New Approaches in Monitoring Multivariate Categorical Processes based on Contingency Tables in Phase II

In some statistical process control (SPC) applications, quality of a process or product is characterized by contingency table. Contingency tables describe the relation between two or more categorical quality characteristics. In this paper, two new control charts based on the WALD and Stuart score test statistics are designed for monitoring of contingency table-based processes in Phase-II. The performances of the proposed control charts are compared with the generalized linear test (GLT) control chart proposed in the literature. The results show the better performance of the proposed control charts under small and moderate shifts. Moreover, new schemes are proposed to diagnose which cell corresponding to different levels of categorical variables is responsible for out-of-control signal. In addition, we propose EWMA-WALD and EWMA-Stuart score test control charts to improve the performance of Shewhart-based control charts in detecting small and moderate shifts in contingency table parameters. Meanwhile, we compare the performances of two proposed EWMA-based control charts with the ones of three existing control charts called EWMA-GLT, EWMA-GLRT and an EWMA-type control chart for multivariate binomial/multinomial processes along with the ones of the corresponding Shewhart-based control charts. A numerical example is given to show the efficiency of the proposed methods. Finally, the effect of parameter estimation in Phase I based on m historical contingency table on the performance of the Shewhart-based control charts is studied. Copyright (c) 2016 John Wiley & Sons, Ltd.