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    題名: 異質性下單階段指數分配位置參數之多重比較程序
    其他題名: One-Stage Multiple Comparison Procedures for the Location Parameters of Exponential Distribution under Heteroscedasticity
    作者: 吳淑妃
    貢獻者: 淡江大學統計學系
    關鍵詞: 異質性;單階段抽樣程序;雙階段抽樣程序;指數分配;與平均之多重比較程序;與控制母體比較之多重比較程序;雙型二設限樣本;Heteroscedasticity;Exponential distribution;One-stage sampling procedures;Two-stage sampling procedures;Multiple comparison procedures with the average;Multiple comparison procedures with the control;Doubly censored sample censored sample
    日期: 2012-08
    上傳時間: 2015-05-12 15:36:18 (UTC+8)
    摘要: 在評估與改善產品可靠度時,需要對產品進行產品抽樣壽命試驗。但產品壽命往往服從非常態分配,而指數分配是很常被使用的壽命分配,所以本研究考慮雙參數指數分配,其位置參數代表最小保證壽命時間,亦稱為槓桿值,由於對k個指數分配母體之位置參數做多重比較有其實用性和學術價值,所以本研究分成兩年對k個指數分配母體之位置參數在異質性下之多重比較做更深入的研究。 第一年我們提出一在異質性下單階段指數分配位置參數與平均之多重比較程序含單邊和雙邊同時信賴區間,我們會比較使用Bonferroni 不等式和Lam’s technique兩種方法之區間長度表現之優劣,並列出臨界值的表,我們舉出一實例來示範本研究提出之單階段多重比較程序,最後我們會做單階段和雙階段程序在不同尺度參數結構下之模擬比較分析,並下結論。 第二年我們提出一使用雙型二設限樣本在異質性下單階段指數分配位置參數與控制母體之多重比較程序,含單邊和雙邊同時信賴區間,並列出臨界值的表,當尺度參數不等且已知時, 亦出一單階段多重比較程序, 並列出臨界值的表,最後我們舉出一實例來示範本研究提出之雙型二設限下之單階段多重比較程序。
    There are many applications of exponential distribution in the analysis of reliability and the life test experiments. We consider the two-parameter exponential distribution in this study, where location parameter is the minimum guarantee time (also called the threshold value). A study on the multiple comparison procedures for the location parameters of k independent exponential distributions has valuable application in pharmaceutical or manufacturing industries. In many practical cases, the scale parameters are unknown and unequal. Therefore, this study is focusing on the multiple comparison procedures for the location parameters of k independent exponential distribution under heteroscedasticity. In the first year, we will propose the one-stage multiple comparison procedures with the average for location parameters of exponential distributions under heteroscedasticity. The proof of given procedure reaching the desired confidence coefficient will be given and the critical values are also provided in this study. One biometrical example is used to demonstrate our proposed procedure. At last, a simulation study is done to compare the performance of one-stage procedures and two-stage procedures under the same total sample size. In the second year, we will propose the one-stage multiple comparison procedures with the control for location parameters of exponential distributions based on the doubly censored sample under heteroscedasticity. The proof of given procedure reaching the desired confidence coefficient will be given and the critical values are also provided in this study. When the scale parameters are known and unequal, one-stage multiple comparison procedures are also proposed and their critical values are also provided. One biometrical example is used to demonstrate our proposed procedure.
    顯示於類別:[統計學系暨研究所] 研究報告

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