A Replacement Policy Based on Down Time for a Cold Standby System with Dependent Lifetime and Repairtime

In this paper we consider a cold standby system of two components with a single repair facility. The lifetime of a component is not necessarily independent of the repair time of the other component because there will be some pressure or load on the repairman if the working unit fails while repairing the other unit in order to reduce the length of down time. The lifetimes and repair times do not depend on the number of times that they have been repaired. But the reward per unit time (from a working unit) and the repair cost per unit time depend on the number of times they have been repaired. Also it is assumed that some extra amount has to be paid during the down time. The replacement policy considered here is to replace the system (both the components) as soon as the down time during any repair exceeds a given duration say ‘d’. A general expression of the cost function is derived by assuming that the joint distribution of the lifetime of a component and the repair time of the other component has Freund bivariate exponential distribution.