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系統識別號 U0002-1902201301404100
中文論文名稱 加速應力允收試驗之最佳化設計
英文論文名稱 Optimal Design for Accelerated-Stress Acceptance Test
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 101
學期 1
出版年 102
研究生中文姓名 林琮庭
研究生英文姓名 Cong-Ting Ling
學號 699190293
學位類別 碩士
語文別 中文
口試日期 2013-01-09
論文頁數 28頁
口試委員 指導教授-蔡志群
委員-彭健育
委員-林千代
中文關鍵字 最佳應力允收時間  品質特徵值  最佳試驗配置 
英文關鍵字 Accelerated-stress acceptance time  quality characteristics  optimal test plan 
學科別分類 學科別自然科學數學
中文摘要 隨著產品市場競爭激烈,如何縮短產品允收時間以加速出貨速
度,即為製造商所面臨到的重要決策問題。解決此問題,可選取一
與產品可靠度有關的品質特徵值 (quality characteristic,QC),
且此品質特徵值隨時間逐漸衰變,再藉由提高環境應力,以加速產品的衰變,進而縮短產品的允收時間,此即所謂的加速應力允收試驗 (accelerated-stress acceptance test)。
本文首先以一組晶片電阻器衰變資料為動機例子,建構一衰變模型。接下來,提高環境應力,探討如何執行一最佳加速應力允收試驗。換言之,在試驗總成本不超過事先給定的預算下,極小化最佳應力允收時間估計值之近似變異數,以求得最佳試驗配置 (optimal test plan)。 最後,本文以 39k ohm 晶片電阻器為例,求其最佳應力允收時間,以及在給定成本函數下的最佳試驗配置,並進行敏感度分析及模擬分析。
英文摘要 Due to the intense market competition, the manufacturers face the important decision issue about how to shorten product acceptance time to speed up the shipment. In such cases, this accelerated test can be solved if there exist
quality characteristics whose degradation over time can be related to reliability, then collecting degradation data. By elevating the environmental stress to accelerate the decay of the products, then acceptance testing time of the products can be shortened. This is called an accelerated-stress acceptance test. In this paper, motivated by a resistor data, we deal with the optimal design for a accelerated-stress acceptance test. In other words, under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal decision variables are obtained by minimizing the approximate variance of the estimated optimal accelerated-stress acceptance testing time. Finally, the chip resistors on
39k ohm is presented to illustrate the proposed method.
論文目次 中文摘要....................................................... i
英文摘要...................................................... ii
目錄................... ..................................... iii
圖目錄........................................................ iv
表目錄......................................................... v
一、緒論....................................................... 1
1.1 前言....................................................... 1
1.2 文獻探討................................................... 2
1.2.1 衰變模型簡介............................................. 2
1.2.2 最佳衰變試驗............................................. 3
1.3 研究動機與目的............................................. 3
1.4 研究架構................................................... 5
二、問題描述................................................... 7
三、最佳加速應力允收試驗....................................... 9
3.1 最佳加速應力允收時間 t_as.................................. 9
3.2 AVar(t_as) 之推導.......................................... 11
3.3 成本函數................................................... 12
3.4 最佳化模型................................................. 13
3.5 最佳試驗配置之求解步驟..................................... 13
四、實例分析-以39k
ohm 電阻器為例.............................. 15
4.1 最佳試驗配置............................................... 16
4.2 敏感度分析................................................. 17
4.3 模擬分析................................................... 19
五、結論及後續研究............................................. 20
附錄........................................................... 21
文獻........................................................... 27

圖1.1 終止時間為tl0(=1000 小時) 之下,電阻器的電阻值相對變化率. . . . 4
圖1.2 最佳加速應力允收時間(t_as) 之示意圖. . . . . . . . . . . . . . . . . . . 5
圖4.1 在應力S1 與終止時間為tl1 之下,電阻器的電阻值相對變化率. . . . . 15

表4.1 在不同預算Cb 下,加速應力允收試驗之最佳試驗配置. . . . . . . . . 17
表4.2 在不同成本條件(Cop,Cmea,Cit) 下,加速應力允收試驗之最佳試驗配置17
表4.3 在不同預測誤差下,加速應力允收試驗之最佳試驗配置. . . . . . . . . 18
表4.4 t_as 之模擬值與真實值比較. . . . . . . . . . . . . . . . . . . . . . . . . 19
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[2] Chhikara, R. S. and Folks, L. (1989). The Inverse Gaussian Distribution, Theory, Methodology, amd Applications, Marcel Dekker, Inc.
[3] Doksum, K. A. and H’oyland, A. (1992). “Model for variable-stress accelerated life testing experiments based on Wiener process and the inverse Gaussian distribution,”
Technometrics, 34, 74-82.
[4] Lawless, J. F. (2002). Statistical Model and Method for Lifetime Data, John Wiley and Sons, New York.
[5] Meeker, W. Q. and Escobar, L. A. (1998). Statistical Method for Reliability Data, John Wiley and Sons, New York.
[6] Nelson, W. B. (1990). Accelerated Testing: Statistical Model,Test Plans, and Data Analysis, John Wiley and Sons, New York.
[7] Park, C. and Padgett, W. J. (2005). “Accelerated degradation model for failure based on geometric Brownian motion and gamma process,” Lifetime Data Analysis, 11, 511-527. 27
[8] Peng, C. Y. and Tseng, S. T. (2009). “Mis-specification analysis of linear degradation models,” IEEE Transactions on Reliability, 58, 444-455.
[9] Suzuki, K., Maki, K., and Yokogawa, S. (1993). “An analysis of degradation data a carbon film and properties of the estimators,” Statistical Sciences and Data Analysis,
(Edited by K. Matusita, M. Puri and T. Hayakawa), VSP, Utrecht Netherlands, 501-511.
[10] Tseng, S. T. and Liao, C. M. (1998). “Optimal design for a degradation test,” International Journal of Operations and Quantitative Management, 4, 293-301.
[11] Tseng, S. T., Peng, C. Y., and Liu, C. M. (2004). “Optimal design of a non-linear degradation test,” Journal of the Chinese Statistical Association, 42, 115-130.
[12] Whitmore, G. A. and Schenkelberg, F. (1997). “Modeling accelerated degradation data using Wiener diffusion with a time scale transformation,” Lifetime Data Analysis , 3, 27-45.
[13] Yu, H. F and Tseng, S. T. (1998). “On-line procedure for determining an appropriate
termination time for an accelerated degradation experiment,” Statistical Sinica, 8, 207-220.
[14] Yu, H. F and Tseng, S. T. (1999). “Design a degradation experiment,” Naval Research Logistics, 46, 689-706.
[15] 劉家銘(2004). h 非線性隨機衰變試驗之設計與分析i,國立清華大學統計學研究所碩士論文。 28
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