進階搜尋


   電子論文尚未授權公開,紙本請查館藏目錄
(※如查詢不到或館藏狀況顯示「閉架不公開」,表示該本論文不在書庫,無法取用。)
系統識別號 U0026-1006201908395300
論文名稱(中文) 加速衰變試驗在Tweedie衰變模型下之規劃
論文名稱(英文) Planning of Accelerated Degradation Test withTweedie Degradation Model.
校院名稱 成功大學
系所名稱(中) 統計學系
系所名稱(英) Department of Statistics
學年度 107
學期 2
出版年 108
研究生(中文) 林姿妤
研究生(英文) Zi-Yu Lin
學號 R26064043
學位類別 碩士
語文別 中文
論文頁數 39頁
口試委員 指導教授-李宜真
口試委員-鄭順林
口試委員-胡政宏
中文關鍵字 加速衰變試驗  Tweedie衰變模型  V-optimality  優化模型 
英文關鍵字 Accelerated degradation test  Tweedie degradation model  V-optimality criterion  Optimization mode 
學科別分類
中文摘要 由於科技進步,加速衰變試驗在工業上是最常被用來推估高質量產品可靠度資訊之重要分析工具,因此如何規劃出有效率之加速衰變試驗,亦是可靠度工程師面臨的重要決策問題之一。許多文獻探討最適設計之問題,著重在樣本數以及應力水準上之配置,並將不同應力的量測次數與量測時間設定為相同,但由衰變資料之實例中能夠看出,不同應力下的量測次數以及量測時間是不相同的,因此在規劃加速衰變試驗時,應將這些設定一併列入考慮。因此本論文研究主題是針對Tweedie加速衰變模型,利用V-optimality準則,在不同的優化模型限制條件下找出最佳實驗配置,並做深入的研究與探討。
具體而言,本論文獲得以下研究結論:在以往文獻中使用之優化模型限制條件,由於過多的限制,雖然能夠使試驗操作較簡單,卻導致推估出的產品壽命第p百分位數之漸近變異數增大。而限制越少之優化模型,推估出之結果是較好的,但在試驗操作上亦是較繁瑣的。因此提出不同之優化模型限制條件,操作者可依照操作過程以及精確度之間做平衡,選擇適合且精確度符合標準之優化模型限制條件。
英文摘要 Due to advances in technology, accelerated degradation test is the industry's most important analytical tool for estimating the reliability of high-quality products. Therefore, how to plan an efficient accelerated degradation test is one of the important decision-making problems faced by reliability engineers. Many literatures explored the issue of optimal design, focusing on the sample size allocation and the level of stress under assumption that the number of measurements and the measurement time are the same among all stress levels. However, it can be seen from the real examples of degradation data that the number of measurements and the measurement time under different stresses could be different, so these settings should be taken into consideration when planning the accelerated degradation test. Therefore, based on the Tweedie degradation model, this study use V-optimality to find the optimal experimental configuration under different optimization model constraints. Two illustrative example are used to demonstrated the planning results by different constraints, and do in-depth research and discussion.
論文目次 第一章 緒論 1
1.1 前言 1
1.2 加速衰變試驗之實驗設計 2
1.3 研究動機與目的 3
1.4 研究架構 4
第二章 文獻回顧與探討 5
2.1 Tweedie衰變模型 5
2.2 壽命分配 6
2.3 問題描述 7
2.4 目標函數 8
第三章 線性加速衰變試驗之最佳化模型 11
3.1 成本函數 11
3.2 最佳化模型 11
3.3 兩應力最佳化模型之限制條件 12
3.4 三應力最佳化模型之限制條件 13
3.5 兩應力之最佳試驗配置演算法 14
第四章 實例說明 17
4.1. 資料介紹 17
4.2. 兩應力最佳配置結果 19
4.2.1 沒有總時間限制之結果 19
4.2.2 有總時間限制之結果 22
4.2.3 總時間限制與不限制之比較 24
4.2.4 探討量測次數的變化 24
4.3. 三應力最佳配置結果 25
第五章 結論與未來研究之方向 27
附錄 29
附錄A 兩應力下總量測時間比之推導 29
附錄B 限制模型Ⅰ^O之最佳化演算法 30
附錄C 限制條件Ⅱ^O之最佳化演算法 33
附錄D Device B資料在參數為 d=3和 d=2下,C_b=2500之結果 35
附錄E 三應力無總量測時間限制之結果 36
參考資料 37
參考文獻 [1] Hong, L., & Ye, Z. (2017). When is acceleration unnecessary in a degradation test?. Statistica Sinica, 1461-1483.
