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.

We have a job with N tandem tasks each of which is executed successively until it is completed. A double modular system of error detection for the processing of each task is adopted. Either type of checkpoints such as compare-checkpoint or compare-and-store-checkpoint can be placed at the end of tasks. Three schemes for the above process of a job are considered and the mean execution time of each scheme is obtained. Three schemes are compared and the best scheme is determined numerically. As an example, a job with 4 tasks is given and 6 types of schemes are compared numerically. Finally, we consider a majority decision system as an error masking system and compute the mean execution time for three schemes.

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.

This paper considers replacement and maintenance policies for an operating unit which works at random times for jobs. The unit undergoes minimal repairs at failures and is replaced at a planned time T or at a number N of working times, whichever occurs first. The expected cost rate is obtained, and an optimal policy which minimizes it is derived analytically. The imperfect preventive maintenance (PM) model, where the unit is improved by PM after the completion of each working time, is analyzed. Furthermore, when the work of a job incurs some damage to the unit, the replacement model with number N is proposed. The expected cost rate is obtained by using theory of cumulative processes. Two modified models, where the unit is replaced at number N or at the first completion of the working time over time T, and it is replaced at T or number N, whichever occurs last, are also proposed. Finally, when the unit is replaced at time T, number N or Kth failure, whichever occurs first, the expected cost rate is also obtained.