傳統的製程能力分析均假設品質特性彼此獨立，但在實際生產過程中，我們所蒐集到的資料往往會存在自我相關特性，因此，此類資料若以傳統製程能力分析的方法進行評估極易產生誤判，而導致不必要的成本浪費。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常常呈現自我相關的情況，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自我相關且產品工程規格屬望目及望小特性情形下多變量自我相關製程能力指標之制定與評估，我們利用自我相關共變異數矩陣Γ(0)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，並據此制定出新的多變量自我相關製程能力指標NMACp(Autocorrelated NMCp)和NMACpm(Autocorrelated 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Γ(0)進行修正並提出新多變量自我相關製程能力指標NMACpu。
接著，於不同時間序列模型下，我們以模擬的方式比較本研究所提出之新指標與 Cpm、MCp、MCpm、NMCp、NMCpm及ND等望目及望小特性指標在反映多變量自我相關製程表現上之優劣。模擬分析結果顯示無論製程平均是否偏離目標值，多變量自我相關製程能力指標與上述指標相較均能正確反映出多變量自我相關製程實際的不良率。最後，我們以二筆北美河流流量資料為例，說明新多變量自我相關指標較能反映河流流量實際變化的情形。

Traditionally, the process capability index is developed assuming that the process output data are independent and follow normal distribution. However, in most environmental cases, the process data have more than one quality characteristic and exhibit property of autocorrelation. We propose two novel multivariate process capability indices for autocorrelated data, NMACp and NMACpm for the nominal-the-best case. For the-smaller-the-better case, Γ(0) is used to modify the ND index proposed by Niverthi and Dey (1995) and a new multivariate autocorrelated process capability index NMACpu is derived.
Furthermore, a simulation study is conducted to compare the performance of the various multivariate autocorrelated indices. The simulation results show that the actual non-conforming rates can be correctly reflected by our proposed indices, which outperform the previous Cpm, MCp, MCpm, NMCp, NMCpm and ND indices under different time series models. Thus, our proposed capability indices can be applied to the performance evaluation of multivariate autocorrelated processes. Finally, a realistic example in hydrological application further demonstrates the usefulness of our proposed capability indices.

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