利用型二設限與逐步設限樣本評估具有浴缸型分配之產品的壽命績效指標

Assessing the lifetime performance index of products with the bathtub-shaped distribution under type II censored and progressive type II censored samples

林躍融(Yueh-Jung Lin)

指導教授 ： 吳錦全

淡江大學/管理學院/統計學系碩士班/碩士(2011年)

https://doi.org/10.6846/TKU.2011.01015

摘要

近年來，製程能力指標被製造商廣泛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具常態分配；然而，許多產品的壽命往往是服從非常態分配，例如：柏拉圖分配、韋伯分配、浴缸型分配等等。對於產品壽命之相關分配，在實務上可利用壽命績效指標 CL 來衡量產品的壽命績效，其中L為規格下界。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，此時可使用設限樣本資料。
　　本文的主要目的是利用右型二設限樣本與逐步右型二設限樣本來評估浴缸型或遞增失敗率函數之雙參數壽命分配之產品的壽命績效指標 CL，並利用 CL 的最大概似估計量 CL_hat，建立相關的檢定程序與信賴區間，再針對壽命績效指標的檢定力及信賴區間進行蒙地卡羅模擬。經由模擬結果顯示，不論樣本個數 n、設限樣本個數 m 和逐步移除序列 R=(R1,R2,…,Rm) 如何變動，檢定力與信賴區間的模擬平均值均非常接近真實值。最後，透過實例分析，說明各種程序的運用，以提供製造商評估產品的壽命是否達到要求水準的方法。

關鍵字

浴缸型分配 ； 右型二設限樣本 ； 逐步右型二設限樣本 ； 壽命績效指標 ； 最大概似估計量 ； 蒙地卡羅模擬

並列摘要

In recent years, many process capability indices (PCIs) have been widely used in quality monitoring by many manufacturing industries. Most PCIs assume that the quality characteristic has a normal distribution. However, the lifetime of many products frequently possesses non-normal distribution, such as exponential, Pareto or Weibull distribution etc. In practice, the lifetime performance index CL is utilized to measure lifetime performance for products with some lifetime distributions, where L is the lower specification limit. 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.
This research constructs a maximum likelihood estimator (MLE) of CL based on the right type II censored sample and progressive right type II censored sample from the bathtub-shape distribution. The MLE of CL is then utilized to develop a new hypothesis testing procedure and the confidence interval in the condition of known L. The purchasers can then employ the new hypothesis and the confidence interval to determine whether the lifetime performance of products adhere to the required level.

並列關鍵字

Bathtub-shape distribution ； Right Type II censored sample ； Progressively right type Ⅱ censored sample ； Lifetime performance index ； Maximum likelihood estimator

參考文獻

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