具廣義伽瑪壽命分佈之系統在隱蔽資料加速壽命試驗下之可靠度分析

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姓名

陳奕君(Yi-chun Chen) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

具廣義伽瑪壽命分佈之系統在隱蔽資料加速壽命試驗下之可靠度分析
(Accelerated Life Tests of Series System with Masked Data Under Generalized Gamma Lifetime Distributions)

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摘要(中)

本文討論物件壽命在不同分配下隱蔽的情形,在物件壽命為廣義伽瑪分配時,我們分別討論單物件和多物件壽命分配之位置參數和應力間具線性關係且服從對稱假設之定應力加速試驗;當物件壽命為指數分配時,我們討論多物件串聯系統的隱蔽機率和物件之壽命有關,物件壽命與應力間具對數線性關係下物件壽命分配服從累積暴露模型之階段加速試驗。我們利用概似比檢定去選擇合適的壽命分配,在以期望值-最大化演算法去求得模型中參數之最大概似估計和以有母數拔靴法估計其標準誤,並且在正常應力條件下,物件和系統之平均壽命及可靠度函數之統計推論。模擬結果顯示,當樣本數夠大時,使用廣義伽瑪分配去配適資料會有不錯的結果,但計算上會較耗時;反之若以指數分配去配適廣義伽瑪分配的資料,其結果會較不理想。

摘要(英)

In this thesis, we consider masked lifetime data with different distributions under Type-I censoring scheme. For generalized gamma lifetime distribution, we discuss the constant stress accelerated life testing in which the location parameters of the generalized gamma lifetime distributions of the components is of a linear relationship with the stress variables.For exponential lifetime distribution, we discuss the step-stress accelerated life testing in which the mean life time of each component is a log-linear function of the levels of the stress variables. We utilize the likelihood ratio test to select the appropriate lifetime distribution. The maximum likelihood estimates via EM algorithm is developed for the model parameters with the aid of parametric bootstrap method to estimate the resulting standard errors when the data are masked. Simulation results show that in large samples using the generalized gamma distribution to fit data is more robust, but the calculation is more time-consuming. Conversely, if using the exponential distribution to fit the generalized gamma data, the results
are not so accurate.

關鍵字(中)

★ 有母數拔靴法
★ 隱蔽資料
★ 階段加速試驗
★ 定應力加速試驗
★ 廣義伽瑪分配
★ 期望值- 最大化演算法

關鍵字(英)

★ step-stress accelerated life testing
★ EM algorithm
★ masked data
★ parametric bootstrap method
★ constant stress accelerated life testing

論文目次

第一章緒論1
1.1 研究動機. . . . . . . . . . . . . . . . 1
1.2 研究背景. . . . . . . . . . . . . . 3
1.3 研究方法. . . . . . . . . . . . 5
第二章單物件定應力加速壽命試驗模型7
2.1 廣義伽瑪分配. . .. . . . . . . . . . . 7
2.2 壽命分配為廣義伽瑪分配之加速壽命試驗. . . . . 9
2.3 壽命分配為指數分配之加速壽命試驗. . . . . . . 12
2.4 單物件壽命分配的概似比檢定. . . . . 13
第三章多物件定應力加速壽命試驗模型15
3.1 壽命分配為廣義伽瑪分配之串聯系統隱蔽模型. . . . 15
3.2 有母數拔靴法之變異數估計. . . . . . . . 20
3.3 多物件壽命分配的概似比檢定. . . . . . . . 23
第四章物件壽命為指數分配之串聯系統型I 設限階段應力加速壽命試驗24
4.1 模型介紹. .. . . . . . . . . . . . 24
4.2 壽命為指數分配下隱蔽模型之最大概似估計. .. 26
4.3 有母數拔靴法之變異數估計. . . . . . . . . . . 30
4.4 隱蔽機率與物件相關之特殊情形. . . . . . . . . . 32
第五章數值分析與模擬研究34
5.1 單物件之定應力加速壽命試驗模型. . . . .. . . . 34
5.2 串聯系統之定應力加速壽命試驗. . . . . . . . . . . . 36
5.2.1 對稱假設之模擬結果. . . . . . . . .. . . . 36
5.2.2 廣義伽瑪分配模擬實例之可靠度分析. . . . . . 39
5.2.3 壽命具指數分配之資料分析. . . . . . . . . 46
5.3 階段加速壽命試驗模型. . . . . . . . . . . . 52
5.3.1 模擬分析. . . . . . . . . . . . . . 52
5.3.2 單組資料之可靠度分析. . . . . . . . . 54
第六章結論與展望58
參考文獻59

參考文獻

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指導教授

樊采虹(Tsai-hung Fan)

審核日期

2011-6-30

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