On Statistical Design of the S² Control Chart

ABSTRACT

The usual S ² chart is constructed with equal false alarm probabilities for the lower and upper control limits. An alternative is the ARL-unbiased S ² chart, where the ARL (average run length) curve attains its maximum when the common-cause variance is at its in-control value. We examine the ARL properties of these S ² charts, and show that neither the usual S ² chart nor the ARL-unbiased S ² chart is optimal in a natural sense. We propose two criteria, under which optimal S ² charts can be constructed. The effects of parameter estimation on our designs are also discussed, and suggestions are made regarding practical implementation.

Key Words:

• ARL-unbiased
• Average run length
• S ² chart
• ShewhartS chart

Mathematics Subject Classification:

• 62P30

Acknowledgments

The authors thank the referee for the suggestions for improving the presentation. The first author thanks Dr. Jinhong You for his assistance in software; his research is supported by a Massey University Postdoctoral Fellowship.