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This paper takes up managerial maintenance policies during different phases for mission executions. When a mission execution is divided into two phases and three phases respectively, replacement, minimal repair and keeping failure status become alternatives for managerial maintenance policies. Further, we give approximations of the above managerial maintenance policies to make the computations simple. In this paper, keeping failure status is considered as the last choice for the last phase of mission executions. We aim to minimize the expected maintenance costs for the total mission executions. All of the discussions are made analytically and their numerical examples are given. [ABSTRACT FROM AUTHOR]

In this paper, we propose a computing algorithm to obtain optimal checking times which minimize the expected cost rate of sequential inspection models. This algorithm is applied to two modified inspection models with finite intervals such that the unit is checked at times T k (k = 1 , 2 , ... , N) for given N and given S ≡ T N . The modified algorithms are proposed and optimal checking times to minimize the expected cost rates are obtained. Numerical examples of each model are given to show how to use the algorithm. This method would be applied to other sequential inspection models by its suitable modifications. [ABSTRACT FROM AUTHOR]

This paper discusses preventive replacement policies for an independent damage process, in which successive shocks occur at random times, and the independent damages caused by shocks are random variables. It is assumed that a unit fails when the damage has exceeded a prespecified level K. We consider three models: Model 1: the unit is replaced at the M th shock for damage Z , at damage K , or at time T , whichever occurs first. Model 2: the unit is replaced at the M th shock for damage Z , at damage K or at shock N , whichever occurs first. Model 3: the unit is replaced at the M th shock for damage Z , at damage K , at shock N or at time T , whichever occurs first. We obtain the expected cost rates for each model and discuss analytical optimal T ∗ and N ∗ to minimize their expected cost rates. Numerical examples are given when the damage has an exponential distribution and shocks occur at a gamma distribution. [ABSTRACT FROM AUTHOR]

The random age replacement policies discussed in literatures are helpful to complete the nonstopping works with random working cycles, however, maintenance policies are more easily performed at periodic times in real applications. For such a viewpoint, this paper proposes that age replacement policies are planned at periodic times while considering the random working cycles. Using the modeling approaches of replacement first and last policies, we discuss two models such that the unit is replaced at periodic times K T and working cycles N , whichever occurs first and whichever occurs last. The expected cost rate models are obtained and their optimal solutions for K and N are discussed. The comparisons between the policies of K and N , and replacement first and last are made from the point of cost. Numerical examples are illustrated when the failure time has a Weibull distribution. [ABSTRACT FROM AUTHOR]

In order to ensure the data security, plans of incremental and differential backups are usually set up to save the costs which suffer from full backups. In this paper, we suppose that failures occur at data updating times and backups are implemented only at the end of data updates, and full backups are done at time T , over time T and update N to balance the costs of data backup and failure recovery. Using the theory of renewal process, we obtain the expected costs of backup and recovery and the expected cost rates for full backups. Optimum solutions of T and N to minimize the expected cost rates are obtained, and their comparisons are discussed from the optimizations of the integrated models in analytical ways. [ABSTRACT FROM AUTHOR]

Preventive replacement policy conducted at a routine time T ∗ has been surveyed extensively in literatures. Another two random replacement times Y 1 and Y 2 for time T ∗ are jointly considered in this paper. We formulate the models of replacement first, replacement last and replacement middle, which are based on the respective assumptions of whichever occurs first, whichever occurs last and whichever occurs middle. Next, we modify replacement first and replacement last by using whichever occurs first and last jointly. Furthermore, we give the model of replacement overtime when the assumptions of whichever occurs first, whichever occurs last and replacing the unit over time T are simultaneously considered. Comparisons among these replacement models are made to find which policy is more economical than the other. [ABSTRACT FROM AUTHOR]

It has been proposed in recent literatures that if replacement time is planned too early prior to failure time, a waste of operation cost, i.e., excess costs, would incur because the system might run for an additional period of time to complete critical operations; and if the replacement time is too late after failure, a great failure cost, i.e., shortage cost, is incurred due to the delay in time of the carelessly scheduled replacement. The above notion of shortage and excess costs are taken into consideration for the replacement first, replacement last and replacement overtime models in this paper. We obtain the expected cost rates and their optimum replacement times. Comparisons among these optimum times are made analytically and numerically. [ABSTRACT FROM AUTHOR]

It has been commonly known in a Database Management System that constant plans of incremental/differential backup schemes are set up and their full backups should be done to balance the costs of data backup and failure recovery. In this paper, we consider a database system that is running for 24/7 and has several random busy states of updates, and we suppose that incremental/differential backups are implemented after each update and full backups are triggered at constant time and random updates . That is, models with decision variables of and for full backups with random incremental/differential backups are considered. We obtain the expected costs of data backup and failure recovery and the expected cost rates for full backups. Optimum solutions to minimize the expected cost rates are discussed in analytical ways. Furthermore, full backups that are made at time and updates are considered as constant and random modes respectively and compared analytically. For the discussions, numerical examples in exponential cases are given. [ABSTRACT FROM AUTHOR]

A new periodic damage model is proposed in this paper, where the damage produced by shocks is only measured at periodic times, without considering the stochastic shocks and the cumulative process of damage in discrete times. We model five replacement policies for the periodic damage models using three approaches of whichever triggering event occurs first, whichever triggering event occurs last, and replacing over a planned measure, which are named as replacement first, replacement last, over-damage replacement, over-damage replacement first, and over-damage replacement last, respectively. In analytical ways, we obtain their optimum replacement policies to minimize the expected cost rates and compare them to find which model is more economical. Finally, numerical examples are given to illustrate the validity of the presented models. [ABSTRACT FROM AUTHOR]

It is well-known in the standard age replacement policy that a finite preventive replacement time does not exist when the failure time is exponential and the optimal preventive replacement time is nonrandom. It is shown that when the failure time is exponential, a finite time exists by introducing the shortage and excess costs. In addition, the random age replacement is proposed and similar discussions are made. Furthermore, the periodic and random inspection policies are taken up, and their optimal policies are shown to correspond theoretically to those of the age replacement ones. It is shown finally that when the random inspection cost is the half of the periodic one, two expected costs are almost the same. [ABSTRACT FROM AUTHOR]

It is an important problem to determine the tenuring collection time or major collection time to meet the pause time goal for a generational garbage collector. From such a viewpoint, this paper proposes two stochastic models based on the working schemes of a generational garbage collector: Garbage collections occur at a nonhomogeneous Poisson process. Minor collections are made when the garbage collector begins to work, tenuring collection is made at a planned time T or at the first collection time when surviving objects have exceeded K for the first model. Major collection is made at time T or at the Nth collection for the second model. Using the techniques of cumulative processes and reliability theory, expected cost rates are obtained, and optimal policies of tenuring and major collection times which minimize them are discussed analytically and computed numerically. [ABSTRACT FROM AUTHOR]