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研究生:黃中彥
研究生(外文):Chung-Yan Huang
論文名稱(外文):Likelihood-based analysis of doubly-truncated data under the location-scale and AFT models
指導教授:江村剛志江村剛志引用關係
指導教授(外文):Takeshi Emura
學位類別:碩士
校院名稱:國立中央大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2018
畢業學年度:106
語文別:英文
論文頁數:65
中文關鍵詞:可靠度信賴帶信賴區間韋伯分布牛頓-拉弗森演算法
外文關鍵詞:ReliabilityConfidence bandConfidence intervalWeibull distributionNewton-Raphson algorithm
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當雙截切(double-truncation)發生於在壽命資料分析時,我們蒐集到的個體失效時間若且唯若落於某個特定的時段內,而該截切的時段(也就是左截切和右截切的時間)因抽樣設計所影響。本篇論文研究壽命變數T於雙截切的情況下,探討對數-位置-尺度模型(log-location-scale model)及加速失敗時間模型(accelerated failure time model)。我們基於概似推論提出估計模型參數的方法,進而利用牛頓-拉弗森演算法(Newton-Raphson algorithm)得到點估計及信賴區間、信賴區域(confidence region)及信賴帶(confidence band)等區間估計。我們利用模擬實驗來查驗所提出方法的準確性,最後以現場可靠度研究(field reliability study) ─ Equipment-S data作為例證。
Double-truncation appears in the lifetime data analysis when the units are collected if and only if their failure occurs within a certain timespan. The timespan is defined by a left-truncation limit and right-truncation limit specified by the sampling design. This thesis studies the lifetime variable under the log-location-scale model and the accelerated failure time model when is subject to double-truncation. We develop likelihood-based inference methods for the parameters in the models. In particular, a Newton-Raphson algorithm is developed for point estimation. Confidence interval, region and band are developed for interval estimation. We conduct simulation studies to examine the accuracy of the proposed methods. The illustrations of the proposed methods are given by real data from a field reliability study, Equipment-S data.
Contents
Chapter 1 Introduction…………………………………………………………………………......1
Chapter 2 The Location-scale model…………………………………………….....3
2.1 The Weibull model………………………………………………………………………....3
2.2 The accelerated failure time model……………………………………5
Chapter 3 Method of estimation……………………………………………………………………6
3.1 Likelihood functions……………………………………………………………………….6
3.2 Score function and Hessian matrix………………………………………7
3.3 Randomized Newton-Raphson (RNR) algorithm………………11
Chapter 4 Interval estimation………………………………………………………………..16
4.1 Wald-type Confidence interval for …………………………….17
4.2 Transformed Confidence interval for ……………………..17
4.3 Wald-type confidence region……………………………………………………18
4.4 Confidence band for …………………………………………………………....19
Chapter 5 Simulation……………………………………………………………………………......22
5.1 Simulation design…………………………………………………………………………..22
5.1.1 The Weibull model.…………………………………………………………………….22
5.1.2 The Weibull AFT model…………………………………………………………….23
5.2 Simulation results………………………………………………………………………..26
Chapter 6 Data analysis…………………………………………………………………………....35
6.1 The Equipment-S data…………………………………………………………………..35
6.2 Numerical results…………………………………………………………….......37
Chapter 7 Concluding remarks…………………………………………………………………..42
Appendix A…………………………………………………………………………………………...........44
Appendix B…………………………………………………………………………………………...........47
Appendix C…………………………………………………………………………………………...........49
Appendix D…………………………………………………………………………………………...........51
References…………………………………………………………………………………………...........55
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