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系統識別號 U0002-1607201818385400
中文論文名稱 在偏常態下加速破壞衰退試驗的貝氏方法
英文論文名稱 Bayesian Methods for Skew-Normal Accelerated Destructive Degradation Test
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 陳奕汝
研究生英文姓名 I-Ju Chen
學號 605190171
學位類別 碩士
語文別 中文
口試日期 2018-06-26
論文頁數 46頁
口試委員 指導教授-蔡志群
委員-林千代
委員-吳裕振
委員-蔡志群
中文關鍵字 加速破壞衰變試驗  偏常態分配  最大概似估計法  貝氏方法  M-H 演算法 
英文關鍵字 Accelerated Destructive Degradation Test  Skew-Normal distribution  Maximum likelihood estimation  Bayesian Methods  Metropolis-Hasting algorithm 
學科別分類
中文摘要 世界邁入高科技時代,高品質和高可靠度產品成為市場主流,然而可靠度和 商品的壽命型態息息相關。在產品之品質特徵值量測過程中,需要對測試產品進 行破壞,並且提高環境應力,才能量測到其品質特徵值,此試驗稱為加速破壞衰 變試驗。林姿吟 (2013) 建構一測量誤差服從偏常態分配的非線性加速破壞衰變 模型。然而其產品第 p 百分位數壽命壽命之 95 %信賴區間過寬,故本文將利用 貝氏方法來估計模型參數,使得模型參數與產品第 p 百分位數壽命之 95 %信賴 區間有效縮短。針對聚合物材料資料,先以一偏常態加速破壞衰變模型描述產品 衰變路徑,分別利用最大概似估計法,與貝氏方法估計模型未知參數,並探討其 壽命資訊。貝氏方法分別使用給定有訊息先驗分配,和無訊息先驗分配之 M-H 演 算法 (Metropolis-Hasting algorithm) 來估計模型參數,接著進行模擬分析比較三 種估計方法,並利用偏差、均方根誤差及覆蓋機率等準則,判定哪一估計方法較 為精準。模擬結果可知使用有訊息先驗分配之估計方法,能有效縮短產品第 p 百 分位數壽命之 95 %信賴區間,且此估計方法相較於最大概似估計法及給定無訊 息先驗分配之貝氏方法都較為精準。
英文摘要 The accelerated destructive degradation test (ADDT) provided an effective
way to assess the reliability information of the highly reliable products whose quality characteristics degraded over time, and can be taken only once on each tested unit during the measurement process. Motivated by a polymer data, Lin (2013) proposed a nonlinear ADDT model with measurement error that follows a skew-normal distribution, and derived the analytical expressions for the product's lifetime distribution. However, the 95% confidence interval of the product's 100pth percentile is not precision. Hence we used Bayesian approach improve the provision of the estimation. More specifically speaking, this article used Metropolis-Hasting algorithm to estimate the parameters of the model, and obtain the posterior credible interval. Finally, a simulation study was conducted to compare the precision of the maximum likelihood and Bayesian estimations.
論文目次 第一章 緒論 1
1.1 前言 1
1.2 文獻探討 3
1.2.1 非破壞衰退模型 3
1.2.2 破壞衰退模型 4
1.2.3 偏常態分配 5
1.2.4 貝氏方法 7
1.3 研究動機與目的 9
1.4 研究架構 11
第二章 問題描述 13
第三章 模型參數估計方法 15
3.1 最大概似估計法 15
3.2 貝氏方法 16
3.2.1 蒙地卡羅.馬可夫鏈 17
3.2.2 有資訊先驗分配 19
3.2.3 無資訊先驗分配 22
第四章 實例與模擬 25
4.1 參數估計 25
4.1.1 最大概似估計 25
4.1.2 有資訊先驗分配 27
4.1.3 無資訊先驗分配 29
4.2 模擬分析 31
第五章 結論及後續研究 37
附錄 39
參考文獻 44
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[33] 林姿吟 (2013). ⟨ 偏常態量測誤差模型下之加速破壞衰變試驗 ⟩,淡江大學數學學系數學所碩士論文。
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