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中文論文名稱 學生t分配模型下之加速破壞衰變試驗
英文論文名稱 Accelerated Destructive Degradation Test Model based on Student's t-distribution
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 108
學期 2
出版年 109
研究生中文姓名 古橋田皓程
研究生英文姓名 Tien-Hao-Cheng Kuchiao
學號 606190139
學位類別 碩士
語文別 中文
口試日期 2020-06-30
論文頁數 32頁
口試委員 指導教授-蔡志群
委員-林千代
委員-彭健育
中文關鍵字 加速破壞衰變測試  學生t分配 
英文關鍵字 Accelerated Destructive Degradation Test  Student’s-t distribution 
學科別分類
中文摘要 加速衰變試驗 (accelerated degradation test, ADT) 為測量產品之品質特徵值 (quality characteristic, QC) 隨著時間衰變,監控產品衰變的實驗方式,以精確提供產品可靠度訊息。有些高可靠度產品需利用破壞性的方式,量測其產品之衰退程度,如測量黏著劑強度的拉斷力量測試,此時導致每個測試樣品,僅只會得到一次的品質特徵值,對於如此的試驗,稱為加速破壞衰變測試 (accelerated destructive degradation test, ADDT)。本文以聚合物材料為動機例子,針對學生t分配 (student’s t-distribution) 建構ADDT衰變模型,並探討產品壽命的相關資訊。結果顯示,以此衰變模型推估產品壽命更為精準,且模擬分析結果得知,模擬結果與漸近理論結果是相近的,而從模型的誤判結果得知,當ADDT衰變模型是來自學生t分配時,誤判成常態分配ADDT衰變模型時,誤判對於產品壽命推估所造成影響是巨大的。
英文摘要 Accelerated destructive degradation test (ADDT) that only one quality characteristic can be taken on each test unit during measurements is useful and effective to provide the reliability information of the products to the customers. Motivated by a polymer data, an ADDT model with student's-t distribution was constructed. The results showed that the proposed model has better accuracy and precision on the lifetime of this polymer material than normal ADDT model. It is known from the simulation analysis that the simulation results are similar to the theoretical ones. In addition, the effect of model misspecification on the products’ lifetime is significant.
論文目次 1.緒論 1
1.1前言 1
1.2文獻探討 3
1.3研究動機與目的 7
1.4研究架構 13
2. ADDT模型 15
2.1 模型建構 15
2.2 產品第p百分位數壽命值估計量及其近似變異數之推導 17
3. ADDT資料分析 18
3.1 實例資料分析 18
3.2 模擬與模型誤判分析 20
4.結論 25
附錄一 26
附錄二 27
參考文獻 30
參考文獻 [1] Boulanger, M. and Escobar, L. A. (1994). “Experimental design for a class of accelerated degradation tests.” Technometrics, Vol. 36, 260-272.
[2] Escobar, L. A., Meeker, W. Q., Kugler, D. L. and Kramer, L. L. (2003). “Accelerated destructive degradation tests: data, models, and analysis.” Chapter 21 in Mathematical and Statistical Methods in Reliability, Lindqvist, B. H. and Doksum, K. A., Editors, River Edge, NJ: World Scientific Publishing Company.
[3] Jeng, S. L., Huang, B. Y. and Meeker, W. Q. (2011). “Accelerated destructive degradation tests robust to distribution misspecification.” IEEE Transactions on Reliability, Vol. 60, 701-711.
[4] Lange, K. L., Little, R. J. A. and Taylor, J. M. G. (1989). “Robust statistical modeling using the t distribution.” Journal of the American Statistical Association, Vol. 84, 881-896.
[5] Meeker, W. Q., Escobar, L. A. and Lu C. J. (1998). “Accelerated degradation tests: modeling and analysis.” Technometrics, Vol. 40, 89-99.
[6] Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analysis. John Wiley & Sons, New York.
[7] Nelson, W. (1981). “Analysis of performance degradation data from accelerated tests.” IEEE Transactions on Reliability, Vol. 30, 149-155.
[8] Peng, C. Y. (2015). “Optimal classification policy and comparisons for highly reliable products.” Sankhya B, Vol. 77, 321-358.
[9] Peng, C. Y. and Cheng, Y. S. (2020). “Student-t processes for degradation analysis.” Technometrics, Vol. 62, 223-235.
[10] Pinheiro, J. C., Liu, C. and Wu. Y. (2000). “Efficient algorithms for robust estimation in linear mixed-effects models using the multivariate t-distribution.” Journal of Computational and Graphical Statistics, Vol. 10, 249-276.
[11] Shaw, W. T. (2006). “Sampling student’s t distribution-use of the inverse cumulative distribution function.” Journal of Computational Finance, Vol. 9, 37-73.
[12] Shi, Y. and Meeker, W. Q. (2013). “Planning accelerated destructive degradation tests with competing risks.” Chapter 22 in Statistical Models and Methods for Reliability and Survival Analysis, 335-356.
[13] Tsai, C. C., Tseng, S. T., Balakrishnan, N. and Lin, C. T. (2013). “Optimal design for accelerated destructive degradation test.” Quality Technology and Quantitative Management , Vol. 10, 263-276.
[14] Tsai, C. C. and Lin, C. T. (2015). “Lifetime inference for highly reliable products based on skew-normal accelerated destructive degradation test model.” IEEE Transactions on Reliability, Vol. 64, 1340-1355.
[15] Yang, G. (2007). Life Cycle Reliability Engineering. Hoboken, John Wiley & Sons, New Jersey.
[16] Yu, H. F. (2003). “Designing an accelerated degradation experiment by optimizing the estimation of the percentile.” Quality and Reliability Engineering International, Vol. 19, 197-214.
[17] 林姿吟 (2015). “偏常態量測誤差模型下之加速破壞衰變試驗”, 淡江大學數學研究所碩士論文.
[18] 李宜真 (2016). “加速試驗之統計設計與分析”, 國立清華大學統計學研究所博士論文.
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