Monitoring two-stage processes with binomial data using generalized linear model-based control charts

Abstract

In this study, we propose a control chart for monitoring two-stage processes whose quality characteristic to be monitored in the second stage follows a binomial distribution. The proposed control chart is based on the deviance residual in which essentially the generalized log-likelihood ratio statistic is obtained from the generalized linear model. To establish the relationship between the first- and second-stage quality characteristics, we propose using a new link function in a generalized linear model framework. The performance of the proposed control chart with the new link function is compared with that under the traditional logit link function in terms of the average run length criterion. In addition, the performance of the proposed control chart is compared with the chart designed based on the original residuals under the new link function as well as the traditional np-chart applied for monitoring the binomial quality characteristic in the second stage.

Keywords:

• Average run length
• binomial data
• deviance residual
• generalized linear model
• two-stage process

Acknowledgements

The authors are thankful to the anonymous referees for constructive comments which led to improvement in the paper.

Disclosure statement

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of this article.

Notes on contributors

Dr. Amirhossein Amiri is an Associate Professor at Shahed University in Iran. He holds a BS, MS, and PhD in Industrial Engineering from Khajeh Nasir University of Technology, Iran University of Science and Technology, and Tarbiat Modares University in Iran, respectively. He is now head of Industrial Engineering Department at Shahed University in Iran and a member of the Iranian Statistical Association. His research interests are statistical quality control, profile monitoring, and Six Sigma. He has published many papers in the area of statistical process control in high quality international journals such as Quality and Reliability Engineering International, Communications in Statistics, Computers and Industrial Engineering, Journal of Statistical Computation and Simulation, Soft Computing and so on. He has also published a book with John Wiley and Sons in 2011 entitled Statistical Analysis of Profile Monitoring.

Dr. Arthur B. Yeh is a Professor of Statistics and Chair of the Department of Applied Statistics and Operations Research at Bowling Green State University. Over the years, Dr. Yeh has conducted and published research in several areas of industrial statistics, including, among others, optimal experimental designs, computer experiments, univariate and multivariate control charts, multivariate process capability indices, univariate and multivariate run-by-run process control and statistical profile monitoring. He currently serves as an Associate Editor for The Statistical Papers. He was an Associate Editor for The American Statistician in the past. He has also served in the past as the President of the Northwest Ohio Chapter of the American Statistical Association, and the Chair of the Toledo Section of the American Society for Quality.

Ali Asgari holds MSc degree in Industrial Engineering from Shahed University in Iran. He has published some papers in the area of statistical process control in journals such as International Journal of Advanced Manufacturing Technology and Scientia Iranica. His research interests are including statistical process control and multistage processes.