# 臺灣博碩士論文加值系統

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 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 1Section 2 The Model Assumptions 7 2.1 The AFT Model with the CE Assumptions 7 2.2 The PH Model with the TFR Assumptions 8Section 3 Extrapolation for the Cumulative Failure Probabilities and the Reliability Function under Normal Condition 10Section 4 Verification of Condition (3.1) 13Section 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) 19Section 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) 26Section 7 Results For The PH/TFR Model (2.2) 28Section 8 Conclusions 35References 37Table 1, 2, 3 39Table 4 40Figures 1 41Figures 2 42Figures 3 43Figures 4, 5 44Figures 6 45
 Bhattacharyya, G. K., and Soejoeti, Z. (1989), “A Tampered Failure Rate Model for Step-Stress Accelerated Life Test,” Communications in Statistics-Theory and Methods, 5, 1627-1643.Cox, D. R. (1972), “Regression Models and Life Tables,” Journal of the Royal Statistical Society, Ser. B, 34, 187-220.David, H. A. (1981), Order Statistics, 2nd ed., John Wiley & Sons, New York.DeGroot, M. H. and Goel, P. K. (1979), “Bayesian Estimation and Optimal Designs in Partially Accelerated Life Testing,” Naval Research Logistics Quarterly, 26, 223-235.Dorp, J. R., Mazzuchi, T. A., Fornell, G. E., and Pollock, L. R. (1996), “A Bayes Approach to Step-Stress Accelerated Life Test,” IEEE Transactions on Reliability, 45, 491-498.Ferguson, T. S. (1967), Mathematical Statistics, A Decision Theoretic Approach. New York: Academic Press.Kalbfleisch, J. D., and Prentice, R. I. (1980), The Statistical Analysis of Failure Time Data, John Wiley & Sons, New York.Kiefer, J. (1959), “K-Sample Analogues of the Kolmogorov-Smirnov and Cramer-V. Mises Tests,” Annals of Mathematical Statistics, 30, 420-447.Lawless, J. F. (1982), Statistical Models and Methods for Lifetime Data, John Wiley & Sons, New York.Lawless, J. F. (1986), “A Note on Lifetime Regression Models,” Biometrika, 73, 509-512.Nelson, W. B. (1980), “Accelerated Life Testing-Step Stress Models and Data Analyses,” IEEE Transactions on Reliability, 29, 103-108.Nelson, W. B. (1982), Applied Life Data Analysis: John Wiley & Sons, New York.Nelson, W. B. (1990), Accelerated Life Testing, Statistical Models, Test Plans, and Data Analysis: John Wiley & Sons, New York.Owen. D. B. (1962), Handbook of Statistical Tables, Addison-Wesley, New York.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.Shaked, M., and Singpurwala, N.D. (1983), “Inference for Step-Stress Accelerated Life Tests,” Journal of Statistical Planning and Inference, 7, 295-306.Thomas, R. E. (1964), “When Is a Life Test Truly Accelerated?” Electronic Desig, 12, 64-70.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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 1 在雙截取和區間設限下之無母數分析 2 再發事件資料之無母數分析 3 逐步應力加速壽命試驗之最佳化問題 4 加速壽命試驗的統計學原理分析與壽命預測-以液晶顯示器模組之Crosstalk現象為例 5 摺疊設計與裂區設計無母數分析法之研究 6 群組資料指數分配型一逐步設限加速壽命試驗之最佳化設計 7 次世代面板框膠之可靠度預估及加速壽命試驗之研究 8 加速壽命實驗在逆高斯分配下的最佳化設計與正確推論 9 閥製品加速壽命試驗法數學模式之研究 10 部分加速壽命測試具多重設限資料下之BurrXII分配參數估計 11 保稅工廠激勵模式與員工工作滿意關係之研究－以高雄關稅局轄區為例 12 具韋伯壽命分佈之串聯系統在隱蔽資料加速壽命實驗下之可靠度分析 13 指數壽命分佈串聯系統之隱蔽區間資料加速壽命試驗之可靠度分析 14 應用步進式高加速壽命試驗於高電壓積層式陶瓷電容之可靠性研究 15 群組資料指數分配加速壽命試驗之貝氏可靠度分析與最佳化設計

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