Statistical variables are divided into two categories: nominal and ordinal, both of which have many uses. In some statistical process monitoring applications, quality of a process or product is described by more than one ordinal quality characteristics called ordinal multivariate process. To show the relationship between these variables, an ordinal contingency table is used and modeled with ordinal log-linear model. In our manuscript, two new statistics including simple ordinal categorical and Generalized-p are developed for Phase II monitoring the ordinal log-linear model based processes. Performance of the proposed statistics are evaluated by using some simulation studies and a real numerical example. Results show the superiority of simple ordinal categorical based control chart. In addition, performance of these statistics is accessed through a sensitivity analysis on the size of the rows and columns of the contingency table. Meanwhile, a sensitivity analysis with three and four categorical factors is performed and similar results are obtained.
