Multivariate Fuzzy Multinomial Control Charts

Abstract

Two approaches for constructing control charts to monitor multivariate attribute processes when data set is presented in linguistic form are suggested. Two monitoring statistics T²_f and W² are developed based on fuzzy and probability theories. The first is similar to the Hotelling’s T² statistic and is based on representative values of fuzzy sets. The distribution of W² statistic, being a linear combination of dependent chi-square variables, is derived using Satterthwaite’s approximation. Resulting multivariate control charts are compared based on the average run length (ARL). A numerical example is given to illustrate the application of the proposed multivariate control charts and the interpretation of out-of-control signals.

Key Words:

• Bootstrap
• categorical data
• fuzzy control
• Satterthwaite’s approximation

Additional information

Notes on contributors

Hassen Taleb

Hassen Taleb is an Assistant Professor of statistics at the Institut Supérieur de Gestion, University of Tunis, Tunisia. His research interests include statistical quality control and fuzzy applications. His publications appeared in the International Journal of Production Research, and Lecture Notes of Artificial Intelligence. Dr. Taleb is a member of Tunisian Management Science Society.

Mohamed Limam

Mohamed Limam is a Professor of Statistics at the University of Tunis, ISG, Tunisia. His research interests include applied statistics, quality control, experimental design, data mining and bioinformatics. His publications appeared in Journal of American Statistical Association, Communications in Statistics, Machine Learning, International Journal of Production Research, Quality Technology & Quantitative Management, and International Journal of Quality and Reliability Management. His is a member of ASQ, and a member of Tunisian Management Science Society.

Kaoru Hirota

Kaoru Hirota is a Professor at the Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Yokohama, Japan. He has experienced (twice) a department head professor of Department of Computational Intelligence and Systems Science. His research interests include fuzzy systems, intelligent robot, image understanding, expert systems, hardware implementation and multimedia intelligent communication. Dr. Hirota is a member of IFSA (International Fuzzy Systems Association (Vice President, 1991–1993 and 2005–2007, Treasurer, 1997–2001, secretary, 2003–2005, Fellow awarded in 2003)), IEEE (Associate Editors of IEEE Transactions on Fuzzy Systems, 1993–1995, and IEEE Transactions on Industrial Electronics, 1996–2000, IEEE CIS Distinguished Lecturer) and SOFT (Japan Society for Fuzzy Theory and Systems (Vice President, 1995–1997, President, 2001–2003)). He is the Editor-in-Chief of Int. J. of Advanced Computational Intelligence and Intelligent Informatics. A Banki Donat Medal, Henri Coanda Medal, Grigore MOISIL Award, SOFT best paper prize in 2002, and honorary professorship at de La Salle University were awarded to Dr. Hirota. He also organized many international conferences/symposiums as a general chair or a program chair such as FUZZ-IEEE’95, InTech2002, and SCIS2002 (more than 10 in total). He has published more than 160 journal papers and more than 375 conference papers in the field of computational intelligence.