A Novel Group Runs Control Chart for Monitoring Simple Linear Profiles Using Modified Hotelling’s T2 Statistic

Profile monitoring is an important area of statistical process monitoring, particularly when the quality of a process is characterised by the relationship between a response variable and one or more explanatory variables. Although synthetic control charts have been developed for monitoring linear profiles, there is scope for improving their ability to detect shifts in process parameters. This paper proposes a novel Group Runs (GR) control chart based on the modified Hotelling’s (T2) statistic for Phase II monitoring of simple linear profiles. The proposed chart integrates the modified (T2) statistic with the Group Runs monitoring scheme to enhance the detection of changes in the parameters of a simple linear profile. The performance of the proposed GR-modified (T2) control chart is evaluated and compared with that of the existing synthetic-modified (T2) control chart under different shift scenarios. The comparative results, assessed in terms of average run length (ARL), demonstrate that the proposed Group Runs chart performs better than the synthetic-modified (T2) chart in detecting small shifts in simple linear profiles. It is also observed that the existing synthetic modified (T2) control chart is better than the proposed GR modified (T2) control chart in detecting larger shifts. The proposed scheme therefore provides an effective alternative for Phase II profile monitoring and contributes to the development of more sensitive control charting techniques for statistical process control.