Improved shewhart-type control charts based on weak runs in multistate trials

In this work we introduce two new classes of Shewhart-type control charts with supplementary runs rules using a three or four region partition of the observed characteristic's range. The study of the control charts' characteristics (run length distribution, average run length) is carried over by considering an extension of the concept of r-weak runs (which was recently introduced for sequences of binary trials) under a multistate framework. Our numerical experimentation provides useful hints for the implementation of the new control charts by a practitioner and reveals that the proposed charts significantly improve the detection power (as compared to other existing charts) especially for small shifts in the process mean.