Naoto Kaio

Distribution-free checkpoint placement algorithms based on min-max principle

In this paper, we consider two kinds of sequential checkpoint placement problems with infinite/finite time horizon. For these problems, we apply approximation methods based on the variational principle and develop computation algorithms to derive the optimal checkpoint sequence approximately. Next, we focus on the situation where the knowledge on system failure is incomplete, i.e., the system failure time distribution is unknown. We develop the so-called min-max checkpoint placement methods to determine the optimal checkpoint sequence under an uncertain circumstance in terms of the system failure time distribution. In numerical examples, we investigate quantitatively the proposed distribution-free checkpoint placement methods, and refer to their potential applicability in practice

Some Remarks on Optimum Inspection Policies

We discuss optimum inspection policies by introducing the inspection density. We derive the optimum inspection policy by using this inspection density. The models discussed are: 1) the basic model, 2) the basic model with checking time, and 3) the basic model with imperfect inspection. For each model, we obtain the approximate optimum inspection policy minimizing the total s-expected cost by applying the calculus of variations.

Optimum Ordering Policies with Lead Time for an Operating Unit in Preventive Maintenance

An ordering policy allows a spare, delivered after a constant lead time, to be put into inventory. Under certain conditions there exists a finite and unique ordering policy maximizing the cost effectiveness, which balances the system effectiveness and the cost and is defined as [s-availability]/[s-expected cost rate].

A Summary of Optimal Ordering Policies

We consider a generalized ordering policy in which, prior to failure, we order a spare unit which can be delivered after a constant lead time. We are interested in the optimal ordering policy which minimizes the s-expected total discounted cost. The general ordering policy is reduced to two typical ordering policies, which are discussed thoroughly. We also discuss a similar ordering policy with minimal repair.

On the optimal ordering policies in maintenance theory : Survey and applications

In this paper, we consider a typical but somewhat generalized order-replacement model arising in the spare part inventory management. The optimal ordering policies minimizing the long-run average cost are analytically derived. We review the mathematical contexts of the order-replacement problems and refer to their applications. A comprehensive bibliography in this research area is provided.

A study of checkpoint generations for a database recovery mechanism

Abstract This paper discusses checkpoint generations for a database recovery mechanism. The density of checkpoint generations is analytically derived from minimizing the expected total overhead to completion of a phase, and this density yields the optimum sequence of checkpoint generations measured in unit of update pages. We further present the numerical examples for the results obtained and show that the sequence gives effective checkpoint generations.

Nonparametric repair-limit replacement policies with imperfect repair

Abstract The repair-limit replacement problem is to determine the timing to stop repairing a unit after it fails. In this paper, we consider a generalized repair-limit replacement problem with lead time and imperfect repair, which is subject to a time constraint. In particular, two kinds of solution procedures are discussed to obtain the optimal repair-time limit which minimizes the total expected cost per unit time in the steady state, where one is a straightforward (algebraic) procedure and the other is a geometric one based on the Total Time on Test (TTT) concept. Finally, a nonparametric solution procedure to estimate the optimal repair-time limit is proposed, and the optimal policies are given directly from the repair-time data. Simulation results tell us that the method proposed gives a good estimate for a sufficiently large number of data set.

Ordering policies with two types of lead times

Abstract In this paper we consider the optimum ordering policy of a one-unit system, where each failed unit is scrapped and each spare is only provided after a lead time by an order. Introducting two types of lead times, we discuss the optimum ordering policy minimizing the expected cost per unit time in the steady-state. We obtain a finite and unique optimum ordering time and its upper limit under certain conditions. Finally, we present the numerical examples using a Gamma distribution.

Optimum planned maintenance with salvage cost

We consider a planned maintenance policy of providing identical spares successively for replacement of a failed unit as corrective maintenance or a non-failed unit as preventive maintenance. We assume that an identical spare is provided by order with a lead time. Then we consider when we should order an identical spare to minimize the expected cost per unit time in the steady state. In particular, we take into account the salvage cost for the non-failed unit. We show that there exists an optimum ordering policy under certain conditions.

A graphical method to repair-cost limit replacement policies with imperfect repair

In this paper, we consider a different type of repair-cost limit replacement problem with imperfect repair from earlier models. We focus on the problem of determining the timing to stop repairing a unit after it fails, and propose a nonparametric method to estimate the optimal repair-cost limit which minimizes the total expected cost per unit time in the steady-state, by applying the total time on test (TTT) concept. Through a numerical example, the optimal policy is calculated from the repair-cost data directly, and the benefit of the proposed method is shown.