量測系統分析(measurement system analysis; MSA)在協助品管人員改善產品品質的過程中扮演關鍵性角色，在執行製程指標能力研究前，品管工程師必須先針對量測系統之重複性與再現性(gauge repeatability and reproducibility; GRR)進行分析藉以評估量測系統之精密度是否適當。傳統量測系統分析方法僅考慮單一品質特性，然而隨著現代科技之發展，工業產品通常具有多重品質特性，因此量測系統分析亦應具有分析多重品質特性(即多變量品質特性)之能力。
本研究針對Majeske (2008)提出之多變量P/T比值(precision-to-tolerance ratio)未考量規格公差相關性之缺點進行修正，並與Wang and Yang (2007)提出之多變量P/T 比值進行比較，模擬結果證實我們提出之P/T比值最為穩健亦較接近實際值。另外，本研究利用修正後P/T比值之信賴區間探討GRR分析時不同參數(品質特性數v、產品個數p、量測人員數o及重複量測次數r)間之關係，並發現品質特性數v與產品個數p兩參數會影響估算P/T比值之準確度。
最後，我們將研究成果加以整理寫成執行多變量GRR分析之標準作業流程(S.O.P.)，此一程序可作為品管人員未來執行多變量量測系統分析之參考。

A gauge repeatability and reproducibility (GRR) study for analyzing gauge variation needs to be conducted prior to the process capability analysis. In this research, we proposed a new precision-to-tolerance ratio (P/T) for multivariate measurement system by considering the correlation coefficients among tolerances. And the simulation results show that our revised P/T ratio outperforms the existing one in terms of robustness and accuracy. Moreover, the optimal allocation of several parameters such as the number of quality characteristics (v), sample size of parts (p), number of operators (o) and replicate measurements (r) is discussed using the confidence interval (C.I.) of the revised P/T. Finally, a standard operating procedure (S.O.P.) to perform GRR study for multivariate measurement systems is summarized based on the research results. Hopefully, it can be served as a useful reference for quality practitioners when conducting GRR study for a multivariate measurement system analysis (MSA) in industries.

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