Optimal Lot-Sizing/Preventive Replacement Policy for an EMQ Model with Minimal Repairs

Age replacement policies are investigated. When a unit reaches age T, a preventive replacement is made. If a failure occurs prior to age T and if the random repair cost is less than a fixed constant, a minimal repair is made. Otherwise the unit is replaced at failure.

Determining the optimal probing lot size for the wafer probe operation in semiconductor manufacturing

A (τ, T) replacement policy is commonly used to prevent system failure. In previous research, it was assumed that the maintenance time can be ignored since it is negligibly short compared with operation time. However, neglecting maintenance time when optimizing maintenance policies for systems for which the maintenance time is not relatively short can lead to sub-optimal or even incorrect solutions to the problem, resulting in higher maintenance costs. An optimal (τ, T) replacement policy is presented for series systems in which the units deteriorate following different stochastic processes independently. The failure of each unit in the time interval [τ, T) occurs in accordance with a nonhomogeneous Poisson process, the failure is immediately removed by a minimal repair and the system continues operating. The failure of any unit in time interval [τ, T) causes the entire system to fail, which is immediately detected, and corrective maintenance is performed on the whole system. If a failure does not occur during time interval [τ, T), the system receives preventive replacement at T A (τ, T) replacement policy was formulated that considers both preventive and corrective maintenance times and that determines an optimal preventive replacement interval that minimizes the expected long-run cost per unit time. A numerical example illustrates that implementing the proposed (τ, T) replacement policy can effectively reduce maintenance costs.

In this paper, a two-unit system with failure interactions is studied. The system is subject to two types of shocks (I and II) and the probabilities of these two shock types are age-dependent. A type I shock, rectified by a minimal repair, causes a minor failure of unit A and type II shock causes a complete system failure that calls for a replacement. Each unit A minor failure also results in an amount of damage to unit B. The damages to unit B caused by type I shocks can be accumulated to trigger a preventive replacement or a corrective replacement action. Besides, unit B with cumulative damage of level z may become minor failed with probability \(\pi (z)\) at each unit A minor failure and rectified by a minimal repair. We consider a more general replacement policy. Under this policy, the system is preventively replaced at the Nth type I shock, or at the time when the total damage to unit B exceeds a pre-specified level Z (but less than a failure level K where \(K>Z\)) or is replaced correctively at first type II shock or when the total damage to unit B exceeding a failure level K, whichever occurs first. To minimize the expected cost per unit time, the optimal replacement policy \((N^{*}\), \(Z^{*})\) is derived analytically and determined numerically. We also show that several previous maintenance models in the literature are special cases of our model.

In reality, most operating systems are repaired or replaced when they have failed. For such systems, it would be reliable to maintain them in a control-limit consideration of repairs or operations. This article addresses a system scheduling policy for preventive replacement with discrete control limits of minimal repair and random work. An operating system which works at random times for multiple jobs (N tandem jobs or N parallel jobs) is considered. The system subjects to two failure mechanisms and maintained imperfectly: type-I (minor) failure rectified by a minimal repair and type-II (catastrophic) failure removed by a corrective replacement. To control the deterioration process, the preventive replacement is planned to undergo before catastrophic failure at number n of minimal repairs or the completion of N multiple jobs. The objective is to determine the optimal discrete scheduling replacement parameters (n* or N*) that minimizes the mean cost rate function in a finite time horizon. Model analysis relating to the existence and uniqueness of optimal solutions is provided. A Numerical example is presented for illustrative purposes.

In this paper, we consider a production-inventory control problem for an Economic Manufacturing Quantity (EMQ) model with machine breakdowns and planned preventive replacement (overhaul) of the production unit. Two types of failure are considered. When type I failure occurs (major failure), the unit is replaced by a new one and the interrupted lot is aborted. Starting a new lot after a replacement or after a complete production run incurs a setup cost. Type II failures (minor failures) are corrected by minimal repairs which take negligible time. After performing a minimal repair, production can be resumed immediately at a cost lower than the setup cost. It is assumed that both preventive and failure replacement times are random and the demand that cannot be satisfied during these replacement times is lost.

This study discusses an opportunity-based age replacement policy for a system which has a warranty period (0, S]. When the system fails at its age x≤S, a minimal repair is performed. If an opportunity occurs to the system at its age x for S<x<T, we take the opportunity with probability p to preventively replace the system, while we conduct a corrective replacement when it fails on (S, T). Finally if its age reaches T, we execute a preventive replacement. Under this replacement policy, the design variable is T. For the case where opportunities occur according to a Poisson process, a long-run average cost of this policy is formulated under a general failure time distribution. It is, then, shown that one of the sufficient conditions where a unique finite optimal T* exists is that the failure time distribution is IFR (Increasing Failure Rate). Numerical examples are also presented for the Weibull failure time distribution.

