(18.210.12.229) 您好！臺灣時間：2021/03/03 17:20

### 詳目顯示:::

:

• 被引用:0
• 點閱:154
• 評分:
• 下載:25
• 書目收藏:0
 Industry develops very quickly in recent years. High quality products are requested with high reliability. So how to use methods in short time to estimate the life of object is interested. Accelerated life test is a practical method, which place product into a test in some special (accelerated) state by characters, for example, with high temperature and voltage. We obtain information in accelerated conditions and estimate exact life time in the normal operating conditions. This method does not only save time but also save cash. Here we consider the optimum accelerated plan that employs the minimization of standard deviation for estimation to find the proper low and high stress for testing. The best compromise plan is a design that minimize the standard deviation of the target estimator with three stress in equal space and with same allocation of observations on the stress. We derive the Fisher information and employ the large sample theory to obtain the standard deviation of $\widehat{t_{p}}$ (p-th quantile of the distribution). The method based on the normal approximation theory to obtain the stress and allocation of the plan may not result in the real optimum state when sample size is less than 1000. So we propose to find the optimum stress and allocation by simulation. In this thesis, we overcome some predicament in generating Inverse Gaussian random variables. For the most common procedure, one uses uniform random variable and solve the inverse of CDF to obtain the required random variable. This is quite time consuming, so we use the method provided by Michael (1976) based on Chi-square distribution with degree of freedom 1. It is known that the bias problem could be serious when censoring is presented. We use the bias correction by applying bootstrap procedure to correct the estimate of $\widehat{t_{p}}$.
 Industry develops very quickly in recent years. High quality products are requested with high reliability. So how to use methods in short time to estimate the life of object is interested. Accelerated life test is a practical method, which place product into a test in some special (accelerated) state by characters, for example, with high temperature and voltage. We obtain information in accelerated conditions and estimate exact life time in the normal operating conditions. This method does not only save time but also save cash. Here we consider the optimum accelerated plan that employs the minimization of standard deviation for estimation to find the proper low and high stress for testing. The best compromise plan is a design that minimize the standard deviation of the target estimator with three stress in equal space and with same allocation of observations on the stress. We derive the Fisher information and employ the large sample theory to obtain the standard deviation of $\widehat{t_{p}}$ (p-th quantile of the distribution). The method based on the normal approximation theory to obtain the stress and allocation of the plan may not result in the real optimum state when sample size is less than 1000. So we propose to find the optimum stress and allocation by simulation. In this thesis, we overcome some predicament in generating Inverse Gaussian random variables. For the most common procedure, one uses uniform random variable and solve the inverse of CDF to obtain the required random variable. This is quite time consuming, so we use the method provided by Michael (1976) based on Chi-square distribution with degree of freedom 1. It is known that the bias problem could be serious when censoring is presented. We use the bias correction by applying bootstrap procedure to correct the estimate of $\widehat{t_{p}}$.
