A Markovian Control Approach to Maintenance Optimization of a System with Stochastic Dependence and Hidden Failures

Abstract

Given partial information, this paper considers both disruption and maintenance scheduling problem for a parallel-series system with failure interactions and hidden failures. By projection on an observed history, the filtering treatment contributes to detecting an unobservable disruption time at which one of subsystems experiences failure. The model is developed by setting it in a Markovian control framework with partial information pattern in which a control process as a repair level impacts on the system availability via maintaining both the inspection and the disruption intensity at a desirable level. Since each repair and maintenance action incurs cost, the problem is to determine an optimal control process that balances the amount of maintenance and maintenance costs. The optimal control process emerges as the solution of deterministic Hamilton Jacobi equations, and a recursive scheme is used to solve them. We illustrate the procedure for the case when the failure time of components is defined as the first passage time of a Wiener process. The proposed model is illustrated through numerical examples.