在非對稱規格下弱度能力指標C_(pp)的貝氏估計

Bayesian Estimations of Incapability Index under Asymmetric Specifications

曾信超(Hsin-Chau Tseng) ； 許淑卿(Shu-Ching Hsu) ； 郭信霖(Hsin-Lin Kuo)

《管理科學研究》 2007特刊 (2007/12) Pp. 97-110

https://doi.org/10.6873/MSR.200712/SP.0007

摘要

製程能力指標是常用來評估製造產業的能力，提供測量製程績效重要的量測方法；而傳統方法大部分是從頻率學派的觀點得到。在本文我們以貝氏方法(Bayes Approach)分別針對非情報事前分配(non-informative prior)、共輒事前分配(Conjugate Prior)與韋伯故障率函數(Weibull Hazard Function)求其有關弱度能力指標的點估計與在一般情形下 μ≠T的100×p%的信用區間。依據貝氏的方法，我們需先確定一個有關參數適當的事前分配，以得到其事後分配；並且在平方誤差損失函數(Squared-Error Loss Function)下，製程能力指標之事後機率的期望值就是其貝氏估計。

關鍵字

弱度能力指標 ； 信用區間 ； 非情報事前分配 ； 共輒事前分配 ； 韋伯故障率函數

並列摘要

Process capability indices are used to measure on whether a manufacturing process meet a set of requirement preset in the workshop, which designed to quantify the relation between the actual performance of the process and its specified requirement. In this paper we consider the problem of estimations of indices C_(pp)(μ≠T) under Bayesian framework. Several priors such as non-informative, conjugate prior and Weibull hazard function have been considered. Some estimates of hyper parameters are also studied. Some Bayesian estimators are derived and lower bound of the credible intervals under some conditions is also given.

並列關鍵字

Incapability Indices ； Credible Interval ； Non-informative Prior ； Conjugate Prior ； Weibull Hazard Function