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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.
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Notes on contributors
A.B. Yeh
Arthur B. Yeh is an Associate Professor of Statistics at the Department of Applied Statistics and Operations Research, Bowhng Green State University, Ohio, U.S.A. His areas of interest in research include bootstrap, optimal experimental designs, multivariate statistical process control, data depth, and statistical computing.
H. Chen
Hanfeng Chen is an Associate Professor of Statistics at the Department of Mathematics and Statistics, Bowling Green State University, Ohio, U.S.A. His areas of interest in research include semi-parametric inference, generalized linear models, multivariate statistical process control, estimating functions, and empirical likelihood.