A replacement policy for a cold standby system with dependent lifetime and repair time

In this paper we consider a cold standby system having two units with a single repair facility. The reward and the repair cost per unit time depend on the number of times a unit has been repaired. Also it is assumed that some extra amount has to be paid for restarting the system after each down time. The replacement policy considered here is to replace the system upon the N^th failure of the first unit. A general expression for long-run expected cost per unit time is derived. An explicit expression of the cost function is derived by assuming that the joint distribution of the lifetime of a unit and the repair time of the other unit has Freund [1] bivariate exponential distribution. Existence of optimum value of N that minimizes the long-run expected cost per unit time is examined analytically and a numerical example is considered for illustration.