修正後百分位數之非常態製程下能力指標CNpk*的估計

Abstract

製程能力指標是被廣泛地用來評估製程產出產品是否符合規格的重要工具，不僅能提供品質保證，也是提供品質改善方面的一個方針。其中，雙邊規格 指標是在製造業中使用最多、最廣泛的指標之一。但Cpk僅適用於製程資料服從常態分配，本篇研究考慮Pearn and Chen (1997) 提出之CNpk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，使得無法保證製程是否達到要求，且CNpk目前並非廣泛使用之製程能力指標，所以尚未發展出CNpk的相對應不良率表。因此，本篇研究提出修正後指標CNpk*，並令CNpk*數值所代表的製程能力意義與 近似，使得使用者能以CNpk*查詢Cpk的NCPPM表。本篇研究考慮五個非常態分配，分別為Gamma分配、Weibull分配、Log-normal分配、Beta分配和Chi-square分配，並利用Matlab軟體求出這五個分配下的CNpk*與其近似不偏估計式CNpk*~。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) have been extensively used to measure whether the process meets the specifications and they provide quality assurance and guide a principal for quality improvement at the same time. Cpk is the most popular index used in the manufacturing industry. However, is only appropriate for process for normal distribution. Pearn and Chen (1997) proposed the capability index CNpk for non-normal process. However, the exact sampling distribution of CNpk is mathematically intractable, therefore, CNpk could not assure the process capability. Since CNpk hasn’t been widely used, the corresponding NCPPM table has not been developed. Thus, in this thesis, we propose a modified index of CNpk called CNpk*. Moreover, users who use CNpk* could refer to nonconformities corresponding to Cpk. In this thesis, we take into account five non-normal distributions, including Gamma distribution, Weibull distribution, Log-normal distribution, Beta distribution and Chi-square distribution. We obtain CNpk* and the approximately unbiased estimator CNpk*~ 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.