串聯系統中元件壽命為指數分配之區間資料的階段加速壽命試驗

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姓名

詹翔豪(Hsiang-Hao Chan) 查詢紙本館藏

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統計研究所

論文名稱

串聯系統中元件壽命為指數分配之區間資料的階段加速壽命試驗
(Step-Stress Accelerated Life Tests of Series Systems with Interval Data Under Exponential Lifetime Distributions)

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摘要(中)

在串聯系統中, 任一元件失效, 將導致系統無法運作, 有時無法確知造成系統失效的元件, 即為隱蔽資料。本文討論觀測值為區間資料之串聯系統, 其中各元件壽命服從指數分配且其平均壽命與應力間具對數線性關係, 並服從累積曝露模型。考慮型I 設限的階段加速壽命試驗, 分別在元件壽命分配彼此獨立及具Marshall-Olkin 二元指數分配下, 利用期望值-最大概似演算法及遺失資訊法則求得參數之最大概似估計與其費雪訊息矩陣, 進而得到系統可靠度之相關推論。

摘要(英)

High reliability products have longer lifetime under normal environment. Accelerated life tests are
usually used to reduce the experiment time. In a series system, the system fails when any of the
components fails, while the cause of system failure may not be observed which is known as masked
data. In this thesis, we consider the step-stress accelerated life tests for series systems with Type-I
censoring, in which the lifetimes of components are exponentially distributed. We not only consider
those distributions are independent, but also consider the Marshall-Olkin bivariate distribution for
two-components series systems. Assume that there exists log-linear relationship between the mean
lifetime of components and the levels of the environmental stress variables under the cumulative exposure model, and the data analyzed are interval data in the sense only the numbers of failures are observed at the times of changing stress levels. Maximum likelihood inference is developed
incorporated with the EM algorithm as well as the missing information principle to achieving the Fisher information. Simulation study is carried out in the reliability analysis. It shows that the proposed method is more accurate and efficient than the bootstrap method.

關鍵字(中)

★ 群集資料
★ 串聯系統
★ 累積曝露模型
★ 型I 設限
★ 階段加速壽命試驗
★ Marshall-Olkin 二元指數分配

關鍵字(英)

★ Interval data
★ Series system
★ Cumulative exposure model
★ Type-I censor
★ Stepstress accelerated degradation test
★ Marshall-Olkin bi-exponential distribution

論文目次

摘要i
Abstract ii
誌謝iii
目錄iv
表目次vi
第一章緒論1
1.1 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻探討. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
第二章獨立元件串聯系統之型I 設限階段應力加速壽命試驗6
2.1 模型介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 EM 演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 費雪訊息矩陣. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 可靠度分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 參數變換. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
第三章具Marshall-Olkin 指數分配串聯系統之群集資料的階段應力加速壽命試驗20
3.1 二元Marshall-Olkin 指數分配. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 型I 設限階段加速壽命試驗之群集隱蔽資料. . . . . . . . . . . . . . . . . . . . . . 22
3.3 EM 演算法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4 費雪訊息矩陣. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.5 可靠度分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.6 參數變換. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
第四章數值分析與模擬研究30
4.1 二元件獨立之串聯系統. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 二元Marshall-Olkin 指數分配之兩元件串聯系統. . . . . . . . . . . . . . . . . . . . 44
第五章結論與展望63
參考文獻64
附錄附錄一: 獨立元件壽命下參數變換之費雪訊息矩陣67
附錄附錄二: 具相關性模型參數之費雪訊息矩陣69
附錄附錄三: 具相關性模型中參數變換之費雪訊息矩陣71

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指導教授

樊采虹

審核日期

2014-7-22

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