Process Monitoring for Multiple Count Data Using a Deleted-Y Statistic

Abstract

A procedure for monitoring discrete multivariate counts is proposed. The procedure is based on two schemes: the first scheme detects a shift in one or two of the p variables; the second procedure detects a shift in all the variables. The first scheme is based on an unbiased estimator for the shift in a particular Poisson count when input variables are not measurable. Run length results show that for most shift conditions this estimator is more effective in detecting a shift in one or two variables than using multiple C charts on the raw counts. The second scheme is based on the average of the p variables. Run length results show that its performance is equal to or better than the performance of multiple C charts on the raw counts. Together the two schemes provide efficient detection of virtually all shift situations.

Key Words:

• C chart
• control chart
• Poisson distribution
• statistical process control

Additional information

Notes on contributors

Katina R. Skinner

Katina Skinner Ph.D., is contractor for educational organizations. Her interests include curriculum design and development, process monitoring, and design of experiments. She is a member of ASQ.

George C. Runger

George C. Runger Ph.D., is a Professor in the department of Industrial Engineering at Arizona State University. His research is on real-time monitoring and control, data mining, and other data-analysis methods with a focus on large, complex, multivariate data streams. He has over one hundred research publications in these areas. His work is funded by grants from the National Science Foundation and corporations. In addition to academic work, he was a senior engineer at IBM. He holds degrees in industrial engineering and statistics.

Douglas C. Montgomery

Douglas C. Montgomery is the ASU Foundation Professor of Engineering and Co-Director of the Program in Statistics at Arizona State University. His interests are in design of experiments, process monitoring and control, and empirical model building. He is a Fellow of ASA, ASQ, IIE, the RSS, and an elected member of the International Statistical Institute. He is an author of 14 books and over 175 archival journal papers. Dr. Montgomery is a former editor of the Journal of Quality Technology and currently Chief Editor of Quality and Reliability Engineering International.