Principal component analysis-based control charts for multivariate nonnormal distributions

Multivariate control charts have been widely used in many industries to monitor and diagnose processes characterized by a large number of quality characteristics. Usually, these characteristics are highly correlated with each other. The direct use of conventional multivariate control charts for situations with highly correlated characteristics may lead to increased rates of false alarms. Principal component analysis (PCA) control charts have been widely used to address problems posed by such high correlations by transforming the set of correlated variables to an uncorrelated set of variables and then identifying the PCs with highest contribution which then allows one to reduce dimensionality. However, an assumption that the data are normally distributed underlies the construction of the control limits of traditional PCA control charts. This assumption has limited the use of PCA control charts in nonnormal situations found in many modern systems. This study presents the development of nonparametric PCA control charts that do not require any distributional assumptions for their construction. We propose to use nonparametric techniques, kernel density estimation, and bootstrapping to establish the control limits of these charts. A simulation study was conducted to evaluate the performance of the proposed charts and compare them with traditional PCA control charts. The comparative performance in terms of average run length showed that the proposed nonparametric PCA control charts performed better than the parametric PCA control charts in nonnormal situations.