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研究生:吳繼澄
論文名稱:加速壽命試驗與擇優母體問題之研究
指導教授:呂理裕呂理裕引用關係
學位類別:博士
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:1999
畢業學年度:87
語文別:中文
中文關鍵詞:加速壽命試驗片段指數分布擇優母體
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對於高可靠度、長壽命的產品或元件,為了研究其失效機制和估計產品的各項可靠度特徵,實務上的作法是採用加速壽命試驗,但多數的學者以統計的觀點,給予如壽命分布等一些假設條件,如Nelson和Kielpinski(1976),Nelson和Meeker(1978),Meeker(1986)以及Tseng(1994)等。然而當假設條件不滿足時,這些統計推論就變的不可靠了,因此本論文的重點之一即在嘗試放寬統計觀點上的假設,在實務與理論二者當中取得平衡。我們主要的作法是分割試驗時間區間成數段子區間,在每段子區間內,將受測元件的失效率近似常數,也就是用片段指數分布函數來近似真實的壽命分布。在處理外插正常應力水準下可靠度特徵問題時,我們也修正Proschan和Singpurwalla(1979,1980)的結果,利用比例危險模型來外插失效率。在第二章和第三章中,我們分別以頻率論和貝氏觀點來套論上述問題,並得到了一些結果。
另一個我們感興趣的部分是擇優母體問題,Tseng(1994)曾針對韋伯母體的到相當豐富的成果,但皆是大樣本近似常態分布下所作的討論,我們則進一步推導出正確選取機率的確切形式,由第四章的模擬結果顯示,由確切形式所得試驗所需之樣本數較為節省。在面臨未知形態參數時,Tseng(1994)是利用貝氏方法進行處理,我們則嘗試建構二階段擇優法則,但其間存在相當的困難,因此本論文的第五章先行討論雙參數指數母體在加速壽命試驗下的二階段擇優法則。
封面
摘要
誌謝
目錄
第一章 緒論
第一節 研究動機與目的
第二節 本文結構
第二章 高可靠度元件在加速壽命試驗下的推論與擇優問題
第一節 引言
第二節 片段指數分佈中參數的估計
第三節 外插正常應力下的失效率及擇優法則的建構
第四節 模擬研究
第三章 應用動態貝氏方法討論加速壽命試驗的推論與擇優問題
第一節 引言
第二節 失效率的貝氏估計值
第三節 外插正常應力下的失效率及擇優法則的建構
第四節 模擬研究與實例分析
第四章 韋伯母體在加速壽命試驗下的擇優問題
第一節 引言
第二節 擇優法則的建構
第三節 試驗所需樣本數之計算
第五章 指數母體在加速壽命試驗下的二階段擇優法則
第一節 引言
第二節 二階段擇優法則的建構
第三節 模擬分析
第六章 結論與未來研究方向
第一節 結論
第二節 未來研究方向
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