製程能力指標(process capacity indices)在製程能力分析中扮演重要角色，因為它提供一個簡單易懂的製程整體表現量測標準。隨著產品功能的多樣化，製程的複雜度亦隨之增加，僅衡量單一品質特性已不足反映製程之能力，因此90年代以後有多位學者致力於具多重品質特性製程能力指標的研究。多重品質特性製程之規格區域是由個別品質特性規格範圍所構成的矩形區域。有別於多重品質特性之規格區域，多維切割製程之規格區域是一種稱之為位置容差(positional tolerance)的特殊規格。位置容差為幾何容差(geometric dimensioning and tolerancing, GD&T)中的一種，它是一種描述切割製程所允許的位置之規格區域，在二維度時為一圓形、三維度時為一球體。 Bothe (2006)、Karl et al. (1994)、Litting et al. (1993)、Davids et al. (1993)及Krishamoorthi (1990)等學者，提出適用於評估此特殊規格區域的多維切割製程的製程能力指標。過去的研究皆假設不同切割方向的變異是一致的，但在許多情況下此假設並不適用，故本研究制定當變異不一致時，新的多維切割製程能力指標，藉以評估多維切割製程生產時在準確度與精密度上的表現。我們在常態性的假設下推導該指標估計量之統計性質，建立其區間估計與假設檢定方法。再利用數值模擬的方式與過去學者所提出之多維切割製程能力指標作一比較。結果顯示，本研究所之新製程能力指標較能正確反映出製程實際表現。最後，利用本研究之多維切割製程能力指標對一數值實例進行分析與說明。

Process capability indices play the important role in the manufacturing industry to determine whether a process is capable of manufacturing good-quality items. At beginning, process capability analysis only focuses on the process with a single characteristic. With the advent of modern technology, manufacturing process become very sophisticated and merely a single quality characteristic cannot reflect the product quality. Normally, the abnormality of an industrial process is caused by the problems of several interrelated quality characteristics. In contrast with the multivariate manufacturing process, the multidimensional machining process has a special specification called the positional tolerance. Positional tolerance is a type of geometric dimensioning and tolerancing (GD&T) which describes the tolerance region between the location of machining results and the target point. Past researchers proposed the capability index for the positional tolerance of a multidimensional machining process under the assumption that two or more dimensional variances are equal. However, this assumption may not be true in the real situation. In this research, two new capability indices for measuring the precision and accuracy of the positional tolerance of a multidimensional machining process are developed under the normal assumption. The statistical properties of the point estimators for the new capability indices are proved, then their confidence intervals and hypothesis testing methods are established using the approximations. The simulation results show that the new capability indices can better reflect the true performance of a multidimensional machining process then the previous indices.

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