The Effect of Estimated Parameters on Poisson EWMA Control Charts

Abstract

Performance of control charts is generally evaluated with the assumption that the process parameters are known. In many control chart applications, however, the process parameters are rarely known and their estimates from an in-control reference sample are used instead. In such cases, the moments of the run length distribution depend on the values of the estimated parameters. The Poisson exponentially weighted moving average (EWMA) is an effective control chart in situations where the number of nonconformities per unit from a repetitive production process is monitored. The objective of this paper is to study the effect of estimating the mean on the performance of the Poisson EWMA control chart. We make use of the Markov Chain approach. Sample-size recommendations and some concluding comments are provided.

Key Words:

• Attributes control chart
• exponentially weighted moving average
• Markov chain
• Poisson distribution
• statistical process control

Additional information

Notes on contributors

Murat Caner Testik

Murat Caner Testik is an Associate Professor and Chair of the Department of Industrial Engineering at Hacettepe University, Ankara, Turkey. His research interests include statistical quality control and data mining for quality improvement. He is the co-author of two book chapters and several publications in the engineering and statistical literature.

B.D. McCullough

B. D. McCullough is a Professor of Decision Sciences at Drexel University. His research focuses on the accuracy of statistical software, the reproducibility of published research, and data mining. His publications have appeared in the economics and statistics literatures.

Connie M. Borrar

Connie Borror is an Associate Professor in the Department of Mathematical Sciences and Applied Computing. Her research areas include response surface methodology, statistical process control, and experimental design with applications in engineering and other sciences. She is the co-author of several journal articles, two books, and three book chapters.