corresponding replacement criterion are specified. A numerical example compares between two systems, one which collects data at no cost, and the other having costly observations. The optimal intervals for data collection and the optimal costs are found in both cases.