[2] Hu, C. H., Lee, M. Y., & Tang, J. (2015). Optimum step-stress accelerated degradation test for Wiener degradation process under constraints. European Journal of Operational Research, 241(2), 412-421.
[3] Hu, C. H., & Lee, M. Y. (2018). Comparison among several commonly used sampling methods for a degradation test. Quality and Reliability Engineering International, 34(3), 436-458.
[4] Jørgensen, B. (1986). Some properties of exponential dispersion models. Scandinavian Journal of Statistics, 187-197.
[5] Jørgensen, B. (1987). Exponential dispersion models. Journal of the Royal Statistical Society: Series B (Methodological), 49(2), 127-145.
[6] Jørgensen, B. (1987). Small dispersion asymptotics. Brazilian Journal of Probability and Statistics, 59-90.
[7] Lim, H., & Yum, B. J. (2011). Optimal design of accelerated degradation tests based on Wiener process models. Journal of Applied Statistics, 38(2), 309-325.
[8] Lim, H. (2015). Optimum accelerated degradation tests for the gamma degradation process case under the constraint of total cost. Entropy, 17(5), 2556-2572.
[9] Liu, X., & Tang, L. C. (2010). A Bayesian optimal design for accelerated degradation tests. Quality and Reliability Engineering International, 26(8), 863-875.
[10] Meeker, W. Q., & Escobar, L. A. (1998). Statistical methods for reliability data. A. Wiley Interscience Publications.
[11] Nelson, W. B. (2009). Accelerated testing: statistical models, test plans, and data analysis (Vol. 344). John Wiley & Sons.
[12] Pan, Z., & Sun, Q. (2014). Optimal design for step-stress accelerated degradation test with multiple performance characteristics based on gamma processes. Communications in Statistics-Simulation and Computation, 43(2), 298-314.
[13] Qin, C. (2017). The First Passage Time of Degradation Processes (Doctoral dissertation).
[14] Tang, L. C., Yang, G. Y., & Xie, M. (2004). Planning of step-stress accelerated degradation test. In Annual Symposium Reliability and Maintainability, 2004-RAMS (pp. 287-292). IEEE.
[15] Tseng, S. T., Tsai, C. C., & Balakrishnan, N. (2011). Optimal sample size allocation for accelerated degradation test based on Wiener process. Wiley StatsRef: Statistics Reference Online.
[16] Tseng, S. T., & Lee, I. C. (2016). Optimum allocation rule for accelerated degradation tests with a class of exponential-dispersion degradation models. Technometrics, 58(2), 244-254.
[17] Wu, S. J., & Chang, C. T. (2002). Optimal design of degradation tests in presence of cost constraint. Reliability Engineering & System Safety, 76(2), 109-115.
[18] Yang, G. (2007), Life Cycle Reliability Engineering, Hoboken, NJ: Wiley.
[19] Ye, Z. S., & Chen, N. (2014). The inverse Gaussian process as a degradation model. Technometrics, 56(3), 302-311.
[20] 李宜真. (2011). 指數分散加速衰變模型最適樣本數配置之研究. 清華大學統計學研究所碩士論文, 1-45.
[21] 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. 清華大學統計學研究所碩士論文, 1-51.
[22] 彭健育. (2008). 高可靠度產品之衰變試驗分析. 清華大學統計學研究所博士論文, 1-104.
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2024-07-23起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2024-07-23起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw