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研究生: 李密合
Lee, Mi-Ho
論文名稱: 利用廣義指數分配預測可維修系統的故障時間
Using Generalized Exponential Distributions to Predict the Failure Times of Repairable Systems.
指導教授: 洪文良 教授
口試委員:
學位類別: 碩士
Master
系所名稱: 南大校區系所調整院務中心 - 應用數學系所
應用數學系所(English)
論文出版年: 2007
畢業學年度: 95
語文別: 中文
論文頁數: 23
中文關鍵詞: 可維修系統廣義指數分配最小維修預防保養
外文關鍵詞: repairable system, generalized exponential distribution, minimal repair, major overhauls
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  • 摘要
    本文主要探討可維修系統,在經歷最小維修和預防保養後,預測系統的未來故障時間。將系統的預防保養效果假設為比例降低壽命模型,而兩個連續的預防保養期間的故障時間則假設為廣義指數分配。並利用最大概似估計及貝氏估計兩種方法來估計參數,比較兩種方法下,模式的預測效果。最後,用一個實例研究的例子來說明所提出的預測程序。實例研究顯示根據絕對誤差,在某些的先驗分配下,貝氏的預測效果較最大概似估計好。

    關鍵字:可維修系統;廣義指數分配;最小維修;預防保養。


    Abstract
    The purpose of this study is to predict future failure time of the repairable system after minimal repair and major overhauls. Usually, the effect of major overhaul of the repairable system is modeled by a proportional age reduction. Furthermore, we use the generalized exponential distribution to model failure process between two successive overhaul epochs. To predict future failure time of this system, we propose two approaches. One is maximum likelihood method and the other is Bayesian. Numerical results show that the Bayesian approach under some prior distributions performs better than the maximum likelihood estimate according to absolute error criterion.

    Keywords:repairable system; generalized exponential distribution;minimal repair;major overhauls.

    目錄 頁次 致謝辭………………………………………………………………Ⅰ 中文摘要……………………………………………………………Ⅱ 英文摘要……………………………………………………………Ⅲ 目錄…………………………………………………………………Ⅳ 圖目錄………………………………………………………………Ⅴ 表目錄………………………………………………………………Ⅵ 第一章 緒論………………………………………………………1 第一節 研究動機及目的…………………………………………1 第二節 研究架構…………………………………………………2 第二章 文獻探討…………………………………………………4 第三章 廣義指數分配模型………………………………………6 第四章 參數估計及預測…………………………………………10 第一節 最大概似估計…………………………………………10 第二節 貝氏估計………………………………………………11 第五章 實例研究…………………………………………………15 第六章 結論及建議………………………………………………22 參考文獻………………………………………………………………23

    [1] Gupta, R.D.; Kundu, D. (1999) Generalized exponential distribution. Australian and New Zealand Journal of Statistics, 41(2), 173-188.

    [2] Jack, N. (1997) Analysing event data from a repairable machine subject to imperfect preventive maintenance. Quality and Reliability Engineering International, 13(4), 183-186.

    [3] Malik, M. A. K. (1979) Reliable preventive maintenance scheduling. AIIE Transaction, 11(3), 221-228.

    [4] Pulcini, G. (2000) On the Overhaul effect for repairable mechanical units: a Bayes approach. Reliability Engineering and System Safety, 70(1), 85-94.

    [5] Pulcini, G. (2001) On the prediction of future failures for a repairable equipment subject to overhauls. Communication in Statistics —Theory and Methods, 30(4), 691-706.

    [6] Shin, I.; Lim, T. J.; Lie, C. H. (1996) Estimating parameters of intensity function and maintenance effect for repairable unit. Reliability Engineering and System Safety, 54(1), 1-10.

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