Directional monitoring of categorical processes with serial dependence

The monitoring of a categorical process with serial dependence in which the current observation depends on its past values is of great importance in many applications, including manufacturing and service management. However, a great majority of existing research works are restricted to the cases where data are binary and of first-order dependency, based on the assumption of a two-state first-order Markov chain. In this article, a general categorical process with serial dependence that can have more than two attribute levels and higher-order dependency structure is under consideration. We adopt the multivariate representation of the categorical variables and integrate directional shift information into an adjusted log-linear model. Based on this, a novel control chart is proposed for detecting shifts in the marginal distribution and in the dependence structure of serially dependent categorical processes. Simulations have demonstrated its efficiency and robustness. The implementation of the proposed control chart through a real example is provided as the guidance for practitioners.