Designs of control charts with supplementary runs rules

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 ARL0 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 X¯ 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 ARL0, and incorporating the X¯ 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.