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

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 (X) over bar and S-2 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.