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A Nonparametric Multivariate Process Capability Index

Abstract For the multivariate manufacturing processes, tremendous difficulties are often encountered when one attempts to measure the process capability by directly extending the univariate approach, that is, comparing the specification limits (tolerance zones) with the actual process spread. In fact, the existing multivariate process capability indices developed along the same line are very complicated to apply even under the normality assumption. The authors of this paper propose a new multivariate process capability index that is directly related to the proportion of nonconforming items. Moreover, the new index is calculated in a nonparametric setting; hence, it does not rely on a particular distribution. The estimation methods of the new index are studied in detail. Simulations for the elliptical and rectangular tolerance zones under different bivariate distributions are carried out to illustrate the new approach. The applications of the new index to real-life examples are also presented.