具 Box-Cox 轉換之累進型 I 設限逐步加速指數壽命實驗的可靠度分析

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徐聖閎(Sheng-hung Hsu) 查詢紙本館藏

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論文名稱

具 Box-Cox 轉換之累進型 I 設限逐步加速指數壽命實驗的可靠度分析

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摘要(中)

加速壽命實驗為將產品置於較正常使用情況惡劣的環境下，使產品提早損壞以便縮短收集產品失效時間資料的實驗時間，進而分析並預測產品在正常使用狀態下之可靠度。本文中主要討論在物件壽命為一指數分佈單一失效因子之 $k$ 階段累進型 { f I} 設限逐步加速壽命實驗，假設其平均壽命與失效因子之間具有 Box-Cox 轉換之關係時之統計推論。使用的統計方法包括最大概似法、拔靴法和貝氏方法。另外並比較與對數線性模型間之穩健性。

摘要(英)

Accelerated life testing puts the product in the environment which is worse than in normal condition, in order to collect the information of product rapidly, and to use this information to predict the lifetime of product under normal condition. In this thesis, we discuss a k-stage progressive type I censoring step-stress accelerated life testing with single stress variable, when the lifetime of product is of exponential distribution and there is a linear relationship between the lifetime of product and the stress variable under Box-Cox transformation. The maximum likelihood, bootstrap and Bayesian methods are used to make statistical inference and reliability analysis. Model comparsion with the usual log-linear model is also made and it shows that the proposed model is more robust.

關鍵字(中)

★ 最大概似法
★ Box-Cox 轉換
★ 型 I 設限
★ 指數分佈
★ 加速壽命實驗
★ 拔靴法
★ 貝氏方法

關鍵字(英)

★ Maximum likelihood method
★ Box-Cox transformation
★ Type I censoring
★ Exponential distribution
★ Accelerated life testing
★ Bootstrap
★ Bayesian method

論文目次

中文摘要i
英文摘要ii
1 緒論1
1.1 研究背景與動機. . . . . . . . . . . . . . . . . . . . . . 1
1.2 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 研究目的與方法. . . . . . . . . . . . . . . . . . . . . . 4
2 最大概似推論6
2.1 模型假設. . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 最大概似估計. . . . . . . . . . . . . . . . . . . . . . . 9
2.3 區間估計. . . . . . . . . . . . . . . . . . . . . . . . . 14
3 貝氏分析20
3.1 先驗分配. . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 MCMC 演算法. . . . . . . . . . . . . . . . . . . . . . 23
3.3 貝氏推論. . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 log-SSALT 模型之貝氏分析. . . . . . . . . . . . . . . 27
4 模擬研究29
4.1 BC-SSALT 模型. . . . . . . . . . . . . . . . . . . . . 29
4.2 log-SSALT 模型. . . . . . . . . . . . . . . . . . . . . . 39
4.3 模型選擇. . . . . . . . . . . . . . . . . . . . . . . . . 46
5 結論50
參考文獻51

參考文獻

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指導教授

樊采虹(Tsai-Hung Fan)

審核日期

2008-10-11

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