非對稱規格區間下Cpk''指標的信賴下界與臨界值

Abstract

如許多品質管制研究者與實踐者所提及，製造業廣泛使用製程能力指標Cpk用以量化衡量製程表現，Cpk指標以良率為基礎且與規格目標T相互獨立，使得Cpk在對稱規格區間下未考量製程與規格中心的關係，甚至在非對稱規格區間遭遇更大的問題。Pearn和Chen(1998)提出製程能力指標Cpk的新推廣，稱做Cpk''，其相較其他已經存在的非對稱規格區間下之 推廣指標來得好。在本篇論文中使用Cpk''之估計量執行假設檢定理論，基於Pearn et al.(2004)提出之累積機率函數開發出一個有效率的演算法去計算不同型I誤差風險、製程能力要求和樣本數下之p值與臨界值。同時也提供另一個演算法去計算Cpk''指標之信賴下界，用以確認產品信賴保證之最小製程能力值。實務應用上可以採用其中一種依據估計量的決策準則去判定使用者工廠內製程能力是否滿足需求。

As noted by many quality control researchers and practitioners, the process capability index Cpk has been widely used in the manufacturing industry to provide quantitative measures on process performance. Cpk is a yield-based index and independent of the target T, it fails to take into account process centering with symmetric tolerances, and encounter an even greater problem with asymmetric tolerances. Pearn and Chen (1998) proposed a new generalization of process capability index Cpk, called Cpk'', which was shown to be superior to other existing generalizations of Cpk for processes with asymmetric tolerances. In this thesis, we implement the theory of hypothesis testing using the natural estimator of Cpk'', and we develop an efficient algorithm which derived the probability density function and cumulative distribution function provided by Pearn et al. (2004) to calculate the p-value as well as the critical values for various values of alpha-risk, capability requirements, and sample sizes. We also provide another algorithm to compute the lower confidence bounds of Cpk'', then we can confirm the minimum true capability of the process, which is necessary to product reliability assurance. The practitioners can use both decision making procedure based on the natural estimator of Cpk'' to determine whether their in-plant processes are capable or not.