Phase-I monitoring of log-linear model-based processes (a case study in health care: Kidney patients)

Processes with multiple correlated categorical quality characteristics are called multivariate categorical processes. These processes are usually shown by contingency tables and are characterized by log-linear models. In this paper, two monitoring approaches including likelihood ratio test (LRT) and F test are developed to monitor multivariate categorical processes based on the contingency table in Phase I. In addition, a change point estimator for multivariate categorical processes is developed in Phase I. The performances of the two proposed approaches are evaluated in terms of probability of signal, while the performance of the proposed change point estimator is evaluated in terms of accuracy and precision criteria through simulation experiments. Meanwhile, we compare the performance of the two proposed control charts with an existing control chart called "-2LRT" control chart for multivariate categorical processes. In the end, a typical application of the proposed methods is illustrated in a real-world health care system.