Optimal Policies of Condition-Based Maintenance Under Multiple Imperfect Inspections

Abstract

This study provides analytical modeling of condition-based maintenance with periodic imperfect inspections for a stochastically deteriorating system. In addition to the critical threshold, for each time point of inspection a replacement threshold is introduced. An inspection consists of checking the system state parameter against the replacement threshold in the upcoming time intervals. A new decision rule is proposed for inspecting the system condition, which is based on the comparison of the time of inspection with the estimated remainder of the time to failure. Based on this decision rule, general expressions are derived for calculating the probabilities of correct and incorrect decisions with considering the results of previous inspections. For the first time it is shown that even in case of perfect inspections the probabilities of incorrect decisions are nonzero when checking system suitability. To determine the optimal replacement threshold at each time of inspection, different criteria are proposed to use such as maximum net income, minimum Bayes risk, and minimum total error probability. The proposed approach is illustrated by deriving the probabilities of correct and incorrect decisions for a linear stochastic deterioration process model. A numerical example is given.