利用上記錄值評估具有Burr XII與Gompertz分配之產品的壽命績效指標

Assessing the lifetime performance indices of products with Burr XII and Gompertz distributions based on the upper record values

潘品豫(Pin-Yu Pan)

指導教授 ： 潘品豫

淡江大學/商管學院/統計學系碩士班/碩士(2013年)

https://doi.org/10.6846/TKU.2013.01025

摘要

近年來製程能力指標被製造商廣泛應用在品質監控上，以評估製程能力是否合乎水準。製程能力愈佳，代表該製程所提供的產品品質等級愈高，其產品的合格率也就愈高。但大部分的製程能力指標都是假設產品的壽命服從常態分配，然而實際上產品的品質特性並不一定服從常態分配。而在某些現實情況下我們只關心下次發生產品壽命高於之前的記錄時才需記錄。為了使製程能力指標可以合理且精確的評估產品的品質，本文利用上記錄值樣本來評估具有Burr XII與Gompertz分配之產品的壽命績效指標。利用製程能力指標的不偏估計量建立相關的檢定程序與信賴區間，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，最後透過數值範例驗證。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

製程能力指標 ； 上記錄值 ； 最大概似估計量 ； Burr XII分配 ； Gompertz分配 ； 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. The better process capability , the higher level of product quality it is, and the conforming rate. The literatures of quality performance mostly assumed the quality characteristics of product with the Normal distribution. In practice, the quality characteristics of product does not necessarily obey the Normal distribution. However, under certain situation, we are only interested in the next occurrence of the life of the product is higher than the previous record need to record. In order to make the process capability indices evaluate the product quality exactly. This research constructs an unbiased estimator of C_L based on the upper record value samples from Burr XII and Gompertz distribution. The unbiased estimation 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

Process capability indices ； upper record value ； maximum likelihood estimator ； Burr XII distribution ； Gompertz distribution ； Monte Carlo simulation

參考文獻

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