An efficient multivariate control charting mechanism based on SPRT

Abstract

This article devises a feasible multivariate Sequential Probability Ratio Test chart (MSPRT chart) to monitor the mean of the multivariate normal distribution. To reduce the time required by the MSPRT chart to detect shifts of a wide range, the charting parameters are optimised to minimise the Average Extra Quadratic Loss (AEQL). The comparative study reveals that the MSPRT chart can improve the performance of the typical Hotelling’s T² chart and the multivariate synthetic (Msynthetic) chart. It also shows that the MSPRT chart outperforms the multivariate Exponentially Weighted Moving Average (MEWMA) chart for moderate and large shifts but the latter prevails in detecting small shifts. For ease of use, we also provide two design tables for the quality engineers to adopt the MSPRT and Hotelling’s T² charts more conveniently. Finally, we used an example concerning the white wine production process to demonstrate the application of the proposed scheme.

Keywords:

• sequential probability ratio test
• hotelling’s T² chart
• synthetic chart
• MEWMA chart
• statistical process control

Acknowledgements

We would like to thank the editor, associate editor and the anonymous referees for their constructive comments and suggestions that have considerably improved the article. Nan Chen is partially supported by Singapore AcRF Tier 1 Funding under R-266-000-078-112.