A general framework for monitoring mixed data

Modern applications of statistical process monitoring involve checking the stability of multivariate processes with mixed data types, such as a combination of continuous, ordinal, and categorical quality variables. Appropriate statistical modeling for such data is often challenging, especially when the observed data are serially correlated, which explains why there is only a limited existing discussion on sequential monitoring of processes with mixed data. This paper introduces a general methodology to solve the problem. The main idea behind our approach is to sequentially transform the original observed data into continuous data through innovative data pre-processing, achieved by encoding the ordinal and categorical variables into continuous numerical variables using dummy and score variables and data transformation and decorrelation. Numerical studies show that the proposed method is effective in monitoring mixed data, in comparison with some state-of-the-art existing methods. The new method is illustrated in a case study involving online monitoring of hotel customers' behaviors. Computer codes in Julia for implementing the proposed methodology are provided in the supplemental material.