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研究生:胡政宏
論文名稱:二階段逐步加速壽命實驗之無母數分析
論文名稱(外文):Nonparametric Analyses for Two-Level Step-Stress Accelerated Life Tests
指導教授:唐正
指導教授(外文):Jeng Tang
學位類別:碩士
校院名稱:國立清華大學
系所名稱:統計學研究所
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:2004
畢業學年度:92
語文別:英文
論文頁數:45
中文關鍵詞:無母數階段性加速壽命實驗
相關次數:
  • 被引用被引用:0
  • 點閱點閱:221
  • 評分評分:
  • 下載下載:53
  • 收藏至我的研究室書目清單書目收藏:0
在本篇論文中,我們將展現二無母數的模型,分別為AFT/CE模型以及PH/TFR模型,用來描述在階段性加速壽命實驗中所獲得的資料。並且介紹一無母數的方法可藉由這些資料推測在常態使用下,累積失敗機率的上界及可靠度函數的下界。
這種方法為無母數的方法,即無須假設一特別形式的加速函數,且所推測出來的上界及下界皆為可用所得資料估計出來的值。為檢定模型中所使用的假設正確與否以及實行適合度檢定,我們考慮了一個調整過的特別實驗。
最後,本文亦介紹了一模擬的數值分析例子。
In this paper we present two nonparametric accelerated life testing models, namely the accelerated failure time/cumulative exposure (AFT/CE) and proportional hazards/tampered failure rate (PH/TFR) models, and develop methods for obtaining the confidence bounds for low-stress cumulative failure probabilities and reliability functions, based on data collected from a step-stress accelerated life test. The approach is nonparametric in the sense that most of the functions, especially the damage rate function, involved in these two models do not assume any specific forms, except they satisfy certain verifiable conditions. The obtained upper bounds for the cumulative failure probabilities and lower bounds for the reliability functions under these two models are estimatable from the test data. To provide formal procedures for verifying the conditions of the damage rate function and for testing the goodness-of-fit (GOF) of the proposed models, the traditional step-stress test is slightly modified to obtain necessary data for these purposes so that the proposed procedures can be carried out. We have complete procedures for the AFT/CE model; but only partial results are obtained for the PH/TFR model. Finally, a simulated numerical example is used to illustrate the proposed methods for the AFT/CE model.
Section 1 Introduction 1
Section 2 The Model Assumptions 7
2.1 The AFT Model with the CE Assumptions 7
2.2 The PH Model with the TFR Assumptions 8
Section 3 Extrapolation for the Cumulative Failure
Probabilities and the Reliability Function under
Normal Condition 10
Section 4 Verification of Condition (3.1) 13
Section 5 Goodness-Of-Fit Test Of The AFT/CE Model (2.1) 15
5.1 Methods For Verifying Assumption (3.1) under the
Proposed Experiment for the AFT/CE Model 16
5.2 A Graphical Approach for the GOF of the AFT/CE
Model 19
5.3 A Formal GOF Test of AFT/CE Model (2.1) 19
Section 6 A Simulated Example 22
6.1 Description of the Simulated Data 22
6.2 Analyses for the Simulated Data 23
6.2.1 Model Checking 23
6.2.2 Checking Condition (3.1) 24
6.3 The UCB of Pr(x0,t0) 26
Section 7 Results For The PH/TFR Model (2.2) 28
Section 8 Conclusions 35
References 37
Table 1, 2, 3 39
Table 4 40
Figures 1 41
Figures 2 42
Figures 3 43
Figures 4, 5 44
Figures 6 45
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Schmoyer, R. L. (1986), “An Exact Distribution-Free Analysis for Accelerated Life Testing at Several Levels of a Single Stress,” Technometrics, 28, 165-175.

Schmoyer, R. L. (1988), “Linear Interpolation With a Nonparametric Accelerated Failure Time Model,” Journal of the American Statistical Association, 83, 441-449.

Schmoyer, R. L. (1991), “Nonparametric Analyses for Two-Level Single-Stress Accelerated Life Tests,” Technometrics, 33, 175-186.

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Tseng, S. T. and Wen, Z. C. (2000), “Step-Stress Accelerated Degradation Analysis for Highly Reliable Products,” Journal of Quality Technology, 32, 209-216.

Tyoskin, O. I. and Krivolapov, S.Y. (1996), “Nonparametric Model for Step-Stress Accelerated Life Test,” IEEE Transactions onReliability, 45, 346-350.

Xiong, C. (1998), “Inference on A Simple Step-Stress Model With Type II Censored Exponential Data,” IEEE Transactions on Reliability, 47, 142-146.
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