逐步型一區間設限之韋伯壽命試驗抽樣設計

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鄭士苹(Shi-ping Zheng) 查詢紙本館藏

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統計研究所

論文名稱

逐步型一區間設限之韋伯壽命試驗抽樣設計
(Sampling plans for the Weibull lifetime under progressive type I interval censorship)

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摘要(中)

傳統的產品壽命試驗若屬於型一設限，則在試驗尚未停止之前不允許將未失效之產品移除。但是，實務上，試驗進行中不易達到連續監控所有產品物件運作而產生區間設限，並且在過程中必須將部份未失效之產品移除而產生逐步設限。因此，實務上產品壽命多見逐步型一區間設限。本文在逐步型一區間設限的壽命試驗之下，針對壽命服從韋伯分布的產品，根據給定生產者風險(型一誤差) 及消費者風險(型二誤差) 的平均壽命檢定，求出試驗成本達到最低時的最佳抽樣設計。

摘要(英)

In the traditional type I censoring life tests, the survived experiment units are not allowed to remove. However, in practice, the experiment units may not be continuously inspected and some survived units are need
to be removed due to some cause. In this thesis, we discuss how to obtain the test sampling plan for attaining the minimum cost under a progressive type I interval censored life tests when the lifetime of interest is distributed to Weibull and the test of mean lifetime is requested under some specific consumer’’s and product’’s risks.

關鍵字(中)

★ 成本函數
★ 逐步型一區間設限
★ 韋伯分布

關鍵字(英)

★ cost function
★ progressive type I interval censoring
★ Weibull distribution

論文目次

摘要.....................................i
Abstract............................... ii
致謝辭.................................iii
目錄.....................................v
圖目錄.................................vii
表目錄................................viii
第一章緒論...............................1
1.1 研究背景及動機.......................1
1.2 論文架構.............................4
第二章文獻回顧...........................5
第三章統計方法..........................11
3.1 模型假設與參數估計..................11
3.2 壽命試驗抽樣設計....................13
第四章數值分析方法與結果................21
4.1 數值分析方法........................21
4.2 數值分析結果與討論..................24
第五章結論與未來研究....................34
參考文獻................................35
附錄A. 最大概似估計式之共變異數矩陣.....37

參考文獻

[1] Aggarwala, R. (2001). Progressive interval censoring : Some mathematical results with applications to inference. Communications in Statistics- Theory and Methods, 30, 1921–1935.
[2] Balakrishnan, N. and Aggarwala, R. (2000). Birkhauser. (ed.), Progressive Censoring: Theory, Methods, and Applications, Boston.
[3] Balakrishnan, N. (2007). Progressive censoring methodology: An appraisal (with discussions). TEST, 16, 211–259.
[4] Balasooryia, U. and Saw, S. L. C. (1998). Reliability sampling plans for the two-parameter exponential distribution under progressive censoring. Journal of Applied Statistics, 25, 707–714.
[5] Cohen, A. C. (1963). Progressively Censored Samples in Life Testing. Technometrics, 5, 327–339.
[6] Cohen, A. C. (1976). Progressively Censored Sampling in the Three Parameter Log-Normal Distribution. Technometrics, 18, 99–103.
[7] Cohen, A. C. (1977). Progressively censored sampling in threeparameter gamma distribution. Technometrics, 19, 333–340.
[8] Huang, S.-R. and Wu, S.-J. (2008). Reliability sampling plans under progressive type-I interval censoring using cost functions. IEEE Transactions on Reliability, 57, 445–451.
[9] Tse, S.-K., Yang, C., and Yuen, H.-K. (2000). Statistical analysis of Weibull distributed lifetime data under type II progressive censoring with binomial removals. Journal of Applied Statistics, 27, 1033–1043.
[10] Tse, S.-K. and Yang, C. (2003). Reliability sampling plans for the Weibull distribution under type II progressive censoring with binomial removals. Journal of Applied Statistics, 30, 709–718.
[11] Xiang, L. and Tse, S.-K. (2005). Maximum likelihood estimation in survival studies under progressive interval censoring with random removals. Journal of Biopharmaceutical Statistics, 15, 981–991.
[12] Yang, C. and Tse, S.-K. (2005). Planning accelerated life tests under progressive type I interval censoring with random removals. Communications in Statistics- Simulation and Computation, 34, 1001–1025.

指導教授

陳玉英(Yuh-ing Chen)

審核日期

2009-6-22

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