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

Hamed Sabahno; Marie Eriksson

doi:10.1038/s41598-024-59549-8

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

Sci Rep. 2024 Apr 23;14(1):9288. doi: 10.1038/s41598-024-59549-8.

Authors

Hamed Sabahno¹, Marie Eriksson²

Affiliations

¹ Department of Statistics, Umeå School of Business, Economics and Statistics, Umeå University, Umeå, Sweden. hamed.sabahno@umu.se.
² Department of Statistics, Umeå School of Business, Economics and Statistics, Umeå University, Umeå, Sweden.

Abstract

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.

Keywords: Healthcare; Max-type control charts; Memory-type control charts; Monte Carlo simulation; Multivariate multiple linear regression profiles; Profile monitoring; SS-type control charts; VP adaptive control charts.