Phase II Monitoring of the Ordinal Multivariate Categorical Processes

Statistical variables are divided into two categories: nominal and ordinal, both of which have many uses. In some statistical process monitoring applications, the quality of a process or product is described by multiple ordinal quality characteristics, which is called ordinal multivariate process. An ordinal contingency table is used to show the relationships between these variables and is modeled on an 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. The performance of the proposed statistics will be evaluated using some simulation studies and real-world numerical examples. The results show the advantages of a simple ordinal category control card. In addition, the performance of these statistics is accessed through sensitivity analysis of the row and column sizes of the contingency table. Meanwhile, a sensitivity analysis with three and four categorical factors is performed and similar results are obtained.