A Single EWMA Chart for Monitoring Process Mean and Process Variance

Abstract

Traditionally, an X¯ -chart is used for detecting an assignable cause that shifts the process mean, and the joint X¯ and R chart is used for detecting assignable cause(s) that shift the process mean and/or the process variability. However, these charts are not sensitive in detecting small changes in process parameters. An alternative to these charts is the exponentially weighted moving average (EWMA) control chart which is quite effective in detecting small changes in process parameters. However, for simultaneous monitoring of the process mean and the process variance, two EWMA charts are generally used. One is used for the process mean and the other for the process variance. This is obviously time consuming. In this paper, we propose a single EWMA control chart for monitoring the mean and variance of a process. The proposed chart is based on only one statistic and is more effective than the joint X¯ and R chart in detecting assignable cause(s). It is an extension to the chart studied by Chen et al. [2]. It is shown also that the proposed EWMA chart performs better than the combination of the EWMA X -chart and the EWMA ln(S²) -chart, except the case when the assignable cause promotes small shifts in the process mean without changing the process variability.

Key Words:

• ARL
• control chart
• EWMA
• process monitoring

Additional information

Notes on contributors

A. F. B. Costa

Antonio F. B. Costa is a Professor in the Department of Production at UNESP-Säo Paulo State University, Brazil. He was a Postdoctoral Fellow in the Center for Quality and Productivity Improvement at University of Wisconsin, Madison, USA. His current research interest is in statistical quality control. He received the Best Paper Award from IIE Transactions. He is a Certified Quality Engineer of the American Society for Quality.

M. A. Rahim

M. Abdur Rahim is a Professor of Quantitative Methods, and Faculty of Business Administration, University of New Brunswick, Fredericton, Canada. His research interests are quality control, inventory control, production, and operations management. He has edited two books and published over sixty refereed journal articles and five book chapters. He is an Associate Editor of the International Journal of Systems Science, Regional Editor of Economic Quality Control, and editorial board member of the International Journal of Production Research, Engineering Optimization, Journal of Quality in Maintenance Engineering and Quality Engineering. He is a senior member of ASQC and IIE.