Developing New Multivariate Process Capability Indices for Non-Normal Data

Generally, an industrial product has more than one quality characteristic. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, several multivariate process capability indices have been developed based on the assumption of normality. Quality characteristics of many manufacturing processes in the chemical, pharmaceutical and electronic industries, however, often do not follow normal distribution. This paper develops two non-normal multivariate process capability indices, RNMCp and RNMCpm that relax the normality assumption. Using the two normal multivariate process capability indices proposed by Pan and Lee, a multivariate weighted standard deviation method (MWSD) is used to modify the NMCp and NMCpm indices for the nominal case. Then the MWSD method is applied to modify the multivariate process capability index established by Niverthi and Dey, the ND index, for the-smaller-the-better case. A simulation study compares the performance of the various multivariate indices. Simulation results show that the actual non-conforming rates can be correctly reflected by the proposed indices, which are more appropriate than the previous MCp, MCpm, NMCp, NMCpm and the ND indices for a non-normal distribution. Two skewed distributions were used in various configurations. The proposed capability indices can thus be applied to the performance evaluation of multivariate processes subject to non-normal distributions.