 1:Introduction 2:Model 3:Asymptotic Normality 4:Accurate Standard Deviation 5:Simulation Procedure 6:Bias Correction by Bootstrap 7:Conclusion 8:Future Research
 1: C. J. Adcock. (1997) "Sample size determination: a review"}, The Statistician 45, No. 2, pp. 261-283.2: R. S. Chhikara and J. L. Folks. (1977) "The Inverse Gaussian Distribution as a Lifetime Model", Technometrics}, Vol. 19, No. 4, pp. 461-468.3: R. S. Chhikara and J. L. Folks. (1989) "The Inverse Gaussian Distribution", New York: Marcel Dekker, INC.4: Kjell A. Doksum and Arnljot H$\acute{o}$yland.(1992) "Models for Variable-Stress Accelerated Life Testing Experiments Based on Wiener Processes and the Inverse Gaussian Distribution", Technometrics, Vol. 34, No. 1, pp. 74-82.5: Bradley Efron and Robert J. Tibshirani. (1993) "An Introduction to the Bootstrap", New York: Chapman and Hall.6: Luis A. Escobar and William Q. Meeker. (1998) "Fisher Information Matrices with Censoring, Truncation,and Explanatory Variables", Statisitca Sinica 8, pp. 221-237.7: Shuen-Lin Jeng and William Q. Meeker. (2000) "Comparisons of Approximate Confidence Interval Procedures for Type I Censored Data", Technometrics}, Vol. 42, No. 2, pp. 135-159.8: Norman L. Johnson and Samuel Kotz. (1970) "Continuous Univariate Distributions-1", New York: John Wiley and Sons, Inc.9: William Q. Meeker, Jr. (1984) "A Comparison of Accelerated Life Test Plans for Weibull and Lognormal Distributions and Type I Censoring", Technometrics, Vol. 26, No. 2, pp. 157-171.10: William Q. Meeker and Luis A. Escobar. (1998) "Statistical Methods for Reliability Data", New York: John Wiley and Sons, Inc.11: Ulrich Menzefricke. (1992) "Designing Accelerated Life Tests when There is Type II Censoring", {\em Commum. Statist.-Theory Meth}, 21(9), 2569-2590.12: John R. Michael, William R. Schucany and Roy W. Haas*. (1976) "Generating Random Variates Using Transformations with Multiple Roots", The American Statistician, Vol. 30, No. 2, pp. 88-90.13: Wayne Nelson and Thomas J. Kielpinski. (1976) "Theory for Optimum Censored Accelerated Life Tests for Normal and Lognormal Life Distributions", Technometrics, Vol. 18, No. 1, pp. 105-114.14: Wayne Nelson and William Q Meeker. (1978) "Theory for Optimum Accelerated Censored Life Tests for Weibull and Extreme Value Distributions", Technometrics, Vol. 20, No. 2, pp.171-177.15: Wayne Nelson. (1990) "Accelerated Testing", New York:John Wiley and Sons, Inc.16: A. Onar and W.J. Padgett. (2000) "Inverse Gausian Accelerated Test Models Based on Cumulative Damage" , J. Statist. Comput. Simul, Vol. 64, pp. 233-247.17: G. A. Whitmore and M. Yalovsky. (1978) "A Normalizing Logarithmic Transformation for Inverse Gaussian Random Variables", Technometrics}, Vol. 20, No. 2, pp. 207-208.
 電子全文
 國圖紙本論文
 連結至畢業學校之論文網頁點我開啟連結註: 此連結為研究生畢業學校所提供，不一定有電子全文可供下載，若連結有誤，請點選上方之〝勘誤回報〞功能，我們會盡快修正，謝謝！
 推文當script無法執行時可按︰推文 網路書籤當script無法執行時可按︰網路書籤 推薦當script無法執行時可按︰推薦 評分當script無法執行時可按︰評分 引用網址當script無法執行時可按︰引用網址 轉寄當script無法執行時可按︰轉寄

 1 逆高斯分配之最佳化設計

 1 3.白棟樑，民國89年9月，衙門變藝廊-太平市戶政事務所充滿藝術氣息，臺灣月刊，213

 1 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 2 逐步加速壽命試驗之貝氏可靠度分析與最佳化設計 3 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 4 逐步應力加速壽命試驗之最佳化問題 5 部分加速壽命測試具多重設限資料下之BurrXII分配參數估計 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 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 8 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 9 次世代面板框膠之可靠度預估及加速壽命試驗之研究 10 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 11 二階段逐步加速壽命實驗之無母數分析 12 產品加速壽命測試規劃之研究-以8025無刷直流風扇為例 13 閥製品加速壽命試驗法數學模式之研究 14 加速壽命測試下利用不同設限方式推估可靠度模式比較 15 應用加速壽命測試方法探討卑金屬積層電容於不同介電厚度下壽命特徵之研究

 簡易查詢 | 進階查詢 | 熱門排行 | 我的研究室