A parameter-free adaptive EWMA chart with variable sample sizes and variable sampling intervals for the process mean

Abstract

In this article, a parameter-free adaptive EWMA (AE) chart, which adopts the variable sample size (VSS), variable sampling interval (VSI) or both (VSSVSI) features, is developed to monitor the mean of a normal process. The simulation method is employed to compute the run-length profiles of the proposed VSS, VSI and VSSVSI based AE charts. The extra quadratic loss and integral relative average run-length/time-to-signal measures are used as a performance criterion in order to evaluate the sensitivities of the control charts. The run-length evaluation shows that the proposed VSS, VSI and VSSVSI based AE charts surpass the VSS, VSI and VSSVSI based EWMA charts, respectively, in detecting small mean shifts but the latter prevails in detecting moderate to large mean shifts. The proposed charts also outperform their fixed sampling rate based AE counterparts. An example is given to compare the implementation of the existing and proposed charts.

Keywords:

• Average run-length
• control chart
• EQL and IRARL
• Monte Carlo simulation
• process mean
• statistical process control

Mathematics subject classification:

• 62N99

Acknowledgments

The authors are thankful to the associate editor and two anonymous reviewers for providing useful comments that led to an improved version of the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).