A value-based preventive maintenance policy for multi-component system with continuously degrading components

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Abstract

A dynamic preventive maintenance policy for system with continuously degrading components is investigated in this paper. Different from traditional cost-centric preventive maintenance policy, our maintenance strategy is formulated from the value perspective. Component value is modelled as a function of component reliability distribution. Maintenance action is triggered whenever the system reliability drops below a certain threshold. Our policy mainly consists of two steps: (i) determine which component to maintain; (ii) determine to what degree the component should be maintained. In Step 1, we introduce the yield-cost importance to select the most important component. In Step 2, the optimal maintenance level is obtained by maximizing the net value of the maintenance action. Finally, numerical examples are given to illustrate the proposed policy.

Introduction

Maintenance plays an important role in industrial production, especially in areas where the loss of system failure is large. Various maintenance policies have been developed to improve system safety, reduce system failures and lower manufacturing cost. Preventive maintenance (PM) is a policy that occurs when the system is still operating, aiming to retain the system or specified components in a certain condition [1], [2], [3], [4]. PM policy focusing on single-component degrading system has been extensively studied [5], [6], [7]. However, in recent years, due to the increasing complexity and variety of production systems, more attention is being paid to PM on multi-component systems [8].

The existing PM policies for multi-component degrading system can be categorized into two classes. The first class assumes that each component only has two states, i.e., functioning or failed. Component degradation is described in terms of failure rate or hazard rate, and so on with the objective to find an optimum strategy that minimizes maintenance cost. Usually, PM is triggered when the system reliability or availability falls below a certain prescribed level. As a result, the problem becomes optimization of PM thresholds or other parameters that lead to cost minimization [9], [10]. For instance, Zhou and Li [11] derived a dynamic PM policy by sequentially optimizing maintenance cost at every maintenance point. Samrout et al. [12] addressed the problem of PM optimization by referring component degradation to as proportional hazard rate. Lin and Wang [13] investigated the PM problem under reliability constraints and adopted importance measures to minimize non-periodic PM cost. For some more recent works, see e.g. [14], [15], [16].

The second class is based on discrete-state Markov chains, where component states are usually divided into several classes such as ‘as good as new’, ‘preventive maintenance due’ and ‘failed’ [17], [18], [19]. Gürler and Kaya [20] proposed an approximation to represent component lifetime as a number of finite stages. Nourelfath and Ait-Kadi [21] addressed the problem of prioritizing resources between components under the reliability constraint. Modelling by discrete Markov chains still owns some disadvantages, e.g., the classification of component states is arbitrary. Moreover, it assumes that failures can only occur at discrete time points. Therefore, it is more appropriate to treat component degradation as a continuous stochastic process.

In the literature, most maintenance policies are cost-centred, i.e., policies are developed by minimizing maintenance cost [22]. However, for companies, as maintenance action is meant to generate profit, it is more reasonable to view maintenance as a value-generating action. Wang [1] highlighted the critical idea that when making the maintenance decision, cost, along with the value resulting from improved reliability, should be considered. Hitherto, few studies have been undertaken to address the problem of value-based maintenance policy [23], [24].

Motivated by the idea of maintenance value, our PM policy is developed from the value perspective. In the previous works, for imperfect maintenance, the repair rate was assumed to be constant and the maintenance cost was invariant [25]. However, maintenance cost of complex system would vary, especially for imperfect maintenance, where maintenance cost would be different if the maintenance degree varies [26], [27]. Resources should be allocated to components with less maintenance cost [28].

In this study, a PM policy for multi-component system concerning continuously degrading components is developed. The maintenance objective is to maximize the maintenance net value. Different from previous stationary maintenance policies, a dynamic PM policy is proposed, with the advantage of incorporating short-term information. The PM policy consists of two steps: (i) determine which component to maintain; (ii) determine to what degree the component should be maintained. The yield-cost importance is introduced to determine the most importance component.

The rest of this paper is organized as follows. Section 2 presents system description and reliability analysis for the system composed of continuously degrading components. Section 3 constructs the PM objective and introduces yield-cost importance to make the maintenance decision. Section 4 gives a numerical example to illustrate the proposed method. Finally, Section 5 concludes the study.

Section snippets

Basic assumptions

In this study, the following assumptions are used:

  • (1)

    Components are mutually independent.

  • (2)

    Each component is continuously monitored.

  • (3)

    Compared to the time period between two consecutive PM actions, the duration of PM activity is negligible.

  • (4)

    Degradation is the only cause of system failure. The effects of aging, wear and other cumulative damages are integrated into a degradation process.

  • (5)

    Only one maintenance crew is available and only one component can be maintained at a time.

  • (6)

    Maintenance action does not

Dynamic PM formulation

To obtain the net value within the time horizon, we need to determine the number of PM actions, which requires long-term information. However, in practice, only short-term information is available. Hence, in this study, we turn to a dynamic policy, which optimizes the maintenance net value for each PM actions.

The difficulty of value-based PM optimization lies in quantifying the benefits generated by maintenance action [1]. Particularly, how to represent the maintenance value in the form of

Example 1 – specifications of the system and components

To show the implementation procedure of the modelling and analysis proposed in this paper, an illustrative example of a 3-component system is used, as shown in Fig. 2.

The system reliability isR(t)=R1(t)(1(1R2(t))(1R3(t))).We assume that the degradation path of component i isXi(t;μi,θi)=xi0+μit+θi,where xi0 denotes the initial degradation level, μi is a fixed parameter and θi is a random parameter following normal distribution, i.e., θi~N(0,σi). The reliability of component i isRi(t)=Φ(Liμit

Conclusion

This study proposes a PM policy for system with continuously degrading components. Considering the case that only one maintenance crew is available, a dynamic PM strategy is developed with the objective of maximizing the maintenance net value. Yield-cost importance is introduced to determine the most important component. The proposed importance measure reduces computational complexity for maintenance decision making. This method can be used for maintenance of complex systems where computational

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    In previous studies, special attention has been paid to structural, economic, and stochastic dependencies of multi-component engineering systems [27,28]. For instance, structural dependence has been widely explored to investigate the impact of the maintenance action of one component on other components [29,9,30]. Economic dependence refers to that the total maintenance cost of a system may be increased or decreased due to joint maintenance of components [31,32].

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