Syouji Nakamura

Replacement and minimal repair policies for a cumulative damage model with maintenance

This paper considers replacement and minimal repair polices for an extended cumulative damage model with maintenance at each shock: shocks occur at a nonhomogeneous Poisson process. A system undergoes maintenance at each shock when the total damage does not exceed a failure level K, undergoes minimal repair at each shock when the total damage exceeds a failure level K, and is replaced at time T∗ or at failure N∗ whichever occurs first. The expected cost rate is obtained and the optimal T∗ and N∗ minimizing the expected cost are analytically discussed. It is shown that this model would be applied to the backup of secondary storage files in a database system as an example.

Optimal backup interval of database by incremental backup method

Some media faults occur at random. To lessen the overhead of backup processing, the operation of a incremental backup with small overhead is adopted between the operations of a full backup. The mean time to full backup and the expected cost of these schemes are derived, using the theory of stocastic processes. The total expected cost of backup operation is obtained and an optimal full backup interval is easily determined.

Optimal Policies for Random and Periodic Garbage Collections with Tenuring Threshold

It is an important problem to determine the tenuring threshold to meet the pause time goal for a generational garbage collector. From such viewpoint, this paper proposes two stochastic models based on the working schemes of a generational garbage collector: One is random collection which occurs at a nonhomogeneous Poisson process and the other is periodic collection which occurs at periodic times. Since the cost suffered for minor collection increases, as the amount of surviving objects accumulates, tenuring minor collection should be made at some tenuring threshold. Using the techniques of cumulative processes and reliability theory, expected cost rates with tenuring threshold are obtained, and optimal policies which minimize them are discussed analytically and computed numerically.

Cumulative Damage Models with Replacement Last

This paper proposes a damage model with replacement last. First, the preventive replacement policies with a damage process is given: the unit is replaced at a damage level Z or a planned time T, whichever occurs last. Second, optimal Z for a given T is derived, and compare such an optimal policy with those of replacement first and standard replacement. It shows that the ratio of replacement costs plays an important role in determining which policy is better. Third, a numerical example is given in an exponential case.

Optimal maintenance policies for cumulative damage models with random working times

Purpose – The purpose of this paper is to consider maintenance policies for an operating system which works at random times for jobs. Each job causes some damage to the system and these damages are additive, and the system fails when the total damage has exceeded a failure level K.Design/methodology/approach – Using techniques of cumulative damage models, the maintenance is made at the N‐th completion of working time for the first model and at a damage level Z with a limit number of working times N for the second model.Findings – The system is maintained at the first completion of the working time over time T for the third model. The system fails with probability p(x) when the total damage is x and undergoes minimal repair at failure for the fourth model. The expected cost rates are obtained and optimal maintenance policies are discussed analytically and computed numerically.Originality/value – The paper discusses four maintenance policies for an operating system which works at successive random times for...

AGE AND PERIODIC REPLACEMENT MODELS WITH OVERTIME POLICIES

This paper proposes two modified replacement policies which combine random replacement with standard age and periodic policies, where units undergo replacement at the first completion of some random working time over a planned time T, which are called replacement overtime. The expected cost rates of age and periodic replacement overtime polices are obtained, and optimal policies which minimize them are discussed analytically. Comparisons between such two overtime policies and standard age and periodic replacements are made in detail. When two costs for replacement overtime and standard age or periodic policies are the same, it is shown as estimated previously that the standard replacements are better than their overtime policies. Furthermore, two modified replacement overtime costs are discussed and computed numerically when such new policies would be better than the standard age and periodic replacements.

Optimal Tenuring And Major Collection Times For A Generational Garbage Collector

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.

Determination of Loan Interest Rate Considering Bankruptcy and Mortgage Collection Costs

Particularly in Japan, risk management relating to bankruptcy of financed enterprises has become very important to a bank after the collapse of a bubble economy. To obtain suitable revenues, a bank has to apply high interest rates to the enterprises with high risk. When enterprises which have made a secure loan from a bank go bankrupt, a bank forecloses such enterprises from its mortgage to recover the loss incurred. However, in actual circumstances, it may need much cost and effort to do so in Japan. This paper proposes a stochastic model to determine an adequate interest rate, taking account of the probabilities of bankruptcy and mortgage collection, and their costs. Numerical examples are given to illustrate this model and a loan interest rate is determined.

An optimal maintenance time of automatic monitoring system of ATM with two kinds of breakdowns

Abstract All automatic teller machines (ATMs) in a bank operate unmanned on weekends and holidays, and an automatic monitoring system continuously watches the operation of ATMs through the telecommunication network. There are two kinds of troubles according to the installed places of ATMs. One is the trouble which occurs inside the branch of a bank where ATMs operate manned except on weekends and holidays, and the other is the one which occurs outside the branch where ATMs always operate unmanned. Two kinds of breakdowns are introduced, and the expected cost for an unmanned operation period is obtained. A maintenance policy which minimizes the expected cost is analytically derived. Finally, a numerical example is given and some useful discussions are made.

Constant and Random Full Backup Models with Incremental and Differential Backup Schemes

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 T and random updates N. That is, models with decision variables of T and N 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 T and updates N are considered as constant and random modes respectively and compared analytically. For the discussions, numerical examples in exponential cases are given.