加速衰變測試下p 分位失效時間之貝氏估計

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魏郁昇(Yu-sheng Wei) 查詢紙本館藏

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統計研究所

論文名稱

加速衰變測試下p 分位失效時間之貝氏估計

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摘要(中)

在產品的可靠度研究中，經常針對高可靠度的產品，在更嚴苛的應力條件下，研究其品質特性隨時間經過之衰變，稱為加速衰變測試。在此測試之下，研究者想求知具有100p%產品會失效的時間，稱之為p 分位失效時間。本文在品質特性隨時間變化為偉能(Wiener)或伽瑪(Gamma)隨機過程下，使用貝氏方法估計p 分位失效時間的下界。本文除了實例分析，也執行模擬研究p 分位失效時間貝氏估計之優劣。

摘要(英)

A study of the reliability of a product with quality characteristics (QC) degraded over time under some more severe stress conditions is called an accelerated degradation test. In this test, the researchers would like to know its p quantile failure time at which 100p% of productswould reach the threshold value of QC. When the QC varying over time can be described as the Wiener or Gamma stochastic process, we employ the Bayesian method to estimate the lower bound for the p quintile failure time. In addition to a case analysis ,we perform a simulation study to investigate the performance of the propsesd Bayesian estimates.

關鍵字(中)

★ 加速衰變測試
★ p 分位失效時間
★ 偉能隨機過程
★ 伽瑪隨機過程

關鍵字(英)

★ Accelerated degradation test
★ p quantile failure time
★ Wiener process
★ Gamma process

論文目次

中文摘要 i
英文摘要 ii
誌謝 iii
目錄 v
圖目次 vii
表目次 viii
第一章研究動機及目的 1
第二章文獻回顧 5
第三章 p 分位失效時間的估計 8
3.1 偉能隨機過程 8
3.2 伽瑪隨機過程 11
第四章模擬研究 14
4.1 模擬方法 14
4.2 模擬結果 17
第五章實例分析 20
第六章結論與未來方向 26
參考文獻 28
附錄 31

參考文獻

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Lim H. and Yum B.J.(2011),“Optimal design of accelerated degradation tests based on Wiener process models”, Journal of Applied Statistics, 38:2, pp.309-325
Meeker W.Q. and Escobar L.A. (1998),“Statistical Methods for Reliability Data.”New York: John Wiley & Sons.
Meeker W.Q. ,Escobar L.A.,and Lu C.J. (1998), “Accelerated degradation tests:modeling and analysis.”, Technometrics, Volume 40, pp. 89-99.
Nelson W. (1990), “Accelerated Testing : Statistical Models, Test Plans, and Data analysis.” New York: John Wiley and Sons.
Onar A. and Padgett W. J. (2000), "Accelerated test models with the inverse gaussian distribution" Journal of statistical Planning and Inference, Volume 29 89 , pp. 119–133.
Pan Z.Q. and Balakrishnan N. (2011),“Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes”Reliability Engineering and System Safety 96, pp. 949–957.
Park C. and Padgett WJ.(2005) “Accelerated degradation models for failure based on geometric Brownian motion and gamma processes”. Lifetime Data Analysis ,Volume 11,pp. 511–527.
Sturtz S.,Ligges U.,and Gelman A. ( 2005)“R2WinBUGS: A Package for Running WinBUGS from R.” Journal of Statistical Software, Volume 12
Wang L.Z., Pan R., Lia X.Y. and Jiang T.M. (2013)” A Bayesian reliability evaluation method with integrated accelerated degradation testing and field information” Reliability Engineering and System Safety, Volume 112, pp. 38–47
Whitmore G.A. and Schenkelberg F. (1997), “Modeling accelerated degradation data using Wiener diffusion with a scale transformation,” Lifetime Data Analysis, Volume 3, pp. 27-45.
Xiea M., Goha T.N., Tangb Y. (2004) “On changing points of mean residual life and failure rate function for some generalized Weibull distributions” Reliability Engineering and System Safety, Volume 84,pp. 293–299

指導教授

陳玉英

審核日期

2013-7-23

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