在非常態製程之下修正後彈性能力指標Cjkp*的估計

Abstract

製程能力指標為生產流程中之一種品質量化指標，為品質管制之重要參考依據，實際上，業界廣泛使用指標Cpk¬的NCPPM表將Cpk值轉換成其相對應的不良率(NCPPM)。 Cpk僅於製程資料服從常態分配時適用。 Johnson、Kotz和Pearn (1994) 提出指標Cjkp，此指標基於製程屬非常態分配所發展出來。然而該指標其抽樣分配不易求得，使得無法得知製程是否達到要求，並且因為指標Cjkp還未廣泛被使用，所以尚未發展出Cjkp的相對應不良率表。因此本論文針對Gamma分配、Weibull分配、Lognormal分配、Beta分配和Chi-square分配，利用curve fitting修正Cjkp指標，使其能套用到Cpk指標，再利用curve fitting 使Cjkp*指標的估計量為近似不偏估計量。這樣業界以修正後Cjkp指標算出的值，經由查詢Cpk的NCPPM表，就能得到其相對應的不良率(NCPPM)。最後，本篇論文應用四種Bootstrap建構信賴區間的方法建構Cjkp之四種信賴下界，並比較五個分配在不同的參數變化下四種信賴下界之涵蓋率。

The process capability indices (PCIs) which are the important references in quality control have been one of a numerical measure index in product process. In practice, practitioners widely use the NCPPM table of Cpk index to transform the Cpk value to the corresponding nonconformities (NCPPM). Cpk is only appropriate for normal processes. Johnson, Kotz and Pearn (1994) proposed the index Cjkp for non-normal processes. However, the exact sampling distribution of Cjkp is mathematically intractable, Cjkp could not assure that the process capability meet the requirement and since Cjkp hasn’t been widely used, the corresponding NCPPM table has not been developed. Therefore, in connection with Gamma, Weibull, Lognormal, Beta, and Chi-square distributions, we use curve fitting to modify the index Cjkp that can be applied to obtain the NCPPM using the existing NCPPM table for index Cpk. Then we use curve fitting to modify the estimator of Cjkp* index being approximately unbiased estimator. Consequently, when practitioners calculate the value of modified Cjkp, they can inquire the corresponding nonconformities (NCPPM) with the NCPPM table of Cpk. Finally, the thesis applies four Bootstrap methods to construct four lower confidence bounds of Cjkp and compares the coverage rates under different parameters for five distributions.