在設限抽樣計畫下對服從Burr type X 分配的產品之壽命績效指標的統計推論與應用

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Title:	在設限抽樣計畫下對服從Burr type X 分配的產品之壽命績效指標的統計推論與應用
Other Titles:	Statistical Inferences for the Lifetime Performance Index of the Products with Burr Type X Distribution under Censored Sampling Plan
Authors:	吳錦全
Contributors:	淡江大學統計學系
Keywords:	Burr type X distribution;Type II censored sample;Progressively type II censored sample;Bayesian method;Lifetime performance index
Date:	2011-08
Issue Date:	2012-05-07 13:41:42 (UTC+8)
Abstract:	在進行產品可靠度的分析及改善時，通常需要做產品的抽樣壽命實驗。而製程能力指標已被製造業應用在品質監控方面，以評估製程能力是否合乎水準。大多數的製程能力指標都是假設產品的品質特性在常態分配下；然而，產品壽命往往是服從偏態分配。對於產品壽命之相關分配，在實務上可利用望大型壽命績效指標L C 來衡量產品的壽命績效。在壽命試驗中常因時間限制以及人力和成本的考量而無法取得完整的樣本資料，使得必須使用設限樣本資料。本計畫主要目的是考慮在設限抽樣計畫下，且產品之壽命服從Burr type X 分配時，分別利用右型II 設限樣本及逐步右型Ⅱ設限樣本等資料來評估壽命績效指標，將分別建構壽命績效指標C L 之最適估計量，進而利用C L 之最適估計量求得壽命績效指標C L 之信賴區間，同時發展一檢定程序，以評估產品之壽命是否達到所要求的水準。最後，將以數值範例或模擬資料說明如何應用所提出之方法，分析評估產品之壽命績效是否達到所要求的水準。此外，也將考慮以貝氏方法做統計推論。 In the researching on the reliability of products and improvement, usually need to carry out life test. Process capability analysis has been widely used in quality monitoring to assess the performance and potential of their processes. Most PCIs assume that the quality characteristic has a normal distribution. However, the lifetime distribution of products frequently possesses are skewed. In practice, the lifetime performance index L C is utilized to measure lifetime performance for products with some lifetime distributions. In lifetime testing experiments, we may not be able to obtain a complete sample due to time limitation or other restrictions. Therefore, censored samples arise in practice. In this plan, we consider the products are from Burr type X distribution and under the censored sampling scheme. We will adopt the type II censored sample and the progressively type II censored sample to assess the lifetime performance index, respectively. We will also apply data transformation technology to construct an optimal estimator of the lifetime performance index C L . The optimal estimator of C L is then utilized to develop a new procedure of statistical inference in the condition of known L. Finally, we will give some practical examples or simulated data to illustrate the use of the procedure of statistical inference under given conditions. Besides, the Bayesian method is also considered for statistical inference of the lifetime performance index.
Appears in Collections:	[Graduate Institute & Department of Statistics] Research Paper

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