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研究生： 呂恩澤
En-ze Lu
論文名稱： 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
Optimal Design in Two-Step-Stress Accelerated Life Tests with Progressively type-I Censored Data
指導教授： 樊采虹
Tsai-Hung Fan
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
畢業學年度： 98
語文別： 中文
論文頁數： 69
中文關鍵詞： 群組資料 、逐步設限 、加速壽命試驗 、最佳化設計 、型一設限
外文關鍵詞： Accelarate life test, step-stress accelarate life test, censoring scheme, grouped data, type-I censoring, Bayesian optimal design
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    • 加速壽命試驗是一種快速測量物件壽命的方法。本文考慮單一應力下兩階段的型一逐步設限加速壽命試驗, 在群組資料下假設物件壽命分配為指數分配, 且物件壽命和應力水準有線性與對數線性兩種模型之下, 分別在V-準則、D-準則和A-準則下決定最佳化試驗時間。在貝氏最佳化試驗中, 我們建議決定先驗分布的方法, 並比較其與傳統方法之差異。研究結果顯示, 若我們對參數有充份的訊息, 則貝氏最佳化設計較傳統方法好。

    Accelerated life test (ALT) is a quickly method for estimating the life of item in reliability. Optimal design on the experimental time is an important issue on the ALT. In this thesis, we consider a two-step-stress accelerated life test under progressively Type-I censoring scheme, and
    assume that the lifetime of each item follows an exponential distribution with grouped data. Determinations of the optimal experimental time based on V-optimality, D-optiamlity and A-optimality criteria with the mean life time of the experiment item being a linear and loglinear function of the stress variable are disscussed, respectively. We also study the corresponding Bayesian designs, and provide a way to select the prior distribution compared with the traditional methods. Empirical studies indicate that if we have more information from the parameters, we can do beter than the
    traditional design.

    摘要.....................i Abstract.....................ii 誌謝.....................iii 目錄.....................iv 圖目次.....................vii 表目次.....................viii 第一章緒論.....................1 1.1 研究動機.....................1 1.2 研景背景.....................2 1.3 研究方法..................... 4 第二章線性模型下之型一逐步設限加速壽命最佳化試驗.....................5 2.1 模型介紹與假設.....................5 2.2 最大概似推論.....................7 2.3 最佳化準則..................... 10 2.3.1 V-最佳化準則.....................10 2.3.2 D-最佳化準則.....................10 2.3.3 A-最佳化準則.....................11 2.4 貝氏最佳化準則.....................12 2.4.1 貝氏V-最佳化準則.....................12 2.4.2 貝氏D-最佳化準則.....................15 2.4.3 貝氏A-最佳化準則.....................16 第三章對數線性模型下之型一逐步設限加速壽命最佳化試驗20 3.1 最大概似推論.....................20 3.2 最佳化準則..................... 23 3.2.1 V-最佳化準則.....................23 3.2.2 D-最佳化準則.....................24 3.2.3 A-最佳化準則.....................25 3.3 貝氏最佳化準則.....................25 第四章數值分析.....................28 4.1 線性模型下傳統最佳化之數值分析.....................28 4.2 線性模型下貝氏設計的數值分析.....................30 4.2.1 選擇眾數之先驗分布.....................30 4.2.2 選擇平均數之先驗分布.....................35 4.3 對數線性模型下傳統最佳化之數值分析...................36 4.4 對數線性模型下貝氏設計的數值分析.....................38 第五章結論與展望.....................66 參考文獻.....................67

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