Process capability indices have been widely used in industries to assess the performance of the manufacturing processes. Various different multivariate capability indices have been introduced. In this paper, a new multivariate capability vector is proposed under the assumption of multivariate normality, to assess the production capability of the processes that involve multiple product quality characteristics. Also, we investigate the relation between this index and process centering, as well as the relation between this index and the lower and upper bounds of percentage of non-conforming items manufactured. Two real manufacturing data set are used to demonstrate the effectiveness of the proposed index.

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