Imperfect preventive maintenance model with two modes of failure

An inspection & imperfect maintenance model for a system with two competing failure modes

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

This paper considers replacement and maintenance policies for an operating unit which works at random times for jobs. The unit undergoes minimal repairs at failures and is replaced at a planned time T or at a number N of working times, whichever occurs first. The expected cost rate is obtained, and an optimal policy which minimizes it is derived analytically. The imperfect preventive maintenance (PM) model, where the unit is improved by PM after the completion of each working time, is analyzed. Furthermore, when the work of a job incurs some damage to the unit, the replacement model with number N is proposed. The expected cost rate is obtained by using theory of cumulative processes. Two modified models, where the unit is replaced at number N or at the first completion of the working time over time T, and it is replaced at T or number N, whichever occurs last, are also proposed. Finally, when the unit is replaced at time T, number N or Kth failure, whichever occurs first, the expected cost rate is also obtained.

A system consisting of a critical and an auxiliary component is studied, and imperfect maintenance models considering degradation interaction and maintenance effect are developed. The auxiliary component assists the critical one in completing the system function, and its failure does not directly lead to the system failure. When the critical component deteriorates to the preventive maintenance (PM) threshold, it is restored by PM. When the auxiliary component deteriorates to a poor condition, significantly affecting the system reliability, the dynamic importance of the auxiliary component is considered, and the maintenance decision is provided according to the state of the auxiliary component. By minimizing the system's long‐term average cost, the optimal PM threshold for the critical component and maintenance threshold for the auxiliary component are derived. Finally, the effectiveness of the proposed model is further demonstrated with examples, comparison with previous model and comprehensive sensitivity analysis.

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.

The preventive maintenance (PM) is scheduled periodically to restore the system condition. However, PM activities cannot generally restore the system to as good as new condition but in an intermediate situation, which is called imperfect PM. The PM interval optimization is useful for improving system reliability. A popular approach to optimization interval is minimizing the maintenance costs. The goal of this work is to obtain optimal PM intervals that minimize expected cost considered PM imperfect, in other words we obtain the optimal PM intervals assuming that the PM action restores the system operating state to be somewhere between as good as new and as bad as old. The results are applied in a real data and the PM is maintained at a decreasing sequence of intervals, which is more practical since most systems need more frequent maintenance with increased usage and age. Furthermore consider a wrong PM perfect hypotheses increase the maintenance cost substantially.

This study explores the feasibility of applying an integrated inventory model with the consideration of incorporating production programs and maintenance to an imperfect process involving a deteriorating production system. The main target of this research is to build an integrated inventory model with the issues of backorder and repair. Additionally, our proposed model tries to provide an optimal number of shipments m and lower cost. Furthermore, this article offers the detailed discussion of two preventive maintenances of the production run period which are named as perfect preventive maintenance and imperfect preventive maintenance. Also, in this study, we develop various special cases that consider the failure rate such as Weibull, geometric and learning effect. Based on the results, the demand and production ratio influences the holding cost and purchase cost and has the highest impact on the integrated model.

This paper studies a manufacturer with a system prone to failure. The manufacturer performs two types of maintenance activities: preventive maintenance (PM), performed periodically, resets the system, and Minimal Repair (MR), performed after breakdowns, restores the system to working condition. It is assumed that two different types of learning take place: (i) repetition learning: due to the repetitive nature of PM, the manufacturer gains experience and learns to perform the PM activities faster and at a lower cost and (ii) failure learning: each failure gives the manufacturer the opportunity to find the root causes, to learn from mistakes and to improve the system. This paper, the first one to quantify failure learning in maintenance literature, assumes that such learning can then be applied during the next PM activity, which brings down the failure rate for the next PM cycle. For the increasing failure rate case, repetition learning increases the PM frequency, whereas failure learning causes the manufacturer to reduce the optimal number of PM activities. However, for the constant failure rate, repetition learning has no effect on the PM frequency, whereas failure learning may actually increase it.

