Optimal maintenance strategy under renewable warranty with repair time threshold

In this paper, we consider a periodic preventive maintenance model, from the manufacturer's perspective, which can be implemented to reduce the maintenance cost of a repairable product during a given warranty period. The product is assumed to deteriorate with age and the warranty policy we adopt in this paper takes into account the two factors of failure time and repair time of the product when the product failure occurs. Under the proposed two-factor warranty, a repair time threshold is pre-determined and if the repair takes more time than that of the threshold, the failed product is replaced with a renewed warranty policy. Otherwise, the product is only minimally repaired to return to the operating state. During such a renewable warranty period, preventive maintenance is conducted to reduce the rate of degradation periodically while the product is in operation. By assuming certain cost structures, we formulate the expected warranty cost during the warranty period from the manufacturer's perspective when a periodic preventive maintenance strategy is adapted. Although more frequent preventive maintenance increases the warranty cost, the chance of product failures would be reduced. The main aim of this paper is to accomplish the optimal trade-off between the warranty cost and the preventive maintenance period by determining the optimal preventive maintenance period that minimizes the total expected warranty cost during the warranty period. Assuming the power law process for the product failures, we illustrate our proposed maintenance model numerically and study the impact of relevant parameters on the optimal preventive maintenance policy.     

Maintenance optimization for second‐hand products following periodic imperfect preventive maintenance warranty period

The maintenance policy for a product's life cycle differs for second‐hand and new products. Although several maintenance policies for second‐hand products exist in the literature, they are rarely investigated with reference to periodic inspection and preventive maintenance action during the warranty period. In this research, we study an optimal post‐warranty maintenance policy for a second‐hand product, which was purchased at age x with a fixed‐length warranty period. During the warranty period, the product is periodically inspected and maintained preventively at a prorated cost borne by the user, while any product failure is only minimally repaired by the dealer. After the warranty expires, the product is self‐maintained by the user for a fixed‐length maintenance period and the costs incurred during this time are fully borne by the user. At the end of the maintenance period, the product is replaced with a product of the user's choice. This study is focused on the determination of an optimal length for the maintenance period after the warranty expiration. As a criterion for the optimality, we adopt the long‐run mean cost during the second‐hand product's life cycle from the user's perspective. Finally, our results are analyzed numerically for sensitive analysis of several relevant factors, assuming that the failure distribution follows a Weibull distribution.     

Optimal maintenance strategy for non‐renewing replacement–repair warranty

In this paper, we study the maintenance policy following the expiration of the non‐renewing replacement–repair warranty (NRRW). For such purposes, we first define the non‐renewing free replacement–repair warranty and the non‐renewing pro rata replacement–repair warranty. Then the maintenance model following the expiration of the NRRW is discussed from the user's point of view. As the criterion to determine the optimal maintenance strategy, we formulate the expected cost rate per unit time from the user's perspective. All system maintenance costs incurred after the warranty is expired are paid by the user. Given the cost structures during the life cycle of the system, we determine the optimal maintenance period following the expiration of the NRRW. Finally, a few numerical examples are given for illustrative purposes. Copyright © 2012 John Wiley & Sons, Ltd.     

Two-dimensional warranty repair strategy based on minimal and complete repairs

For repairable products, the warrantor has options in choosing the degree of repair applied to an item that has failed within the warranty period. We focus on a particular warranty repair strategy, related to the degree of the warranty repair, for non-renewing, two-dimensional, free of charge to the consumer warranty policy. We consider a rectangular warranty region and divide it into three disjoint subregions, so that each of these subregions has a preassigned degree of repair for a faulty item. Our main goal is to determine the subregions, so that the associated expected warranty servicing cost per item sold is minimised. A comparison between our strategy and previously studied, more restrictive, ones is provided.     

A new preventive maintenance strategy for items sold under warranty

When products are sold under warranty, the manufacturer incursadditional costs for warranty servicing. Preventive maintenanceactions can be used to reduce this cost and these are worthwhileonly if the extra cost incurred is less than the reduction achieved.In this paper we propose a new preventive maintenance policywhere the parameters are selected optimally to minimize thetotal warranty servicing cost.     

Optimal warranty policies for systems with imperfect repair

We investigate a system whose basic warranty coverage is minimal repair up to a specified warranty length. An additional service is offered whereby first failure is restored up to the consumers’ chosen level of repair. The problem is studied under two system replacement strategies: periodic maintenance before and after warranty. It turns out that our model generalizes the model of Rinsaka and Sandoh [K. Rinsaka, H. Sandoh, A stochastic model with an additional warranty contract, Computers and Mathematics with Applications 51 (2006) 179–188] and the model of Yeh et al. [R.H. Yeh, M.Y. Chen, C.Y. Lin, Optimal periodic replacement policy for repairable products under free-repair warranty, European Journal of Operational Research 176 (2007) 1678–1686]. We derive the optimal maintenance period and optimal level of repair based on the structures of the cost function and failure rate function. We show that under certain assumptions, the optimal repair level for additional service is an increasing function of the replacement time. We provide numerical studies to verify some of our results.     

