Multivariate process capability indices are applied to account the capability of the processes which the quality of the products depends on two or more related characteristics. We call a tolerance region asymmetric, when the target value of at least one characteristic is not the mid-point of the tolerance interval. This paper introduces a superstructure index to measure the capability of multivariate normal process in asymmetric tolerance regions, which could be applied for symmetric cases, too. In addition, the effects of two modification factors in the index which weigh the mean departure from target and process variability are investigated. Furthermore, some examples are presented to demonstrate the applicability and effectiveness of the proposed index.

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