A condition-based order-replacement policy for a single-unit system

This paper presents a condition-based order-replacement policy for a single-unit system, aiming to optimize the condition-based maintenance and the spare order management jointly. The concerned system deteriorates stochastically and gradually, and is inspected periodically. Under the proposed policy, both the preventive replacement and the spare order are decided based on the observed deterioration level of the system. Therefore, the decision variables for this order-replacement problem include the inspection interval, the ordering threshold, and the preventive replacement threshold. The analytical modeling of the condition-based order-replacement policy is presented in detail in this paper. The policy performance is evaluated in terms of the long-run average cost per unit time, the mean availability, and the rate of preventive replacement, for which the mathematical models are also derived. Numerical examples illustrate the performance of the condition-based order-replacement policy, especially the influences of the lead time of the spare order over the different performance criteria.     

Optimal inspection policy for three-state systems monitored by control charts

This paper presents the formulations of the expected long-run cost per time unit for a system monitored by a static control chart and by an adaptive control chart respectively. The static chart has a fixed sampling interval and a fixed sample size. The adaptive chart has a fixed sample size but variable sampling intervals. The system is supposed to have three states, normal working state, failure delay time state, and failed state. Two levels of repair are used to maintain the system. A minor repair is used to restore the system if a detectable defect is confirmed by an inspection. A major repair will be performed if the system fails. The expected cost per time unit for maintaining such a system is obtained. The objective of such analysis is to find an optimal sampling policy for the inspection process. An artificially generated data example and a real data example are used to compare the expected cost per time unit for both the static and adaptive control charts.     

Optimal spare ordering policy for preventive replacement under cost effectiveness criterion

This paper presents a spare ordering policy for preventive replacement with age-dependent minimal repair and salvage value consideration. The spare unit for replacement is available only by order and the lead-time for delivering the spare due to regular or expedited ordering follows general distributions. To analyze the ordering policy, the failure process is modelled by a non-homogeneous Poisson process. By introducing the costs due to ordering, repairs, replacements and downtime, as well as the salvage value of an un-failed system, the expected cost effectiveness in the long run are derived as a criterion of optimality. It is shown, under certain conditions, there exists a finite and unique optimum ordering time which maximizes the expected cost effectiveness. Finally, numerical examples are given for illustration.     

A novel replacement policy for a linear deteriorating system using stochastic process with dependent components

In this study, a mechanical system with linear deterioration and preventive maintenance is considered. The state of the system over time is represented by a semicontinuous stochastic process with dependent components. The system cycles through on and off periods during its lifetime. The state of the system deteriorates linearly as a function of the usage time during on periods. When the system is offline, preventive maintenance is conducted, which improves the system state by a random amount. The system's on and off times and random improvement amounts are assumed to have general distributions. For such a system, our objective is to determine the expected value and variance for the number of preventive maintenance activities needed during the system lifetime and to propose a novel replacement policy for the system based on delay‐time modeling. Finally, the effectiveness of the obtained asymptotic results and the proposed replacement policy are tested through simulation.     

Joint optimization of spare parts ordering and maintenance policies for multiple identical items subject to silent failures

In this paper the joint maintenance and spare parts ordering problem for more than one identical operating items is studied. The operating items may suffer two types of silent failures: a minor failure, which results in item malfunctioning, and a major failure, which renders the item completely out-of-function. Inspections are periodically held to detect any failures and the inspected items are preventively maintained, repaired or replaced according to their condition. Two ordering policies are investigated to supply the necessary spare parts: a periodic review and a continuous review policy. The expected total maintenance and inventory cost per time unit is derived and the proposed models are optimized for real case data. In addition, the sensitivity of the proposed models is studied through numerical examples and the effect of some key problem characteristics on the optimal decisions is discussed.     

A number-dependent replacement policy for a system with continuous preventive maintenance and random lead times

This paper considers a number-dependent replacement policy for a system with two failure types that is replaced at the nth type I (minor) failure or the first type II (catastrophic) failure, whichever occurs first. Repair or replacement times are instantaneous but spare/replacement unit delivery lead times are random. Type I failures are repaired at zero cost since preventive maintenance is performed continuously. Type II failures, however, require costly system replacement. A model is developed for the average cost per unit time based on the stochastic behavior of the system and replacement, storage, and downtime costs. The cost-minimizing policy is derived and discussed. We show that the optimal number of type I failures triggering replacement is unique under certain conditions. A numerical example is presented and a sensitivity analysis is performed.     

