Design of Hotelling T2 control chart using various covariance structures

Hafiza Nida, Muhammad Kashif, Muhammad Imran Khan, Liaquat Ahmad and Muhammad Aslam

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 16, 5828-5839

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.

Date: 2024
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DOI: 10.1080/03610926.2023.2234520

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