Optimizing Imperfect Preventive Maintenance Policy for a Multi-unit System with Different Virtual Ages

Optimal preventive maintenance policy for leased equipment using failure rate reduction

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.

PurposeWhile steady-state analysis is useful, it does not consider the inherent transient characteristics of repairable systems' behavior, especially in systems that have relatively short life spans, or when their transient behavior is of special concern such as the motivating example used in this paper, military systems. Therefore, a maintenance policy that considers both transient and steady-state availability and aims to achieve the best trade-off between high steady-state availability and rapid stabilization is essential.Design/methodology/approachThis paper studies the transient behavior of system availability under the Kijima Type II virtual age model. While such systems achieve steady-state availability, and it has been proved that deploying preventive maintenance (PM) can significantly improve its steady-state availability, this improvement often comes at the price of longer and increased fluctuating transient behavior, which affects overall system performance. The authors present a methodology that identifies the optimal PM policy that achieves the best trade-off between high steady-state availability and rapid stabilization based on cost-availability analysis.FindingsWhen the proposed simulation-based optimization and cost analysis methodology is applied to the motivating example, it produces an optimal PM policy that achieves an availability–variability balance between transient and steady-state system behaviors. The optimal PM policy produces a notably lower availability coefficient of variation (by 11.5%), while at the same time suffering a negligible limiting availability loss of only 0.3%. The new optimal PM policy also provides cost savings of about 5% in total maintenance cost. The performed sensitivity analysis shows that the system's optimal maintenance cost is sensitive to the repair time, the shape parameter of the Weibull distribution and the downtime cost, but is robust with respect to changes in the remaining parameters.Originality/valueMost of the current maintenance models emphasize the steady-state behavior of availability and neglect its transient behavior. For some systems, using steady-state availability as the sole metric for performance is not adequate, especially in systems that have relatively short life spans or when their transient behavior affects the overall performance. However, little work has been done on the transient analysis of such systems. In this paper, the authors aim to fill this gap by emphasizing such systems and applications where transient behavior is of critical importance to efficiently optimize system performance. The authors use military systems as a motivating example.

There have been many publications dealing with preventive maintenance policies for stochastically deteriorating systems. However, most of them study systems having one device subject to failure. Much of the limited research dealing with multi-device production systems has been conducted through simulation experiments. In this paper, the preventive maintenance problem for serial production systems is formulated as a mathematical model. This formulation permits management to analyse the impact of a preventive maintenance policy on a serial production system without resorting to simulation. Numerical examples are used to provide managerial implications for maintaining a serial production system. The results show that the operating characteristics of the stations are interrelated; therefore, it is important to examine the joint effects of a maintenance policy on the various stations of the production system simultaneously rather than study each station separately.

Thompson1 considers a linear control model to ascertain the optimal preventive maintenance policy for production equipment and, simultaneously, its optimal sale date. He assumes age‐dependent deterministic continuous deterioration, production rate and linear efficiency of maintenance expenditures. In the present paper we first consider a linear maintenance model under a budget constraint. The impact of such a restriction is an earlier switch in the optimal bang‐bang policy. Then a non‐linear, non‐autonomous generalization of Thompson's model is analysed by the maximum principle. The optimal maintenance policy is shown to be downward sloping provided that in each time period the production rate is greater than the sum of interest and deterioration rate. The monotonicity of the optimal rate of preventive maintenance holds also under the additional possibility of random machine failure provided the production rate is greater than the sum of the rate of interest, the rate of deterioration and the rate of stochastic failure at each age. Moreover, it is shown that the higher the failure rate the smaller the optimal expenditures for preventive maintenance at any fixed age of the machine. In particular, the optimal maintenance rate at age t in a model without random failure is greater than those in any case including stochastic failure at the same age.

Burn-in is a widely used method to eliminate the initial failures. Preventive maintenance policy such as age replacement is often used in field operation. In this paper burn-in and maintenance policy are taken into consideration at the same time. The properties of the corresponding optimal burn-in times and optimal maintenance policy are discussed.

ABSTRACTA framework for reliability and maintenance analysis of job shop manufacturing systems is proposed in this paper. An efficient preventive maintenance (PM) policy in terms of failure effects analysis (FEA) is proposed. Subsequently, reliability evaluation and component importance measure based on FEA are performed under the PM policy. A job shop manufacturing system is applied to validate the reliability evaluation and dynamic maintenance policy. Obtained results are compared with existed methods and the effectiveness is validated. Some vague understandings for issues such as network modelling, vulnerabilities identification, the evaluation criteria of repairable systems, as well as PM policy during manufacturing system reliability analysis are elaborated. This framework can help for reliability optimisation and rational maintenance resources allocation of job shop manufacturing systems.

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.

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

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

Optimal preventive maintenance policy of the balanced system under the semi-Markov model

In recent decades, philosophy behind maintenance has varied consistently due to the changes in complexity of designs, advances in automation and mechanization, adaptation to the fast growing market demand, commercial computation in the sectors, and environmental issues. In mid-forties, simplicity of designs, limited maintenance opportunities, and immaturity of trade culture made enough to perform only fix it when it broke approach, i.e. corrective maintenance, after failures. Last quarter of the 21th century made essential to constitute more conservative and preventive maintenance policies in order to ensure safety, reliability, and availability of systems with longer lifetime and cost effectiveness. Preventive maintenance can provide an economic saving more than 18% of operating cost of systems. In this basis, various stochastic models were proposed as a tool to constitute a maintenance policy to measure system availability and to obtain optimal maintenance periods. This paper presents a general perspective on common stochastic models in maintenance planning such as Homogenous Poisson Process, Non-Homogenous Poisson Process, and Imperfect Maintenance. The paper also introduces two common maintenance policies, block and age replacement policy, using these stochastic models.

Reliability modeling and optimal random preventive maintenance policy for parallel systems with damage self-healing

As an airframe has finite lifetime and has to be designed lightweight, the maintenance of airframe is indispensable to operate aircraft without any serious troubles. After an airframe begins to operate, it suffers stresses and the stress causes the damage such as cracks of the airframe. Cracks grow with operation time and cause catastrophic phenomenon such as the mid-air disintegration when they become greater than a critical size. So, the managerial crack size is prespecified and Preventive Maintenance (PM) undergoes when the inspected crack size exceeds it. In this paper, optimal PM policies of airframe crack failure are discussed. Airframe states are represented as the Markov renewal process, and one-step transition probabilities are discussed. The total expected cost from the start of operation to the end by failure is defined and the optimal PM policies which minimize it is discussed.

Hundreds of scholarly papers on optimisation of preventive maintenance policies for items under warranty have been published in the reliability related literature. They typically have two limitations: they make a simplified assumption on the relationship between age and usage for items under two-dimensional warranty and they assume that it is cost-effective to conduct preventive maintenance (PM) on each sold product item. These assumptions may not reflect the reality. This paper therefore proposes a copula-based approach to modelling the relationship between age and usage of items under two-dimensional (2D) warranty. It investigates the probabilistic properties of the bivariate failure rate functions of age and usage and derives optimal PM policies for users who bought multiple product items. It also proposes approaches to incorporating maintenance effectiveness in bivariate copulas for depicting the dependence between age and usage. A case study and numerical examples are provided to illustrate the findings.