Variable parameters memory-type control charts for simultaneous monitoring of the mean and variability of multivariate multiple linear regression profiles

Variable parameters (VP) schemes are the most effective adaptive schemes in increasing control charts' sensitivity to detect small to moderate shift sizes. In this paper, we develop four VP adaptive memory-type control charts to monitor multivariate multiple linear regression profiles. All the proposed control charts are single-chart (single-statistic) control charts, two use a Max operator and two use an SS (squared sum) operator to create the final statistic. Moreover, two of the charts monitor the regression parameters, and the other two monitor the residuals. After developing the VP control charts, we developed a computer algorithm with which the charts' time-to-signal and run-length-based performances can be measured. Then, we perform extensive numerical analysis and simulation studies to evaluate the charts’ performance and the result shows significant improvements by using  the VP schemes. Finally, we use real data from the national quality register for stroke care in Sweden, Riksstroke, to illustrate how the proposed control charts can be implemented in practice.