Design of Hotelling T² control chart using various covariance structures

Abstract

The objective of this research is to evaluate different serial correlated structures in Hotelling T² and Shewhart control charts in monitoring multivariate statistical process control. For this purpose, the false alarm rate and shift detection performance were calculated by considering different autocorrelations in the presence of three covariance matrices for the errors. Both simulated data and real data are used for validating the analysis. The result of the simulation shows that the false alarm rate decreases with the increase in the magnitude of autocorrelation in all three low, moderate, and high error covariance structures. In real data, two quality variables of the production process are used. By ignoring autocorrelation in real data, it is concluded that ARL₀ shows the process in controlling on the average for nominal value. The performance of Hotelling T² in ARL₁ varies as the shift changes only in x¹ otherwise ARL₁ have small values as compared to the individual Shewhart chart by increasing shifts in both variables.

KEYWORDS:

• Hotelling T²
• principal component analysis
• average run length
• autocorrelation
• simulation

Acknowledgments

The authors are deeply thankful to the editor and reviewers for their valuable suggestions to improve the quality and presentation of the paper.