Group runs revised m-of-k runs rule control chart

Runs rules are commonly used to increase the sensitivity of the Shewhart chart, for detecting small and moderate mean shifts. This paper presents a group runs (GR) revised m-of-k (R - m/k) runs rule chart for the mean. The proposed GR R - m/k runs rule chart has superior zero-state and steady-state performances to the basic GR, synthetic and R - m/k runs rule charts, for detecting small and moderate shifts, while maintaining the same efficiency toward large shifts. For zero-state case, the proposed chart can be designed to outperform the exponentially weighted moving average (EWMA) chart, except for small shifts. However, the EWMA chart prevails for steady-state case.