A New Control Scheme Always Better Than X-Bar Chart

Abstract

A new control scheme is proposed by borrowing the idea of the Benjamini–Hochberg procedure for controlling the false discovery rate in multiple testing. It is shown theoretically that the proposed 2-span control scheme outperforms the Shewhart X-bar chart in terms of the average run length under any size of mean shifts. Some simulations are carried out to demonstrate that the proposed scheme having various span sizes always outperforms the X-bar chart in terms of the average run lengths.

Keywords:

• Average run length
• Mean shift
• Multiple testing
• P-value
• Quality control

Mathematics Subject Classification:

• Primary 90B99
• Secondary 62F03

Acknowledgments

This work was supported by Korean Science and Engineering Foundation through National Core Research Center for Systems Bio-Dynamics at POSTECH.