A bivariate optimal replacement policy for a system subject to a generalized failure and repair process

Traditionally, in the studies of the optimal maintenance policies for repairable systems, the nonhomogeneous Poisson process model, which corresponds to the minimal repair process, has been intensively applied. However, in many practical situations, the repair type is not necessarily minimal. In this article, a new repair process based on a new counting process model (so‐called the generalized Polya process) is introduced. Then, the issue of the optimal replacement problem is discussed. A bivariate preventive replacement policy is developed and the properties of the optimal policy are studied. Illustrative examples are also presented. In addition, a comparison with a conventional replacement policy is performed.     

Optimizing replacement policy for a cold-standby system with waiting repair times

This paper presents the formulas of the expected long-run cost per unit time for a cold-standby system composed of two identical components with perfect switching. When a component fails, a repairman will be called in to bring the component back to a certain working state. The time to repair is composed of two different time periods: waiting time and real repair time. The waiting time starts from the failure of a component to the start of repair, and the real repair time is the time between the start to repair and the completion of the repair. We also assume that the time to repair can either include only real repair time with a probability p, or include both waiting and real repair times with a probability 1 − p. Special cases are discussed when both working times and real repair times are assumed to be geometric processes, and the waiting time is assumed to be a renewal process. The expected long-run cost per unit time is derived and a numerical example is given to demonstrate the usefulness of the derived expression.     

An extended replacement policy for a deteriorating system with multi-failure modes

In this paper, the maintenance problem for a deteriorating system with k + 1 failure modes, including an unrepairable failure (catastrophic failure) mode and k repairable failure (non-catastrophic failure) modes, is studied. Assume that the system after repair is not “as good as new” and its deterioration is stochastic. Under these assumptions, an extended replacement policy N is considered: the system will be replaced whenever the number of repairable failures reaches N or the unrepairable failure occurs, whichever occurs first. Our purpose is to determine an optimal extended policy N^∗ such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal extended policy N^∗ can be determined analytically or numerically. Finally, a numerical example is given to illustrate some theoretical results of the repair model proposed in this paper.     

Optimal replacement policy for obsolete components with general failure rates

Identical components are considered, which become obsolete once new‐type ones are available, more reliable and less energy consuming. We envision different possible replacement strategies for the old‐type components by the new‐type ones: either purely preventive, where all old‐type components are replaced as soon as the new‐type ones are available; either purely corrective, where the old‐type ones are replaced by new‐type ones only at failure; or a mixture of both strategies, where the old‐type ones are first replaced at failure by new‐type ones and next simultaneously preventively replaced after a fixed number of failed old‐type components. To evaluate the respective value of each possible strategy, a cost function is considered, which represents the mean total cost on some finite time interval [0, t]. This function takes into account replacement costs, with economical dependence between simultaneous replacements, and also some energy consumption (and/or production) cost, with a constant rate per unit time. A full analytical expression is provided for the cost function induced by each possible replacement strategy. The optimal strategy is derived in long‐time run. Numerical experiments conclude the paper. Copyright © 2008 John Wiley & Sons, Ltd.     

A cooperative inventory policy with deteriorating items for a two-echelon model

A cooperative inventory policy between supplier and buyer is proposed. Unlike other studies, we consider the case of deteriorating items and permit the completed back-order in the problem. We solve the problem without the condition of equal replenishments periods during a specified planning horizon and present a procedure to find the optimal solution. A case is presented to demonstrate the application of the proposed approach. The sensitivity analysis for a cooperation policy between supplier and buyer also are explored.     

A note on a single-vendor and multiple-buyers production-inventory policy for a deteriorating item

In this note we examine the total cost function of a single-vendor multiple-buyers production-inventory policy for a deteriorating item by Yang and Wee [P.C. Yang and H.M. Wee, A single-vendor multiple-buyers production-inventory policy for a deteriorating item, European Journal of Operational Research 143 (2002) 570–581]. Two possible flaws in the cost function of Wee and Yang’s model are pointed out. A proposal to eradicate the flaws is given.     

A replacement model for an additive damage model with restoration

A system existing in a random environment receives shocks at random points of time. Each shock causes a random amount of damage which accumulates over time. A breakdown can occur only upon the occurrence of a shock according to a known failure probability function. Upon failure the system is replaced by a new identical one with a given cost. When the system is replaced before failure, a smaller cost is incurred. Thus, there is an incentive to attempt to replace the system before failure. The damage process is controlled by means of a maintenance policy which causes the accumulated damage to decrease at a known restoration rate. We introduce sufficient conditions under which an optimal replacement policy which minimizes the total expected discounted cost is a control limit policy. The relationship between the undiscounted case and the discounted case is examined. Finally, an example is given illustrating computational procedures.     

