A Maintenance Policy for a Partially Observed/Observable Parallel System with Two Components Subjected to Stochastically Dependent Degradation Processes

Abstract This paper addresses the maintenance optimization of a parallel system comprising two components subject to stochastically dependent degradation processes. The focus is placed on the scenario of partial observability, where the condition of only one component is observed/observable. The degradation of the components is described using a bivariate gamma process with random effect. The dependence is modeled assuming that the two components share the same random effect. The failure time distribution and the predictive distribution of the unobserved component are derived. A maintenance policy based on a single inspection within a finite time horizon is also formulated. At the inspection time, four actions are possible: do nothing, replace either component, or replace both. Decisions are made by using a non-parametric condition-based decision rule informed by the observed degradation level. The system is assumed to operate over a finite time horizon. The optimal policy is obtained by minimizing the expected maintenance cost, incorporating preventive and corrective costs as well as downtime and inspection costs. The optimal policy is determined by using a numerical approach, showing that information from the observable component enables effective maintenance decisions for the whole system even when the degradation of the other component is completely hidden. For the sake of comparison, the proposed maintenance policy is extended to the case where the inspection involves both components. Although it is not the main goal of the study, this latter result represents an additional (minor) contribution of the paper.