Control Chart T2Qv for Statistical Control of Multivariate Processes with Qualitative Variables

Wilson Rojas-Preciado (), Mauricio Rojas-Campuzano, Purificación Galindo-Villardón and Omar Ruiz-Barzola
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Wilson Rojas-Preciado: Faculty of Social Sciences, Technical University of Machala (UTMACH), Machala 070102, Ecuador
Mauricio Rojas-Campuzano: Center for Statistical Studies and Research, Polytechnic School of the Littoral, Guayaquil 090150, Ecuador
Purificación Galindo-Villardón: Department of Statistics, University of Salamanca, 37004 Salamanca, Spain
Omar Ruiz-Barzola: Department of Statistics, University of Salamanca, 37004 Salamanca, Spain

Mathematics, 2023, vol. 11, issue 12, 1-32

Abstract: The scientific literature is abundant regarding control charts in multivariate environments for numerical and mixed data; however, there are few publications for qualitative data. Qualitative variables provide valuable information on processes in various industrial, productive, technological, and health contexts. Social processes are no exception. There are multiple nominal and ordinal categorical variables used in economics, psychology, law, sociology, and education, whose analysis adds value to decision-making; therefore, their representation in control charts would be useful. When there are many variables, there is a risk of redundant or excessive information, so the application of multivariate methods for dimension reduction to retain a few latent variables, i.e., a recombination of the original and synthesizing of most of the information, is viable. In this context, the T2Qv control chart is presented as a multivariate statistical process control technique that performs an analysis of qualitative data through Multiple Correspondence Analysis (MCA), and the Hotelling T2 chart. The interpretation of out-of-control points is carried out by comparing MCA charts and analyzing the χ 2 distance between the categories of the concatenated table and those that represent out-of-control points. Sensitivity analysis determined that the T2Qv control chart performs well when working with high dimensions. To test the methodology, an analysis was performed with simulated data and with a real case applied to the graduate follow-up process in the context of higher education. To facilitate the dissemination and application of the proposal, a reproducible computational package was developed in R, called T2Qv, and is available on the Comprehensive R Archive Network (CRAN).

Keywords: multivariate; statistical process control; qualitative; control charts; R; T2 hotelling; graduate tracking; higher education (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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