A General Approach for Monitoring Serially Dependent Categorical Processes

摘要

We consider the statistical surveillance for serially dependent categorical processes, where observations exhibit temporal dependence and have several attribute levels. In the literature, relevant methods focus on serially dependent binary data with two attribute levels and are mainly constructed from a first-order Markov chain. However, they cannot be applied to multinary data with three or more attribute levels. In addition, a Markov chain seems not to be a good choice because it cannot characterize the joint dynamics among the current observation and its past values. In this article, we adopt a multivariate categorical setting of the data and develop a general approach for monitoring serially dependent categorical processes, from binary to multinary, and from first-order dependency to higher-order dependency. Simulation results have demonstrated its robustness to various shifts in marginal probabilities and dependence structure, including autocorrelation coefficients and dependence order.