Monitoring serially dependent categorical processes with ordinal information

In many industrial applications, there is usually a natural order among the attribute levels of categorical process variables or factors, such as good, marginal, and bad. We consider monitoring a serially dependent categorical process with such ordinal information, which is driven by a latent autocorrelated continuous process. The unobservable numerical values of the underlying continuous variable determine the attribute levels of the ordinal factor. We first propose a novel ordinal log-linear model and transform the serially dependent ordinal categorical data into a multi-way contingency table that can be described by the developed model. The ordinal log-linear model can incorporate both the marginal distribution of attribute levels and the serial dependence simultaneously. A serially dependent ordinal categorical chart is proposed to monitor whether there is any shift in the location parameter or in the autocorrelation coefficient of the underlying continuous variable. Simulation results demonstrate its power under various types of latent continuous distributions.