A note on replacement policy for a system subject to non-homogeneous pure birth shocks

A system is subject to shocks that arrive according to a non-homogeneous pure birth process. As shocks occur, the system has two types of failures. Type-I failure (minor failure) is removed by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The occurrence of the failure type is based on some random mechanism which depends on the number of shocks occurred since the last replacement. Under an age replacement policy, a planned (or scheduled) replacement happens whenever an operating system reaches age T. The aim of this note is to derive the expected cost functions and characterize the structure of the optimal replacement policy for such a general setting. We show that many previous models are special cases of our general model. A numerical example is presented to show the application of the algorithm and several useful insights.     

Availability and maintenance modeling for systems subject to dependent hard and soft failures

This paper develops availability and maintenance models for single‐unit systems subject to dependent hard and soft failures. A hard failure stops the system immediately, whereas a soft failure only reduces the performance capacity of the system. Dependence between these 2 types of failures is reflected in the fact that each soft failure directly increases the hazard rate of the hard failure. On the basis of such interaction, we derive recursive equations for the system reliability and availability functions. To detect both types of failures, inspections are executed periodically. Furthermore, we investigate the optimal inspection policy via the minimization of the expected cost per unit time. The applicability of the developed availability and maintenance models is validated by a case study on an electrical distribution system.     

A bivariate optimal replacement policy for a cold standby repairable system with preventive repair

In this paper, the repair-replacement problem for a deteriorating cold standby repairable system is investigated. The system consists of two dissimilar components, in which component 1 is the main component with use priority and component 2 is a supplementary component. In order to extend the working time and economize the running cost of the system, preventive repair for component 1 is performed every time interval T, and the preventive repair is “as good as new”. As a supplementary component, component 2 is only used at the time that component 1 is under preventive repair or failure repair. Assumed that the failure repair of component 1 follows geometric process repair while the repair of component 2 is “as good as new”. A bivariate repair-replacement policy (T, N) is adopted for the system, where T is the interval length between preventive repairs, and N is the number of failures of component 1. The aim is to determine an optimal bivariate policy (T, N)^∗ such that the average cost rate of the system is minimized. The explicit expression of the average cost rate is derived and the corresponding optimal bivariate policy can be determined analytically or numerically. Finally, a Gamma distributed example is given to illustrate the theoretical results for the proposed model.     

自保护相依多部件系统的预防维修建模及策略优化

自保护技术作为自愈技术的一种,能够使系统在环境或工况条件变化的干扰下以较高可靠性运行。本文构建了一个新的具有相依主要部件和辅助部件的系统可靠性模型,其中主要部件的退化速率与工作中的辅助部件的数量有关。此外,基于定期检测和预防维修策略,本文利用半再生过程技术求解了系统的长期运行平均成本,并以长期运行平均成本最小化为目标给出了系统的最优预防维修策略。最后,以镗刀系统为例,利用所提方法给出了预防更换阈值和检测周期的最优值,以期望为实际维修行为决策提供理论参考。     

A sequential condition‐based repair/replacement policy with non‐periodic inspections for a system subject to continuous wear

This paper studies a condition‐based maintenance policy for a repairable system subject to a continuous‐state gradual deterioration monitored by sequential non‐periodic inspections. The system can be maintained using different maintenance operations (partial repair, as good as new replacement) with different effects (on the system state), costs and durations. A parametric decision framework (multi‐threshold policy) is proposed to choose sequentially the best maintenance actions and to schedule the future inspections, using the on‐line monitoring information on the system deterioration level gained from the current inspection. Taking advantage of the semi‐regenerative (or Markov renewal) properties of the maintained system state, we construct a stochastic model of the time behaviour of the maintained system at steady state. This stochastic model allows to evaluate several performance criteria for the maintenance policy such as the long‐run system availability and the long‐run expected maintenance cost. Numerical experiments illustrate the behaviour of the proposed condition‐based maintenance policy. Copyright © 2003 John Wiley & Sons, Ltd.     

A discrete approach to designing optimal hedging-point control policies for production-inventory systems with general stochastic behavior

The hedging-point policy for a production-inventory system is investigated under the effect of probabilistic machine breakdowns and repairs assuming general discrete distributions for the repair time and the time to failure. Using a methodology whereby inventory levels can assume only discrete values, an optimal safety stock size that minimizes the total expected cost per unit time is determined.