Optimal periodic replacement policy for repairable products under free-repair warranty

This paper investigates the effects of a free-repair warranty on the periodic replacement policy for a repairable product. Cost models are developed for both a warranted and a non-warranted product, and the corresponding optimal periodic replacement policies are derived such that the long-run expected cost rate is minimized. For a product with an increasing failure rate function, structural properties of these optimal policies are obtained. By comparing these optimal policies, we show that the optimal replacement period for a warranted product should be adjusted toward the end of the warranty period. Finally, examples are given to numerically illustrate the impact of a product warranty on the optimal periodic replacement policy.     

A general age-replacement model with minimal repair under renewing free-replacement warranty

A general age-replacement model in which incorporates minimal repair, planned and unplanned replacement, is considered in this paper for products under a renewing free-replacement warranty policy. For both warranted and non-warranted products, cost models from the user’s perspective are developed, and the corresponding optimal replacement ages are derived such that the long-run expected cost rate is minimized. The impacts of a product warranty on the optimal replacement model are investigated analytically. Furthermore, we show that the optimal replacement age for a warranted product is closer to the end of the warranty period than for a non-warranted product. Finally, numerical examples are given for illustration.     

Optimum policy for a production system with major repair and preventive maintenance

This study applies periodic preventive maintenance (PM) to a repairable production system with major repairs conducted after a failure. This study considers failed PM due to maintenance workers incorrectly performing PM and damages occurring after PM. Therefore, three PM types are considered: imperfect PM, perfect PM and failed PM. Imperfect PM has the same failure rate as that before PM, whereas perfect PM makes restores the system perfectly. Failed PM results in system deterioration and major repairs are required. The probability that PM is perfect or failed depends on the number of imperfect maintenance operations conducted since the previous renewal cycle. Mathematical formulas for expected total production cost per unit time are generated. Optimum PM time that minimizes cost is derived. Various special cases are considered, including the maintenance learning effect. A numerical example is given.     

Optimal preventive maintenance of a production system with an intermediate buffer

In this paper we consider a model consisting of a deteriorating installation that transfers a raw material to a production unit and a buffer which has been built between the installation and the production unit. The deterioration process of the installation is considered to be nonstationary, i.e. the transition probabilities may depend not only on the working conditions of the installation but on its age as well. The problem of the optimal preventive maintenance of the installation is considered. Under a suitable cost structure it is shown that, for fixed age of the installation and fixed buffer level, the optimal policy is of control-limit type. When the deterioration process is stationary, an efficient Markov decision algorithm operating on the class of control-limit policies is developed. There is strong numerical evidence that the algorithm converges to the optimal policy. Two generalizations of this model are also discussed.     

Optimal preventive maintenance,protection, and replacement of a revenue-earning asset

The problem of determining the optimal pattern of expenditure on preventive maintenance or protection for a revenue-earning asset subject to catastrophic breakdown or destruction is discussed. It is assumed that the probability of breakdown at any time depends on the age of the asset and on the current rate of prevention expenditure. The objective considered is the maximization of the expected present value of revenues earned net of prevention and replacement costs. Three distinct cases are discussed: (a) when revenue is earned only until breakdown; (b) when there is automatic replacement following a breakdown; and (c) when there is the option of periodic replacement. Use of the Pontryagin maximum principle enables the determination of the optimal prevention schedules in all cases. In addition, when periodic replacement is possible the optimal replacement interval can be determined. Numerical methods are required to obtain solutions.     

有延迟修理的两部件串联系统的预防维修策略

研究由两个部件串联组成的系统的预防维修策略, 当系统的工作时间达到T时进行预防维修, 预防维修使部件恢复到上一次故障维修后的状态. 当部件发生故障后进行故障维修, 因为各种原因可能会延迟修理. 部件在每次故障维修后的工作时间形成随机递减的几何过程, 且每次故障后的维修时间形成随机递增的几何过程. 以部件进行预防维修的间隔T和更换前的故障次数N组成的二维策略(T,N)为策略, 利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式, 并给出了具体例子和数值分析.     

