一般而言，工業製程中常有多個彼此相關的品質特性皆可能造成產品與製程異常。目前已有多位學者致力於多重品質特性(多變量)製程能力指標之研究，但彼等之研究多著重在品質特性呈常態之情況。實務上，一些與環境績效或與能源使用有關的多重關鍵品質特性卻常呈現非常態分配且為相依資料的情況，然而，甚少學者探討此類狀況下多變量製程能力指標之制定。因此，本研究擬探討當多重品質特性呈非常態分配且產品工程規格屬望目及望小特性情形下非常態多變量製程能力指標之制定與評估，我們利用Weighted Standard Deviation (WSD)方法對Pan與Lee (2010) 所訂定之常態多變量製程能力指標NMCp與NMCpm指標進行修正，並據此制定出新的非常態多變量製程能力指標RNMCp(Revised NMCp)和RNMCpm(Revised NMCpm)。此外，針對Niverthi與Dey (1995) 訂定望小特性下的多變量常態製程能力指標(ND index)，我們亦利用WSD法進行修正並提出改良的非常態多變量製程能力指標RNMCpu。
最後，我們以模擬的方式比較於不同右(左)偏分配組合下，本研究所提出之新指標與MCp、MCpm、NMCp、NMCpm及ND在反映非常態多變量製程表現上之優劣。模擬分析結果顯示無論製程平均是否偏離目標值，新非常態多變量製程能力指標與上述指標相較均能正確反映非常態多變量製程真實的不良率。

Generally, an industrial product has more than one quality characteristic. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, several multivariate process capability indices have been developed based on the assumption of normality in the past few years. However, the environmental performance, such as air pollution and energy utilization data may not follow normal distribution. Thus, in this research, we develop two non-normal multivariate process capability indices; RNMCp (Revised NMCp) and RNMCpm (Revised NMCpm) by relieving the normality assumption for both nominal-the-best and smaller-the-better cases. Based on the two normal multivariate process capability indices proposed by Pan and Lee (2010), we use weighted standard deviation method (WSD) to revise their NMCp and NMCpm indices. In addition, we also use WSD method to revise a multivariate process capability index (ND index) established by Niverthi and Dey (1995).
Finally, we conduct simulation studies to compare the performance of correctly reflecting the true nonconforming rate among these multivariate indices. Simulation results show that our proposed indices outperform MCp, MCpm, NMCp, NMCpm and ND indices under different combinations of two right skewed/left skewed distributions regardless of the process mean hitting the target or not.

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