This article develops an integrated model in considering the situations of an imperfect process with imperfect maintenance and inspection time for the joint determination of both economic production quantity (EPQ) and preventive maintenance (PM). This imperfect process has a general deterioration distribution with increasing hazard rate. Even with periodic PM, such a production system cannot be recovered as good as new. This means that the system condition depends on how long it runs. Also, the PM level can be distinct due to the maintenance cost. For convenience, it is assumed the age of system is reduced in proportional to the PM level. Further, during a production cycle, we need an inspection to see if the process is in control. This inspection might demand a considerable amount of time. In this article, we take PM level and inspection time into consideration to optimise EPQ with two types of out-of-control states. To see how the method works, we use a Weibull shock model to show the optimal solutions for the least costs.

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

Many systems are required to perform a series of missions with finite breaks between any two consecutive missions. In such a case, one of the most widely used maintenance policies is a selective maintenance in which a subset of feasible maintenance actions is chosen to be performed with the aim at achieving the subsequent mission success under limited maintenance resources. Traditional selective maintenance optimization reported in the literature only focuses on binary state systems. Most systems in industrial applications, however, have more than two states in the deterioration process. In this work, a selective maintenance policy for multi-state systems (MSS) consisting of binary state elements is investigated. Taking the imperfect maintenance quality into consideration, the Kijima model is reviewed, and a cost-maintenance quality relationship which considers the age reduction factor as a function in terms of maintenance cost is established. Moreover, with the assistance of the universal generating function (UGF) method, the probability of the repaired MSS successfully completing the subsequent mission is formulated. In place of enumerative methods, a genetic algorithm (GA) is employed to solve the complicated optimization problem where both multi-state systems, and imperfect maintenance models are taken into account. The effectiveness of the proposed method is demonstrated via a case study of a power station coal transportation system. Finally, a comparative analysis between the strategies with and without considering imperfect maintenance is conducted, and it is concluded that incorporating imperfect maintenance quality into selective maintenance achieves better outcomes.

This paper studies the problem of multi-stage preventive maintenance (PM) optimization on the basis of reliability thresholds. According to the change rule of product's failure rate and by means of setting the reliability thresholds, the replacement cycle is divided into three maintenance stages, they are: (1) Stage I: do not carry out PM; (2) Stage II: carry out periodic PM; (3) Stage III: carry out sequential PM. In each stage, the failures are restored with minimal repair. Age reduction factor and quasi-renewal coefficient are adopted to derive the recursive relations of failure rate function in each stage. A multi-stage PM optimization model is established based on the reliability thresholds, with the aim to minimize the equipment's expected cost rate. Taking the gearbox, rotor and bearing of wind turbine as an example, a case study is conducted to illustrate the effectiveness of the proposed method.

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.

Shutting down a power plant for any reason is a costly process. Loss of production revenues from one unit can exceed millions of dollars per day. It is therefore good practice to keep outages as short and efficient as possible. A major component of planned outages is Preventive Maintenance (PM). It is important that PM be applied only where needed. Unnecessary PM is costly, not only in terms of labor and material costs, but in additional lost time and production. Further, there are cases where PM is contraindicated by standard reliability models, i.e. components with decreasing failure rates. This can paradoxically introduce failures, incurring additional repair costs and production loss. The risk management group at the South Texas Project Electric Generating Station (STPEGS) has successfully developed software to optimize PM schedules by minimizing total costs and risks associated with corrective maintenance (CM) and PM. The optimum PM interval is determined as a multiple of outage cycles. Components are evaluated based on maintenance type, risk ranking, cost of performing CM at power, and regulatory or internal commitments. This information provided to systems engineering assists in determining whether to advance PM from an upcoming outage, or defer PM to a subsequent outage. Components with maintenance that can be performed online are outside of the scope of this paper and are not considered here.

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.