Preventive replacement policy with cumulative repair-cost limit for a system under increasing failure rate shock model

Abstract

A system is subject to shocks and these shocks are divided into two types: non-lethal and lethal shocks. Non-lethal shocks increase the failure rate of the system along with the age of the system and make the system eventually into a minor failure. Lethal shock whenever occurs makes the system critical failure. This shock process is called an increasing failure rate shock model. A minor failure is corrected by minimal repair, while a critical failure is rectified by replacement. In this paper, we propose a periodical replacement policy for a system, incorporating with the concept of cumulative repair-cost limit. While carrying out minimal repair, the repair cost and the accumulated repair cost are calculated. The system is replaced at age T or a minor failure at which the accumulated repair cost exceeds a predetermined 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 T*.