An Optimal Replacement Problem for a Shock Model With Different Modes of Failures Using Alpha Series Processes

Abstract

This paper studies a shock model for a repairable system with two-type failures by assuming that two kinds of shocks in a sequence of random shocks will make the system failed, one based on the inter-arrival time between two consecutive shocks less than a given positive value and the other based on the shock magnitude of single shock more than a given positive value . Further it is assumed that the system after repair is not ‘as good as new’, but the consecutive repair times of the system form a stochastic increasing α-seires process. Under these assumptions, we determine an explicit expression for the average cost rate and an optimal placement policy N* based on the number of failure of the system is determined such that the long-run average cost per unit time is minimized. The explicit expression of long-run average cost per unit time is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, a numerical example is given.