Optimal replacement policy and observation interval for CBM with imperfect information

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. Subsequently, optimal observation interval is found when the collection of data is costly. The proposed model uses the Proportional Hazards Model (PHM) introduced by D. R. Cox to model 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 and the corresponding replacement criterion are specified. A numerical example compares the systems when the observation is free and when it is costly, and finds the optimal observation interval and cost.