Replacement and Preventive Maintenance Models with Random Working Times

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.

Preventive maintenance (PM) can slow the deterioration process of a repairable system and restore the system to a younger state. The proposed PM model of this paper focuses on the restoration effect of degradation rate reduction which can only relieve stress temporarily and slow the rate of system degradation while the hazard rate is still monotonically increased. This PM model considers a deteriorating but repairable system (or equipment) with a finite life time period. This PM model is modified based on an original degradation-rate-reduction PM model over a finite time span of which the searching range for the optimal solution of the time interval between each PM is limited. It is demonstrated that the proposed degradation-rate-reduction PM model over a finite time period can have a better optimal solution than the original PM model. The algorithm of finding the optimal solution for the modified PM model is developed. Examples are provided and are compared with the corresponding original PM model.

This chapter deals with a preventive maintenance problem for consecutive-k-out-of-n and connected-(r, s)-out-of-(m, n): F systems. The system failure probability of two types of multi-unit systems is analytically derived by utilizing the system failure paths. Dependence mechanisms between components in the systems are illustrated and the system failure paths under dependence models are shown. The expected cost rates of corrective maintenance, age preventive maintenance, and condition-based maintenance policies are estimated. The optimal maintenance policies to minimize the expected cost rates in two preventive maintenance models are obtained and three maintenance policies are compared by numerical examples.

Stress-reducing preventive maintenance model for a unit under stressful environment

Optimal rearrangement and preventive maintenance policies for heterogeneous balanced systems with three failure modes

Optimal maintenance–replacement policy of products with competing failures after expiry of the warranty

본 논문에서는 수리가 가능한 시스템에 대하여 혼합보증이 종료된 이후의 교체모형과 예방보전모형을 고려하는데, 만약 보증기간이 종료된 이후에 시스템에 고장이 발생하면 최소수리를 수행한다. 최적의 교체정책과 최적의 예방보전정책을 결정하기 위한 기준으로는 기대비용과 기대비가동시간에 근거한 총밸류함수를 사용한다. 그리고 시스템의 고장시간이 와이블분포를 할 때 수치적 예를 통해서 제안된 최적의 교체정책 및 예방보전정책을 자세히 설명하고자 한다. This paper considers the replacement model and the preventive maintenance model following the expiration of combination warranty for a repairable system. If the system fails after the combination warranty is expired, then it is minimally repaired at each failure. The criterion used to determine the optimal replacement policy and the optimal preventive maintenance policy is the overall value function based on the expected cost rate per unit time and the expected downtime per unit time. The numerical examples are presented for illustrative purpose when the failure time follows a Weibull distribution.

Purpose Making decisions on preventive maintenance (PM) policy and buffer sizing, as is often studied, may not result in overall optimization. The purpose of this paper is to propose a joint model that integrates PM and buffer sizing with consideration of quality loss for a degenerating system, which aims to minimize the average operation cost for a finite horizon. The opportunistic maintenance (OM) policy which could increase the output and decrease the cost of the system is also explored. Design/methodology/approach A joint PM and buffer size model considering quality loss is proposed. In this model, the time-based PM and the condition-based PM are taken on the upstream and the downstream machine, respectively. Further, the OM policy based on the theory of constraints (TOC) is also considered. An iterative search algorithm with Monte Carlo is developed to solve the non-linear model. A case study is conducted to illustrate the performance of the proposed PM policies. Findings The superiority of the proposed integrated policies compared with the separate PM policy is demonstrated. Effects of the policies are testified. The advantages of the proposed TOC-based OM policy is highlighted in terms of low-cost and high-output. Originality/value Few studies have been carried out to integrate decisions on PM and buffer size when taking the quality loss into consideration for degenerating systems. Most PM models treat machines equally ignoring the various roles of them. A more comprehensive and integrated model based on TOC is proposed, accompanied by an iterative search algorithm with Monte Carlo for solving it. An OM policy to further improve the performance of system is also presented.