WITHDRAWN: A trivariate optimal replacement policy for a deteriorating system based on cumulative damage and inspections

Different type of maintenance problems have been investigated during the past decades. With the growth in complexity of modern systems, the cost of purchasing new systems becomes higher ever than before. Surprisingly, very little attention in the literature has been paid to the failure replacement in these preventive maintenance models. However, in practice most systems incur increasingly expensive down time costs when the systems suffer the unexpected failures. The major changes to the standard maintenance model in this research are the addition of a failure replacement cost for a failed system and the reliability limit for which system has to be replaced. The overall objective of this research is to propose an efficient algorithm to obtain the optimal maintenance policy. The optimal preventive maintenance policy is investigated with incorporating the costs of minimal repair, imperfect preventive maintenance, failure replacement and preventive replacement. The specific maintenance actions for a repairable system are when to perform an imperfect preventive maintenance or to replace the system while the system is in the operating condition. In another case, the specific maintenance actions for a repairable system are whether to replace the system, or to perform a minimal repair when the system fails. The number of imperfect preventive maintenance and the control limits of the optimal maintenance policy are calculated under the expected average cost rate criterion.

Optimisation of a single-component maintenance system: A smoothed perturbation analysis approach

In this paper, a bivariate replacement policy (n, T) for a cumulative shock damage process is presented that included the concept of cumulative repair cost limit. The arrival shocks can be divided into two kinds of shocks. Each type-I shock causes a random amount of damage and these damages are additive. When the total damage exceeds a failure level, the system goes into serious failure. Type-II shock causes the system into minor failure and such a failure can be corrected by minimal repair. When a minor failure occurs, the repair cost will be evaluated and minimal repair is executed if the accumulated repair cost is less than a predetermined limit L. The system is replaced at scheduled time T, at n-th minor failure, or at serious failure. The long-term expected cost per unit time is derived using the expected costs as the optimality criterion. The minimum-cost policy is derived, and existence and uniqueness of the optimal \( n^{*} \) and \( T^{*} \) are proved. This bivariate optimal replacement policy (n, T) is showed to be better than the optimal \( T^{*} \) and the optimal \( n^{*} \) policy.

This paper investigates the effects of unsuccessful repairs on the optimal periodic replacement policy for a repairable product with multiple attempts of minimal repair under the free-repair warranty. The motivation for this study is based on the novel notion of ‘multi-attempt minimal repair’, first introduced by Cha and Finkelstein (2024a, 2024b), in which they highlighted various practical reasons and examples to illustrate that minimal repair attempts may sometimes fail and need to be repeated until success is achieved. Their repair model and useful properties served as the motivation for this study. For both the warranted and non-warranted products, cost models are developed from the user’s perspective, and the corresponding optimal replacement policies are derived to minimize the long-run expected cost rates. By comparing these optimal policies, we show that the optimal planned time for preventive replacement should be adjusted toward the end of the warranty period, and the effects of unsuccessful minimal repair produce different degrees of impact, respectively, on the warranted and non-warranted product. Finally, detailed numerical examples and computation results illustrate our findings, and some insightful observations about practical and managerial implications are concluded.

An EOQ lot sizing model with random supplier capacity

SYNOPTIC ABSTRACTThis paper deals with the effect on the {optimal lot sizes, cycle length, and cost} of the system for several products produced on several machines with repetitive common cycle length when the solution is constrained by limited storage space or capital. In order to solve the constrained production lot size problem it is necessary to determine the maximum volume or value of the inventory (MV) required for a given production plan. One simple measure of the storage space or capital required is the sum of the peak values of the individual product inventory levels (SMV). Since the peak inventory levels for all products do not occur simultaneously, SMV is usually much larger than the exact MV and, therefore, would be expected to yield a higher cost solution.In this paper efficient computational procedures are developed to find the exact MV and the corresponding constrained optimal lot sizes and cycle length when the products are made on a single machine. Techniques to determine the MV are explo...

This paper proposes a bivariate (T, L2) replacement policy with double repair-cost limits for a system subject to increasing failure rate model. External shocks are divided into two types: type-I shock and type-II shock. Each type-II shock makes the system suffer a minor failure, while each type-I shock increases the failure rate of the system by a certain amount and it will induce the system into critical failure. When a minor failure occurs, the repair cost is evaluated and minimal repair is executed if the repair cost is less than a single repair-cost limit L1 and the accumulated repair cost is less than a cumulative repair-cost limit L2, otherwise, the system is replaced by a new one. In addition, the system is replaced at scheduled time T or at critical failure. By formulating the optimisation problem, the optimal T* and L2* which minimise the long-run expected cost per unit time are found, respectively. We develop the corresponding computational algorithm to obtain the optimal replacement policy and present a numerical example to illustrate the effectiveness of the proposed model.