Statistical design of variable sample size and sampling interval (X)over-bar control charts with run rules

In this paper, improved Shewhart control charts based on hybrid adaptive and run rule schemes are introduced to enhance the statistical performances of the traditional static scheme, designed with consideration given to the fixed values of sample size, the width of the control limits and the sampling frequency. The proposed hybrid adaptive schemes consider both variable sampling interval and variable sample size combined with run rules. The objective of this research is to develop a statistical comparison between adaptive schemes, charts with run rules and hybrid adaptive schemes with run rules to help decision-makers in the selection of the best performing chart for an expected value of shift in the mean of a controlled parameter. An extensive set of numerical results is presented to test the effectiveness of the proposed models in detecting small and moderate shifts in the process mean. The optimal statistical designs of the charts are obtained through a heuristic algorithm, properly modified to cope with the problem.