Condition-based Maintenance for a Wiener Deterioration Process under Consideration of Heterogeneity in Spare Unit Population

Abstract

This research focused on a single-unit system thatdeteriorates in accordance with a Wiener process. The deterioration state iscompletely observed by sensors at equally spaced time intervals. The decision-makermust select one of three actions: do nothing, preventive replacement or correctivereplacement. Most of the recent research on condition-based maintenance (CBM)was based on the assumption that the deterioration process is the same in thetarget unit population. However, the spare units for replacement maydeteriorate at different rates due to population heterogeneity, which isreflected in the assumption that the spare unit population consists of somesubpopulations. The deterioration process is deemed on the basis of the currenttype probability vector and deterioration state. On the basis of thispopulation heterogeneity, the optimal decision-making problem of CBM isformulated as a Markov decision process. The objective is to minimize the totalexpected discounted cost over an infinite horizon. This research proved thatthe total expected discounted cost is monotonically non-decreasing in typeprobability vector and deterioration state. It also proved that the optimalmaintenance policy is a control limit policy. A numerical example demonstratedthat the total expected discounted cost with considering populationheterogeneity is reduced more than that without considering populationheterogeneity when the spare unit population is assumed to be heterogeneous.Sensitivity analysis is conducted in the diffusion coefficient in the Wienerprocess and the spare unit population distribution.