Optimum number of minimal repairs for a system under increasing failure rate shock model with cumulative repair‐cost limit

In this paper, a replacement model for a system subject to an increasing failure rate shock process, incorporating a cumulative repair‐cost‐limit, is presented. The shocks are divided into two types: type I and type II shocks. Type I shocks increase the failure rate of the system along with the age of the system and make the system eventually into a minor failure. Type II shocks whenever they occur make the system a critical failure. A minor failure is corrected by minimal repair, while a critical failure is rectified by replacement. The system is replaced at n‐th minor failure, or a minor failure at which the accumulated repair cost exceeds a pre‐determined threshold L, or at a critical failure. The minimum‐cost replacement policy is studied and a sensitivity analysis is conducted to evaluate the effect of model parameters on the optimal number n*.