Designing of Run Rules t control charts for monitoring changes in the process mean

In the literature, the Shewhart t control chart has already been investigated and used to detect shifts in a process; anyway, it has a poor statistical sensitivity in the detection of small or moderate process shifts. In this work, new Phase II Run Rules t control charts are proposed, and their parameters are determined. A Markov chain methodology is used to evaluate the statistical performance of these charts. We provide an extensive numerical analysis consisting of several tables and figures to discuss the statistical performance of the proposed charts for several scenarios. The obtained results show that the proposed control charts are more sensitive to process shifts than Shewhart t control chart and robust against errors in errors in estimating the process standard deviation or changing standard deviation. Finally, an illustrative example from the food industry is provided for illustration.