On Control Charts Based on the Generalized Poisson Model

Abstract

The Poisson distribution is widely used to fit count data such as the number of nonconformities in a product unit. However, this distribution fails to fit the defect data in a high-quality manufacturing environment when over-dispersion occurs. In this paper, the generalized Poisson distribution is studied as an alternative distribution. The generalized Poisson distribution is flexible and capable of dealing with over-dispersed data. In particular, the interpretation of parameters is discussed and statistical monitoring procedures for count data that can be modeled by the generalized Poisson distribution are studied. Based on the generalized Poisson distribution, two different procedures are discussed for an effective process monitoring. Sensitivity analyses of the two monitoring procedures are also presented. To validate the use of the generalized Poisson distribution, three statistical tests for testing the Poisson distribution against the generalized Poisson alternative are also investigated and compared.

Key Words:

• Average run length
• control chart
• generalized Poisson distribution
• hypothesis testing
• monitoring procedure

Additional information

Notes on contributors

B. He

B. He is a Senior Engineer working for Philips Electronics. He obtained his BS from the University of Science & Technology of China in 1999, and his PhD from the National University of Singapore in 2004. He is a member of IEEE.

M. Xie

Min Xie is a Professor of Industrial and Systems Engineering, National University of Singapore. He received his PhD in Quality Technology from Linkoping University in 1987. His research area includes quality, reliability and applied statistics. Prof Xie is an author or co-author of over 100 journal papers and 6 books in this field. He serves as editor or associate editor of IJRQE, QTQM, IIE Transactions, IEEE Transactions on Reliability and several other journals. He is a Fellow of IEEE.

T. N. Goh

Thong Ngee Goh is a Professor of Industrial and Systems Engineering at the National University of Singapore. He obtained his PhD from the University of Wisconsin-Madison. Prof Goh has been internationally recognized for his expertise in quality engineering and management. He is an author of numerous papers and a few books. He is an elected Fellow of ASQ as well as Academician of IAQ.

K. L. Tsui

Kwok-Leung Tsui is a Professor in the School of Industrial and Systems Engineering at Georgia Institute of Technology. He has a B.Sc. in Chemistry and an M.Ph. in Mathematics both from the Chinese University of Hong Kong, and a Ph.D. in Statistics from the University of Wisconsin at Madison. He had worked in the Quality Assurance Center of AT&T Bell Laboratories in 1986–90. Dr. Tsui was a recipient of the 1992 NSF Young Investigator Award. He is a Fellow of the American Statistical Association (ASA), and was the (elected) President and Vice President of the ASA Atlanta Chapter in 1992–1993. Dr. Tsui was the chair of the INFORMS Section in the Quality, Statistics, and Reliability (QSR) in 2000, and is the founding chair of the INFORMS Section in Data Mining (DM). Dr. Tsui is also a US representative in the ISO Technical Committee on Statistical Methods (TC 69). Dr. Tsui researches, teaches, and consults on statistical methods for quality, logistics, and data mining. His research interest includes classification tree, support vector machine, Mahananlobis-Taguchi System, inventory forecasting and control, statistical process control, experimental design, robust design and Taguchi method, design and modeling of computer experiments, and coordinate measuring machine modeling.