Economic discrete replacement policy subject to increasing failure rate shock model

Abstract

This paper presents an economic discrete replacement model for a single-unit system subjected to external shocks. In this model, the system is affected by both external shocks and its ageing process. The external shocks are divided into two types, namely non-lethal and lethal, depending on their effect to the system. A non-lethal shock damages the system by increasing the failure rate of a certain degree, while a lethal shock causes the system into instantaneous failure. The failure rate also increases with the system’s ageing process. The system is replaced at the instant of the nth non-lethal shock, or on failure, whichever occurs first. The research proposed a model where the long run expected cost per unit time is formulated by introducing relative costs and derived as a criterion of optimality. By minimizing the cost, an optimal number, n^*, is then found. The optimal number, n^*, is also verified to be finite and unique under certain conditions .