This article studies the designs of the control charts with the supplementary
runs rules (zone rules). It also investigates, compares and ranks 15 resultant control charts based on steady-state
Average Run
Length (
ARL) that is evaluated by computer simulation. The in-control ARL
0 values of the charts are made equal to the users' specified value. Numerous insights and new findings have been discovered, including: (1) The optimization technique can considerably improve the performance of the control charts with
runs rules; (2) Some combinations of
runs rules that exclude the basic Shewhart
chart have excellent performance, especially when sample size is small; (3) The relative effectiveness (ranking) of the charts is significantly influenced by the sample size and the required in-control ARL
0, and incorporating the
chart with
runs rules is effective only when the sample size is small; (4) The steady-state ARL of the charts with
runs rules differs from the conventional zero-state ARL to some degree. Finally, the proposed design algorithm and the results of some studies provide the quality practitioners with a systematic approach to design the control charts with
runs rules and to predict their performance in a production setting.