Preventive maintenance (PM) is a maintenance program with activities initiated at predetermined intervals, or according to prescribed criteria, and intended to reduce the probability of failure, or the degradation of the functioning of an item. In the literature, a number of PM models have been introduced to depict the effectiveness of PM. Based on these models, approaches to scheduling PM policies have been considerably studied. This paper attempts to review existing PM models, and investigate their inter-relationships. We then categorize these models into three classes: linear, nonlinear, and a hybrid of both. These three PM model classes depict the relationships of the hazard functions before, and after a PM. Possible extensions to these three PM models are discussed. The statistical properties for models are derived, and approaches to optimizing the PM policy are given.

An Efficient Jaya Algorithm for Joint Optimization of Preventive Maintenance and Quality Policy in Production Systems

In this paper, an imperfect preventive maintenance model with two modes of failures is proposed and analyzed for the deteriorating system. We introduce the concept of two modes of failures: maintainable and non-maintainable. The deteriorating system experiences minimal repair when the system fails and experiences preventive maintenance at a periodic interval. The hazard rate of maintainable failures is reduced by preventive maintenance, but the hazard rate of non-maintainable failures isn't changed by preventive maintenance. Therefore, the preventive maintenance is imperfect. Generally, it is assumed that the dependence of two modes of failures is independent, but, in fact, the maintainable failure is influenced by the non-maintainable. The paper considers the dependence of two modes of failures and introduces the doubly stochastic Poisson in order to describe the dependence of two modes of failure. The optimal interval between the preventive maintenance and the optimal number of preventive maintenances are determined for minimizing the expected cost rate. Finally, the feasibility of model is illustrated by a numerical example.

We discuss models of preventive maintenance (PM) under different assumptions on the failure/repair processes. The main emphasis is on the PM modeling under the Brown‐Proschan model for minimal/perfect repairs. We also present the generalization of this model for the failure/repair process governed by the generalized Polya process. Some comparisons with conventional PM models are discussed (Nonhomogeneous Poisson process, renewal process, and geometric process of failure/repairs). Several practical examples are considered.

When maintenance models are developed for complex continuous operating systems, with large production losses, it is important to take into account the maintenance duration, in order to provide an effective maintenance program. In this work, a preventive maintenance model is presented in order to coordinate the component replacements in a multi-component system. The model is based on the partial periodic renewal policy. At each partial renewal, a group of components to be replaced is defined. When all components are replaced simultaneously, we consider that the system undergoes an overhaul which resets it to the new state. Moreover, the model takes into account for non-negligible replacement times, where different assumptions are considered. The relevant effect of maintenance times on the optimal policy is clearly shown by the numerical results, provided by the application in an oil refinery.

Among the different maintenance techniques applied to wind turbine (WT) components, online condition monitoring is probably the most promising technique. The maintenance models based on online condition monitoring have been examined in many studies. However, no study has considered preventive maintenance models with incorporated probabilities of correct and incorrect decisions made during continuous condition monitoring. This article presents a mathematical model of preventive maintenance, with imperfect continuous condition monitoring of the WT components. For the first time, the article introduces generalized expressions for calculating the interval probabilities of false positive, true positive, false negative, and true negative when continuously monitoring the condition of a WT component. Mathematical equations that allow for calculating the expected cost of maintenance per unit of time and the average lifetime maintenance cost are derived for an arbitrary distribution of time to degradation failure. A numerical example of WT blades maintenance illustrates that preventive maintenance with online condition monitoring reduces the average lifetime maintenance cost by 11.8 times, as compared to corrective maintenance, and by at least 4.2 and 2.6 times, compared with predetermined preventive maintenance for low and high crack initiation rates, respectively.

Most preventive maintenance (PM) models require, as inputs, information on the behaviour of the equipment under failure-only maintenance (FM). Once a schedule of PM has been applied, data arising from failures are affected by the PM. Over life the behaviour that would occur under FM changes. But PM also tends to delay aging processes. This paper examines: 1) how data collected under four kinds of PM policy can be modified to re-assess the FM characteristics, and 2) how to tell whether an apparent change in them is important. The approach takes account of engineering as well as statistical factors. It concludes that: 1. Estimation of distributions and costs as they would be under FM from data collected under PM cannot be accurate but a suboptimal policy can be worse. 2. A different type of PM policy might be required following changes to costs and/or distribution. The optimum under one model might not be the overall optimum. 3. The solutions suggested in the paper remain unproved due to the ``data problem''. Mathematical research alone can never produce workable procedures. A viable methodology will need years of experimentation with real systems. 4. The potential savings are huge.