A Copula-based Maintenance Modeling for Parallel Systems with Non-self Announcing Failures and Dependent Components

Abstract

Based on a copula function this paper addresses a maintenance scheduling problem for parallel systems whose components are dependent and their failures are detected only by inspections. To carry out preventive maintenance actions, the decision process is steered by the excursions of the state process X(t) describing the total number of failed components up to age t. Since both the maintenance costs and the level of maintenance are driven by the inspection interval τ and the preventive replacement threshold j, using the standard renewal theory arguments, the paper aims to jointly determine both optimal inspection and optimal replacement policy which truly balances two factors. The model is examined for the case when the dependence structure is modelled by the FGM copula function and the marginal lifetime distribution of components conforms to a Weibull distribution. Further, a sensitivity analysis is performed to examine some important features of the model's parameters. We will see the unified framework developed not only generalizes age replacement policy and other classic maintenance models, but also allows considerable flexibility such that different scenarios can be explored.