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系統識別號 U0002-1607201823402200
中文論文名稱 位置尺度分配下多重應力加速壽命試驗之最佳樣本數配置
英文論文名稱 Optimal Sample Size Allocation for Accelerated Life Test with Multiple Levels of Stress under Location-Scale Distributions
校院名稱 淡江大學
系所名稱(中) 數學學系數學與數據科學碩士班
系所名稱(英) Master's Program, Department of Mathematics
學年度 106
學期 2
出版年 107
研究生中文姓名 林廷翰
研究生英文姓名 Tin-Han Lin
學號 604190073
學位類別 碩士
語文別 中文
口試日期 2018-06-26
論文頁數 30頁
口試委員 指導教授-蔡志群
委員-林千代
委員-吳裕振
中文關鍵字 加速壽命試驗  位置尺度分配  最佳比例配置 
英文關鍵字 Accelerated Life Test  Location-Scale Distributions  Optimal Sample Size Allocation 
學科別分類
中文摘要 加速壽命試驗 (Accelerated Life Test, ALT) 是工業界最常被拿來使用推估高可靠度產品的可靠度資訊之重要分析工具,例如產品壽命第p百分位數或產品平均失效時間 (Mean Time To Failure, MTTF)。因此規劃有效率的加速壽命模型,尤其是決定加速應力所需之最佳樣本數配置,是可靠度工程師經常面臨到的決策問題。本文以絕緣體的電擊擊穿時間資料為動機例子,建構一加速壽命模型,其模型的隨機誤差項為位置尺度分配,並極小化產品壽命第p百分位數估計量之漸近變異數,進行樣本數最佳化配置的探討。由推導結果可知在進行樣本數最佳化配置,只需要依照比例配置於最高加速應力及最低加速應力上,且不論加速壽命模型的隨機誤差項屬於位置尺度家族裡何種分配,都不影響樣本數最佳化配置的結果。
英文摘要 Accelerated life test is widely used to assess the lifetime information (e.g., p-th quantile or mean-time-to-failure (MTTF)) of the highly reliable products. Hence, how to design an efficient accelerated life test plan for assessing the product’s lifetime information at normal-use stress such as the optimal sample-size allocation turns out to be a challenging issue for reliability analysts. In this paper, motivated by a mylar-polyurethane data, we first proposed an accelerated life model that random error is a location-scale distribution. Next, by using the optimality criterion that minimized the asymptotic variance of the estimator of the product's p-th percentile lifetime, this article derived the analytical expression of the optimal sample-size allocation for a k-stress accelerated life test. We demonstrated that a necessary condition of the sample-size allocation for k-stress based on the criterion is to assign tested units into the lowest and highest stress levels. A Monte Carlo simulation study was conducted to demonstrate the simulated values are quite close to the asymptotic values when sample sizes are large.
論文目次 第一章 緒論......................1
1.1 前言......................1
1.2 文獻探討......................2
1.2.1 加速壽命模型......................2
1.2.2 樣本數配置最佳化......................2
1.3 研究動機與目的......................3
1.4 研究架構......................6
第二章 問題描述......................7
第三章 模型參數估計......................9
3.1 最大概似估計......................9
3.2 費雪訊息矩陣......................10
第四章 最佳樣本數配置......................15
第五章 實例探討與模擬分析......................17
5.1 實例探討......................17
5.2 模擬分析......................21
第六章 結論及後續研究......................23
附錄......................24
參考文獻......................29
參考文獻 [1] Bagdonavicius, V. and Nikulin, M. (2002). Accelerated Life Models: Modeling and Statistical Analysis. Chapman & Hall/CRC, Boca Raton, Florida.
[2] Cox, D. R. (1964). “Some applications of exponential ordered scores,” Journal of the Royal Statistical Society. Series B, vol. 26, 103-110.
[3] Gaylor, D. W. and Sweeny, H. C. (1965). “Design for optimal prediction in simple linear regression,” Journal of the American Statistical Association, vol. 60, 205-216.
[4] Jayatilleka, S., Apploances, M. and Okohba, N. G. (2003). “Use of accelerated life test on transmission belts for predicting product life, identifying better designs, materials and suppliers,” IEEE Proceedings Annual Reliability And Maintainability Symposium, 101-105.
[5] Kalkanis, G. and Rosso, E. (1989). “The inverse power law model for the lifetime of a mylar-polyurethane laminated DC HV insulating structure,” Nuclear Instruments and Methods in Physics Research, A281, 489-496.
[6] Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data, John Wiley and Sons, New York.
[7] McCool, J. I. (1980). “Confidence limits for Weibull regression with censored data,” IEEE Transactions on Reliability, vol. 29, 145-150.
[8] Meeker, W. Q. and Escobar, L. A. (1998). Statistical Methods for Reliability Data, John Wiley and Sons, New York.
[9] Nadarajah, S. (2004). “Information matrix for logistic distributions,” Mathematical and Computer Modelling, vol. 40, 953-958.
[10] Nelson, W. B. (1980). “Accelerated life testing-step-stress models and data analyses,” IEEE Transactions on Reliability, vol. 29, 103-108.
[11] Nelson, W. B. (1990). Accelerated Testing: Statistical Model, Test Plans, and Data Analysis, John Wiley and Sons, New York.
[12] Nelson, W. B. and Kielpinski, T. J. (1976). “Theory for optimum censored accelerated life tests for normal and lognormal life distributions,” Technometrics, vol. 18, 105–114.
[13] Nelson, W. B. and Meeker, W. Q. (1978). “Theory for optimum accelerated censored life tests for Weibull and extreme value distributions,” Technometrics, vol. 20, 171–177.
[14] Ng, H. K. T., Balakrishnan, N. and Chan, P. S. (2006). “Optimal sample size allocation for tests with multiple levels of stress with extreme value regression,” Naval Research Logistics, vol. 54, 237-249.
[15] 李宜真 (2011). 〈指數分散加速衰變模型最適樣本數配置之研究〉,國立清華大學統計學研究所碩士論文。
[16] 陳玟穎 (2012). 〈V-optimality準則下之指數分散加速衰變模型的最適樣本數配置〉,國立清華大學統計學研究所碩士論文。
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