Optimal inspection and replacement policy based on experimental degradation data with covariates

In this article, a novel maintenance model is proposed for single-unit systems with an atypical degradation path, whose pattern is influenced by inspections. After each inspection, the system degradation is assumed to instantaneously decrease by a random value. Meanwhile, the degrading rate is elevated due to the inspection. Considering the double effects of inspections, we develop a parameter estimation procedure for such systems from experimental data obtained via accelerated degradation tests with environmental covariates. Next, the inspection and replacement policy is optimized with the objective to minimize the Expected Long-Run Cost Rate (ELRCR). Inspections are assumed to be non-periodically scheduled. A numerical algorithm that combines analytical and simulation methods is presented to evaluate the ELRCR. We then investigate the robustness of maintenance policies for such systems by taking the parameter uncertainty into account with the aid of large-sample approximation and parametric bootstrapping. The application of the proposed method is illustrated by degradation data from the electricity industry.