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研究生:吳婉君
論文名稱:加速衰變試驗之最佳化設計
指導教授:曾勝滄曾勝滄引用關係桑慧敏桑慧敏引用關係
學位類別:碩士
校院名稱:國立清華大學
系所名稱:工業工程與工程管理學系
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
中文關鍵詞:加速衰變試驗布朗運動最佳化設計
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加速衰變試驗是估計高可靠度產品壽命的方法之一,
然而如何在有限的試驗成本下,
安排一個加速衰變試驗的應力水準、樣本、觀測間隔與觀測次數,
使得該加速衰變試驗在有限的成本下有較好的績效是許{}多實驗者所面臨的問題。
本研究將以(廣義)隨機衰變模型來描述加速狀態的產品衰變路徑。
此模型假設各應力水準的衰變路徑誤差為飄移量0的布朗運動。
以LED產品的加速衰變試驗為例,
推導正常使用條件的壽命值及其變異數。
在加速的應力水準已知、
各應力水準下的樣本數比例固定與觀測間隔和觀測次數相同的情形下,
安排一個在試驗成本不超出其上限的加速衰變試驗,
使其壽命估計值之變異數達到最小。
並與衰變試驗最佳試驗配置之績效作比較。
加速衰變試驗比未加速的衰變試驗可大量縮短試驗時間,
但需要較多的試驗樣本,且壽命估計之變異會較大,
符合進行加速是為了縮短試驗時間的目的。
Accelerated Degradation Test (ADT) is widely used to assess lifetimes of highly reliable products. How to design an ADT under the restrictions of the finite experiment cost and to make the test have the better performance is the question for the experimenters. The problem is to find the optimal test plans for the sample size, inspection frequency, and the termination time such that the variance of the estimated 100p-th percentile is minimized subject to the constraint that the total experimental cost doesn't exceed a pre-determined budget.
In this talk, the (general) random degradation model is used
to describe the accelerated degradation path that the error term follows a zero-drift Wiener process. In the case of the LED's accelerated degradation model, the estimated lifetime (100p-th percentile) in normal use condition and its variance are figured out. They are used in designing an ADT giving the accelerated stress level is known, the ratio of the sample size in each stress level is fixed and the observation interval and observation times are the same in every stress level. Finally, Compare the performances between the optimal design of ADT and that of Degradation Test. ADT is benefit on curtail the experiment time, but it needs more test sample items and has larger lifetime variance. In the other word, ADT can shorten experiment time but spends more. This is helpful to inference the lifetime of the high-reliable products.
摘要
研究背景及目的
隨機衰變模型
加速衰變試驗之最佳化設計
結論與未來研究方向
參考文獻
Boulanger, M. and Escobar, L. A. (1994),
{\it ``Experimental Design for a Class of Accelerated Degradation Tests,''}
Technometrics, vol. 36, p.260-272.
Buonocore, A., Nobile, A. G.,and Ricciardi, L. M. (1987),
{\it ``A New Integral Equation for the Evaluation of the
First-Passage-Time Probability Densities,''}
Advances in Applied Probability, vol. 19, p.784-800.
Chhikara, R. S. and Folks, J. L. (1989),
{\it The Inverse Gaussian Distribution,}
Marcel Dekker,Inc.,New York.
Doksum, K. A. and H\'{o}yland, A. (1992),
{\it ``Models for Variable-stress Accelerated Life Testing Experiment
Based on Wiener Process and the inverse Gaussian Distribution,''}
Technometrics, vol. 34, p.74-82.
Durham, S. D. and Padgett, W. J. (1997),
{\it ``Cumulative Demage Models for System Failure With Application
to Carbon Fibers and Composites,''}
Technometrics, vol. 39, p.34-44.
Lu, C. J. and Meeker, W. Q. (1993),
{\it``Using Degradation Measures to Estimate a Time-to-Failure Distribution'',}
Technometrics, vol. 35, p.161-174.
Meeker, W. Q. and Escobar, L. A. (1998),
{\it ``Statistical Methods for Reliability Data,''}
John Wiley \& Sons,Inc., New York.
\bibitem{Nelson1990} Nelson, W. (1990),
{\it Accelerated Testing: Statistical Models, Test Plans and Data Analysis,}
John Wiely and Sons,Inc., New York.
Sacerdote, L. and Tomassetti, F. (1996),
{\it ``On Evaluations and Asymptotic Approximations of First-Passage-Time Probabilities'',}
Advances in Applied Probability, vol. 28, p.270-284.
Tseng, S. T. and Yu, H. F. (1997),
{\it ``A Termination Rule for Degradation Experiments'',}
IEEE Transaction on Reliability, vol. 46, p.130-133.
Tseng, S. T. and Lioa, C. M. (1998
{\it ``Optimal Design for a Degradation Test'',}
International Journal of Quality Management,
vol. 4, no. 3, p.293-301.
廖承茂(2000),``衰變試驗設計與分析之研究,''
清華大學統計學研究所博士論文
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