Multivariate nonnormal process capability analysis

There is a great deal of interest in the manufacturing industry for quantitative measures of process performance with multiple quality characteristics. Unfortunately, multivariate process capability indices that are currently employed, except for a handful of cases, depend intrinsically on the underlying data being normally distributed. In this paper, we propose a general multivariate capability index based on the Mahanalobis distance, which is very easy to use. We also approximate the distribution of these distances by the Burr XII distribution and then estimate its parameters using a simulated annealing search algorithm. Finally, we give an example, based on real manufacturing process data, which demonstrates that the proportion of nonconformance (PNC) using our proposed method is very close to the actual PNC value, which also justifies its adoption in this paper.