On a parametric model for the mean number of system repairs with applications

Abstract

In reliability engineering and other disciplines, there are many situations, in which one deals with the number of events in a time period that happen as an outcome of a stochastic process. Examples are the number of repairs of a system in an age-based block replacement and the number of repairs for a product sold under warranty in a specific period. In these circumstances, the mean number of failures (repair) plays a crucial role in assessing reliability characteristics and the optimal time of maintenance of the system. In this paper, we study a parametric function for the mean number of repairs of the system that covers a wide range of repair degrees, such as better than minimal repair, minimal repair and worse than minimal repair. Using the suggested model, we propose an approximation for the renewal function in the case that the repairs are complete. We also give applications of the proposed function in age-based block replacement and optimal warranty policy.