False Signal Rates for the (X) Control Charts with Runs Tests When Process Parameters Are Estimated

Abstract

This article investigates the effect of the size of the preliminary samples on the false signal rate (FSR) for the control chart with supplementary rules when the process parameters are unknown and the control limits have to be estimated. The conditional probability method is used to derive the analytical formulae for computing the FSR. Numerical results are presented and discussed. Suggestions are given to practitioners in designing and using the control chart with supplementary rules.

Keywords:

• Conditional probability
• False signal rate
• Sample size
• Supplemen-tary rules
• X¯ chart

Mathematics Subject Classification:

• 62P30

Acknowledgments

The authors thank the editor and the two referees for helpful comments on the earlier version of this article. The project is partially sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, P. R. China.