修正後權重變異數指標之非常態製程下能力指標Cpk*(WV)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。Wu et al. (1999) 提出指標Cpk(WV)，此指標基於製程為非常態所發展出來。實際上，業界廣泛使用指標Cpk及其相對應的不良率(NCPPM)表格。新發展出的指標Cpk(WV)尚未有其相對應的不良率表格，因此業界希望能以既有的Cpk不良率表格來做查詢。所以我們針對Gamma分配、Weibull分配、Log-normal分配、Beta分配和Chi-square分配想辦法利用Matlab的curve fitting修正Cpk(WV)指標，使其能套用到Cpk指標，再次利用Matlab的curve fitting使Cpk(WV)指標的估計量為近似不偏估計量，如此業界能以修正後Cpk(WV)指標的值來查詢Cpk的不良率表格，就能得到其相對應的不良率(NCPPM)。此外，本篇研究應用bootstrap方法建構出指標之四種信賴下界，再比較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. Cpk has been popularly used in the manufacturing industry for measuring process performance based on yield. Wu et al. (1999) based on the non-normal process and proposed the index Cpk(WV). Cpk(WV) can not appropriate for process under normal distribution. Industries hope to use the NCPPM table of index Cpk to inquire the corresponding nonconformities not the table of index Cpk(WV). For this problem, in connection with Gamma, Weibull, Lognormal, Beta, and Chi-square distributions, we think to use curve fitting by “Matlab” computer program to modify the index Cpk(WV) that can apply to index Cpk. Finally, we use curve fitting to modify the estimator of Cpk*(WV) index is approximately unbiased estimator. Therefore, when industries calculate the value of modified Cpk(WV), they can inquire the corresponding nonconformities (NCPPM) with the NCPPM table of Cpk. In addition, we apply bootstrap methods to construct four lower confidence bound methods of the index. Under different parameter setting, we compare the coverage rates of the four lower confidence bound methods.