在偏態製程下修正後製程能力指標Cs*的估計

Abstract

製程能力指標廣泛地被用來評估製程產出產品是否符合規格的重要工具，不僅提供品質保證也是提供品質改善方面的一個方針。其中Cs指標為衡量非常態分配的重要指標。但實際上業界廣泛運用的指標為Cpk ，學界也因此發展出相對應Cpk值的不良率表以方便查詢，而本篇研究考慮Wright (1995) 提出之Cs指標，其於製程資料為非常態分配時也能精確的評估製程良率。然而該指標估計式的抽樣分配不易求得，使得使用者無法保證製程是否達到要求，且因為Cs並未被廣泛使用，所以尚未發展出相對應不良率表，因此此篇論文以五種非常態分配分別為Gamma分配、Weibull分配、Log-normal分配、Beta分配和Chi-square分配為基礎藉以修正Cs指標使其能夠套用至Cpk不良率表中，並且找出修正過後Cs指標的近似不偏估計量。因此，本篇研究應用Curve fitting tool得出五種分配下的校正因子來改善原指標，並且利用Curve fitting tool修正該指標之估計量使其成為近似不偏估計量。另外，本篇研究應用複式抽樣法建構出指標之四種信賴下界，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 important in quality control have been one of a numerical measure index in product process. Cpk is the most popular index used in the manufacturing industry. However, Cpk is only appropriate for process in normal distribution. Wright (1995) based on the non-normal process and proposed the index Cs. However, the exact sampling distribution of Cs is mathematically intractable; therefore, Cs could not assure that the process capability meets the requirement and since Cs has not been widely used, the corresponding NCPPM table has not been developed. To solve this problem, we consider five non-normal distributions, including Gamma distribution, Weibull distribution, Log-normal distribution, Beta distribution and Chi-square distribution. We use curve fitting by the computer program Matlab to obtain the modified index of Cs called Cs* that can be applied to the NCPPM table of index Cpk directly. In the second part, we obtained approximately unbiased estimator Cs~* for the five distributions by Matlab computer program. Further, four bootstrap methods were applied to construct the lower confidence bound of the index. We compare the coverage rates of the four bootstrap methods with different parameter setting for each distribution.