Multivariate Ordinal Categorical Process Control Based on Log-Linear Modeling

In many applications, the quality of products or services tends to be measured by multiple categorical characteristics, each of which is classified into attribute levels such as good, marginal, and bad. Here there is usually natural order among these attribute levels. However, traditional monitoring techniques ignore such order among them. By assuming that each ordinal categorical quality characteristic is determined by a latent continuous variable, this paper incorporates the ordinal information into an extended log-linear model and proposes a multivariate ordinal categorical control chart based on a generalized likelihood-ratio test. The proposed chart is efficient in detecting location shifts and dependence shifts in the corresponding latent continuous variables of ordinal categorical characteristics based on merely the attribute-level counts of the ordinal characteristics.