Control charts for attributes with maxima nominated samples

We develop quality control charts for attributes using the maxima nomination sampling (MNS) method and compare them with the usual control charts based on simple random sampling (SRS) method, using average run length (ARL) performance, the required sample size in detecting quality improvement, and non-existence region for control limits. We study the effect of the sample size, the set size, and nonconformity proportion on the performance of MNS control charts using ARL curve. We show that MNS control chart can be used as a better benchmark for indicating quality improvement or quality deterioration relative to its SRS counterpart. We consider MNS charts from a cost perspective. We also develop MNS attribute control charts using randomized tests. A computer program is designed to determine the optimal control limits for an MNS p-chart such that, assuming known parameter values, the absolute deviation between the ARL and a specific nominal value is minimized. We provide good approximations for the optimal MNS control limits using regression analysis. Theoretical results are augmented with numerical evaluations. These show that MNS based control charts can yield substantial improvement over the usual control charts based on SRS.