When a unit repeats some works over again and undergoes minimal repairs at failures, it is more practical to replace it preventively at the end of working cycles or at its failure times. In this case, it would be an interesting problem to know which is better to replace the unit at a number of working cycles or at random failures from the point of cost. For this purpose, we give models of the expected cost rates for the following replacement policies: (1) The unit is replaced at a working cycle N and at a failure number K, respectively; (2) Replacement first and last policies with working cycle N and failure number K, respectively; (3) Replacement overtime policies with working cycle N and failure number K, respectively. Optimizations and comparisons of the policies for N and K are made analytically and numerically.

It is an important problem to determine major collection times to meet the pause time goal for a generational garbage collector. From such a viewpoint, this paper proposes two stochastic models based on working schemes of a generational garbage collector: Garbage collections occur in a nonhomogeneous Poisson process, tenuring collection is made at a threshold level K, and major collection is made at time T or at Nth collection including minor and tenuring collections for the first model and at time T or at Nth collection including tenuring collections for the second model. Using the techniques of cumulative processes and reliability theory, expected cost rates are obtained, and optimal policies of major collection times which minimize them are discussed analytically and computed numerically.

The main purpose of this paper is to propose overtime replacement policies for the system which has a finite life cycle. The newly proposed overtime technique, where the system is replaced preventively at the first completion of some working cycle over a planned time T, is employed into modelings to avoid operational interruptions for successive jobs. We consider two overtime replacement model with finite operating interval which S is given as (i) constant interval, and (ii) random interval. The expected replacement costs per unit of time are obtained and their optimal solutions are discussed analytically. Further, numerical examples are given when the failure time has a Weibull distribution and working cycles are exponentially distributed.