Estimating Process Capability Indices of Multivariate Non-Normal Processes

The capability analysis of production processes where there are more than one correlated quality variables is a complicated task. The problem becomes even more difficult when these variables exhibit non-normal characteristics. In this paper, a new methodology is proposed to estimate process capability indices (PCIs) of multivariate non-normal processes. In the proposed methodology, the skewness of the marginal probability distributions of the variables is first diminished by a root transformation technique. Then, a Monte Carlo simulation method is employed to estimate the process proportion of non-conformities (PNC). Next, the relationship between PNC and PCI is found, and finally PCI is estimated using PNC. Several multivariate non-normal distributions such as Beta, Weibull, and Gamma are taken into account in simulation experiments. A real-world problem is also given to demonstrate the application of the proposed procedure. The results obtained from both the simulation studies and the real-world problem show that the proposed method performs well and is able to estimate PCI properly.