Optimal inspection of a complex system subject to periodic and opportunistic inspections and preventive replacements

This paper proposes two optimization models for the periodic inspection of a system with “hard-type” and “soft-type” components. Given that the failures of hard-type components are self-announcing, the component is instantly repaired or replaced, but the failures of soft-type components can only be detected at inspections. A system can operate with a soft failure, but its performance may be reduced. Although a system may be periodically inspected, a hard failure creates an opportunity for additional inspection (opportunistic inspection) of all soft-type components. Two optimization models are discussed in the paper. In the first, soft-type components undergo both periodic and opportunistic inspections to detect possible failures. In the second, hard-type components undergo periodic inspections and are preventively replaced depending on their condition at inspection. Soft-type and hard-type components are either minimally repaired or replaced when they fail. Minimal repair or replacement depends on the state of a component at failure; this, in turn, depends on its age. The paper formulates objective functions for the two models and derives recursive equations for their required expected values. It develops a simulation algorithm to calculate these expected values for a complex model. Several examples are used to illustrate the models and the calculations. The data used in the examples are adapted from a real case study of a hospital’s maintenance data for a general infusion pump.     

A geometric process maintenance model with preventive repair

In this paper, a geometric process maintenance model with preventive repair is studied. A maintenance policy (T, N) is applied by which the system will be repaired whenever it fails or its operating time reaches T whichever occurs first, and the system will be replaced by a new and identical one following the Nth failure. The long-run average cost per unit time is determined. An optimal policy (T^∗, N^∗) could be determined numerically or analytically for minimizing the average cost. A new class of lifetime distribution which takes into account the effect of preventive repair is studied that is applied to determine the optimal policy (T^∗, N^∗).     

Multi-objective open shop scheduling by considering human error and preventive maintenance

This study presents an open shop scheduling model by considering human error and preventive maintenance. The proposed mathematical model takes into account conflicting objective functions including makespan, human error and machine availability. In order to find the optimum scheduling, human error, maintenance and production factors are considered, simultaneously. Human error is measured by Human Error Assessment and Reduction Technique (HEART). Three metaheuristic methods including non-dominated sorting genetic algorithm-II (NSGA-II), multi-objective particle swarm optimization (MOPSO) and strength Pareto evolutionary algorithm II (SPEA-II) are developed to find near-optimal solution. The Taguchi method is applied by adjusting parameters of metaheuristic algorithms. Several illustrative examples and a real case study (auto spare parts manufacturer) are applied to show the applicability of the multi-objective mixed integer nonlinear programming model. The proposed approach of this study may be used for similar open shop problems with minor modifications.     

Optimal replacement policies with minimal repair and age-dependent costs

In this paper, we study a modified minimal repair/replacement problem that is formulated as a Markov decision process. The operating cost is assumed to be a nondecreasing function of the system's age. The specific maintenance actions for a manufacturing system to be considered are whether to have replacement, minimal repair or keep it operating. It is shown that a control limit policy, or in particular a (t, T) policy, is optimal over the space of all possible policies under the discounted cost criterion. A computational algorithm for the optimal (t, T) policy is suggested based on the total expected discounted cost.     

Optimal number of minimal repairs before ordering spare for preventive replacement

This paper presents a model for determining the optimal number of minimal repairs before ordering spare for preventive replacement. By introducing the costs of ordering, repair, downtime, replacement, and the salvage value of an un-failed system, the expected long-term cost rates and cost effectiveness are derived. It is shown that, under certain conditions, the optimal number of minimal repairs, which minimizes the cost rate or maximizes the cost effectiveness, is given by a unique solution of an equation. A numerical example is also given for illustration of the proposed model.     

The relationship between preventive maintenance and manufacturing system performance

A common lament of the preventive maintenance (PM) crusaders is that production supervisors are often unwilling to lose valuable machine time when there are job waiting to be processed and do not assign high enough priority to PM. Maintenance activities that depend dynamically on system state are too complicated to implement and their overall impact on system performance, measured in terms of average tardiness or work-in-process (WIP) inventory, is difficult to predict. In this article, we present some easy to implement state-dependent PM policies that are consistent with the realities of production environment. We also develop polling models based analyses that could be used to obtain system performance metrics when such policies are implemented. We show that there are situations in which increased PM activity can lower total expected WIP (and overall tardiness) on its own, i.e., without accounting for the lower unplanned downtime. We also include examples that explain the interaction between duration of PM activity and switchover times. We identify cases in which a simple state-independent PM policy outperforms the more sophisticated state-dependent policies.     

Probabilistic analysis of a system with dependent units having a single repair facility subject to preventive maintenance

The paper deals with the availability and the reliability analysis of a system with dependent units having a single repair facility subject to preventive maintenance. The system initially consists of n-identical units (connected in parallel) each with failure rate λ_n. The failure rate of a unit at any given instant of time depends upon the number of units operating at that instant. The time to repair of a failed unit and the time for maintenance of the repair- facility are arbitrarily distributed whereas the time to failure of a unit is exponentially distributed. The results obtained have been compared with those obtained when the repair facility is not subject to preventive maintenance.