New Approach for Process Capability Analysis Using Multivariate Quality Characteristics

The evaluation of manufacturing processes aims to ensure that the processes meet the desired requirements. Therefore, process capability indexes are used to measure the capability of a process to meet customer requirements and/or engineering specifications. However, most of the manufacturing products have more than one quality characteristic (QC), in which case, the multivariate QCs should be evaluated together using a single capability index. The research in this article proposes a methodology for estimating the multivariate process capability index (PCI). First, the dimensions of the multivariate QCs are reduced into a new single variable using the proportion of the process specification region, by comparing each variable datapoint to its specification limits. Moreover, nonnormal data are transformed to normality using a root transformation algorithm. Then, a large data sample is generated using the parameters of the new variable. The generated data are compared to the specification limits to estimate the percent of nonconforming (PNC). Finally, the capability index of a given process datapoints is estimated using the PNC. Accordingly, managerial insights for the implementation of the proposed methodology in real industry are presented. The methodology was assessed by well-known multivariate samples from four different distributions, in which an algorithm was developed for generating these samples with their given correlations. The results show the effectiveness of the proposed methodology for estimating multivariate PCIs. Also, the results from this research outperform the previous published results in most cases.