New adaptive CUSUM charts for process mean

Abstract

In this article, we develop an unbiased estimator of the mean shift, and then use it to enhance the sensitivity of the existing adaptive CUSUM (ACUSUM) chart. Moreover, a new ACUSUM chart is proposed using the structure of the Crosier CUSUM chart and the new mean shift estimator. A comprehensive zero-state run length comparison is conducted between the proposed and existing ACUSUM charts in terms of the average run length measures, which shows that the former uniformly outperform the latter. A real dataset is also used to explain the implementation of existing and proposed ACUSUM charts.

Keywords:

• Adaptive CUSUM
• Average run length
• Control chart
• Extra quadratic loss
• Integral relative average run length
• Monte Carlo simulation
• Process mean
• Statistical process control

Acknowledgments

The authors are thankful to the anonymous reviewer for providing useful comments that led to an improved version of the article.