The effect of parameters estimation on the performance of variables control charts under repetitive sampling

Abstract

The repetitive sampling scheme is utilized in control charts to enhance their detection ability in process shifts. Their performance is usually evaluated under the assumption that the process parameters are known. In this article, we investigate the performance of the $\overline{X}$ and S² charts under repetitive sampling when the process parameters are estimated from a preliminary in-control (Phase I) sample. We also present the exact expressions of the average run-length (ARL), standard deviation of run-length (SDRL) and average sample number (ASN) measures. A numerical analysis demonstrates that the effect of parameters estimation is significant when the Phase I sample and the sample size are small.

Keywords:

• Average run-length
• average sample number
• control chart
• parameter estimation
• repetitive sampling

Acknowledgements

The authors would like to thank the Editor and the referees for their useful comments which resulted in improving the quality of this article.