Monitoring Process Mean and Variance with a Single Generally Weighted Moving Average Chart

Abstract

Two generally weighted moving average (GWMA) charts are usually used concurrently for a simultaneous monitoring of the process mean and process variance. In this article, we propose a new GWMA chart, called the Max-GWMA chart, which uses a single statistic for a simultaneous monitoring of the process mean and variance. The statistic of the Max-GWMA chart is based on the maximum of the absolute values of two GWMA statistics, one for controlling the mean while the other the variance. We show that the Max-GWMA chart outperforms the combined GWMA chart, in terms of the average run length (ARL), standard deviation of the run length (SDRL) and diagnostic abilities performances. The combined GWMA chart consists of two GWMA charts that are run concurrently, one for monitoring the mean and the other the variance.

Keywords:

• Average run length (ARL)
• Combined GWMA chart
• Max-GWMA chart
• Process mean
• Process variance
• Single control chart
• Standard deviation of the run length (SDRL)

Mathematics Subject Classification:

• 62P30
• 62E15

Acknowledgments

This study is carried out in the School of Mathematical Sciences, Universiti Sains Malaysia (USM), and is supported by the Academic Staff Training Schemce (ASTS) of the School of Management, USM, and the Research University Grant (USM-RU-PGRS) no. 1001/PMATHS/843063.

Notes

Remark: Boldfaced entries represent ARL₁s and SDRL₁s of the Max-GWMA chart that are lower than the corresponding ones of the GWMA _YGWMA _S chart.

Remark: Boldfaced entries represent ARL₁s and SDRL₁s of the Max-GWMA chart that are lower than the corresponding ones of the GWMA _YGWMA _S chart. [19pc]