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研究生： 林祖樑
Lin, Zu-Liang
論文名稱： 可修復系統非週期性預防維護策略之研究
A Study on Non-Periodic Preventive Maintenance Policies for Deteriorating Repairable Systems
指導教授： 黃宇翔
Huang, Yeu-Shiang
學位類別： 博士
Doctor
系所名稱： 管理學院 - 工業與資訊管理學系
Department of Industrial and Information Management
論文出版年： 2010
畢業學年度： 99
語文別： 英文
論文頁數： 83
中文關鍵詞： 貝氏 、非齊次卜瓦松過程 、預防維護 、可修復系統 、可靠度
外文關鍵詞： Bayesian, non-homogeneous Poisson process, preventive maintenance, repairable system, reliability
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    • 複雜系統經常隨著時間而產生退化(deterioration)現象，退化的結果可能引起系統失效造成重大損失。因此，實施預防維護(preventive maintenance, PM)能減緩系統老化的程度並改善系統可靠度。何時施行以及如何進行預防維護等決策問題通常依據此系統的實際年齡來決定。然而，當系統退化程度與某些物理性變數(例如：金屬材料磨損程度或油品潤滑度)或系統性能量測變數(例如：系統失效頻率或所生產產品之不良率)有高度相關時，對系統進行狀態預防維護策略(condition-based PM policy)似乎比採取年齡相關預防維護策略(age-dependent PM policy)更適合。本研究針對可修復系統，假設系統失效服從冪次型強度函數(power law intensity)之非齊次卜瓦松過程(non-homogeneous Poisson process, NHPP)，考慮不完美維護(imperfect PM)以及最小維修(minimal repair)的情況下，分別對上述二種應用最廣泛的預防維護策略推導單位時間期望總成本最小化之最適預防維護策略(optimal PM strategy)。然而，當失效模型的參數在不確知的情況下，模型的推導與相關分析將難以進行。我們整合專家們過去的理論與實務經驗以及系統失效資料，建構年齡相關預防維護策略之貝氏決策分析(Bayesian decision analysis)來處理這類的難題。最後透過實例來說明本研究所提出之最適預防維護模型的實際應用，並進行模型相關參數之敏感度分析與其最適預防維護策略之探討。

    Since a complex system usually deteriorates with age, and such deterioration may cause malfunctions and result in severe damage and losses, preventive maintenance (PM) is often carried out to keep the system functioning in a good state. The decision of when and how to perform a PM activity is commonly based on system age. However, when the deterioration is highly correlated with some physical (e.g., material wear or lubricant degradation) or system performance variables, such as quality of produced items or number of system breakdowns, a condition-based PM policy seems more appropriate than an age-dependent one. In this study, the deterioration of the system is modeled by a non-homogeneous Poisson process with a power law failure intensity, and a widely used age reduction model is applied to describe the restoration degree of imperfect PM activities. We derive the optimal non-periodic PM schedules which minimize the expected total cost per unit time for two popular and highly attractive PM policies in the literature: the age-dependent and the condition-based PM policies. However, since the determination of such the optimal PM schedules may involve numerous uncertainties which typically make the analyses difficult to perform because of the scarcity of data, a Bayesian decision model, which utilizes all available information effectively, is also proposed in the age-dependent PM context to deal with such difficulties. Numerical examples are given to illustrate the importance and the effectiveness of the proposed models. Sensitivity analyses and discussion on the optimal PM strategies for the proposed models are also presented.

    Contents 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 1.1 Background and Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Scope and Importance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 System Deterioration Process. . . . . . . . . . . . . . . . . . . . . . . . . . . .6 2.2 Maintenance Policies. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 8 2.2.1 Periodic PM model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.2 Age-dependent PM model. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.3 Condition-based PM model . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Bayesian Decision Analysis for Repairable Systems . . . . . . . . . . 14 3 Non-Periodic Preventive Maintenance . . . . . . . . . . . . . . . . . . . . . . .17 3.1 Assumptions and Notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 PM Activities and Maintenance Costs . . . . . . . . . . . . . . . . . . . . .21 4 Age-Dependent PM Policy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 4.1 Optimization Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2 Bayesian Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 4.2.1 Prior and Posterior Analyses. . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2.2 Natural Conjugate Prior Distribution . . . . . . . . . . . . . . . . . . . . . 32 5 Condition-Based PM Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.1 System Reliability as the Condition Variable . . . . . . . . . . . . . . . . 37 5.2 Model Formulations and Analyses. . . . . . . . . . . . . . . . . . . . . . . .38 5.2.1 Model 1 (optimum Nm). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.2.2 Model 2 (optimum Nm and r(Nm)) . . . . . . . . . . . . . . . . . . . . . . 43 5.2.3 Model 3 (optimum Nm and ri, i = 1, 2, ..., rNm). . . . . . . . . . . . . 46 6 Illustrative Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 6.1 Age-dependent PM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 6.2 Condition-based PM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 7.1 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 7.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 7.3 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72 Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 A Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 A.1 Air Conditioner Failure Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

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