An efficient charting scheme for multivariate categorical process with a sparse contingency table

Multivariate categorical quality characteristics, whose distribution can be displayed by a contingency table, are routinely encountered in many applications. When most of the cell entries in the contingency table are very small or zeros counts, which is so-called sparse contingency table in the literature, existing methods developed in the literature are often inadequate for use, due to the inaccuracy of the maximum likelihood estimate of its probability distribution, and the inflation of online charting statistics. This paper studies the multivariate statistical process control problem for such sparse contingency table. We integrate the group least absolute shrinkage and selection operator (LASSO) method with the Ridge method to estimate the in-control distribution of a contingency table and propose an efficient EWMA control chart, based on a modified Pearson χ² statistic, to monitor the changes in it. Numerical results show that our proposed approach has the best overall performance, compared with its competitors. Finally, a real data example is used to demonstrate the effectiveness of the proposed control chart.