利用設限樣本評估具有Gompertz與Burr X分配之產品的壽命績效指標

Assessing the lifetime performance indices of products with Gompertz and Burr X distributions under censored samples

洪承弘(Cheng-Hong Hong)

指導教授 ： 吳錦全

淡江大學/管理學院/統計學系碩士班/碩士(2012年)

https://doi.org/10.6846/TKU.2012.00745

摘要

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壽命服從常態分配，然而現實上許多產品的壽命是服從非常態分配。對於產品壽命之相關分配，在實務上可利用壽命績效指標C_L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、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。
　　本文分為兩部分，第一部分探討在逐步右型二設限樣本下，利用貝式估計量評估具有Gompertz分配之產品的壽命績效指標；第二部分探討在雙型二設限樣本下，利用不偏估計量評估具有Burr X分配之產品的壽命績效指標。除了建立相關的檢定程序與信賴區間外，並針對壽命績效指標的檢定力與信賴區間進行蒙地卡羅模擬比較其真實值，最後透過實例分析驗證。利用此檢定程序與信賴區間，可提供製造商評估產品品質是否達到顧客所要求的水準。

關鍵字

逐步右型二設限 ； 雙型二設限 ； 貝式估計量 ； Gompertz分配 ； Burr X分配 ； 壽命績效指標 ； 蒙地卡羅模擬

並列摘要

Process capability indices (PCIs) have been widely used in quality monitoring by many manufacturing industries. Most PCIs assume that quality characteristic has a normal distribution. However, the lifetime of many products frequently possesses non-normal distribution. In practice, the lifetime performance index C_L is utilized to measure lifetime performance for products, 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 has two parts. First, it constructs a Bayesian estimator of PCIs based on the progressively right type II censored sample from the Gompertz distribution. Second, it constructs a unbiased estimator of PCIs based on the doubly type II censored sample from the Burr X distribution. The estimation of PCIs are then utilized to develop a hypothesis testing procedure and the confidence interval in the condition of known L, and using Monte Carlo simulation to compare the true value. 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

Progressively right type II censored ； Doubly type II censored ； Bayesian estimator ； Gompertz distribution ； Burr X distribution ； Lifetime performance index ； Monte Carlo simulation

參考文獻

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