Minimal repair models with non-negligible repair time

Abstract

In existing minimal repair models, it is usually supposed that the repair time of systems is negligible, and thus the occurrences of breakdowns obey non-homogeneous Poisson Process within a replacement interval. However, for the case that the mean working time of a system is not far longer than its mean repair time, ignoring repair time may lead to a large error in calculating the system long-run average cost rate. In this paper, taking random repair time into account, we generalize several calendar time-based minimal repair policies, including periodic replacement policy with minimal repair, reference time policy, and bivariate T−N maintenance policy. By using probability decomposition technique and indicator function method, the system long-run average cost rate under each minimal repair policy is gained explicitly. Various special cases are discussed. An application of the periodic replacement policy with minimal repair is presented in warranty field. Finally, a comprehensive sensitivity analysis is conducted to investigate the relative error on the long-run average cost rate caused by ignoring repair time, and to compare calendar time-based minimal repair policies with age-based minimal repair policies in terms of the long-run average cost rate.