A Study on the Performance of Matrix Control Charts Based on the Normal Distribution

With the explosive growth of data, matrix data has become increasingly common in fields such as genetic engineering, remote sensing satellites, and environmental and atmospheric sciences. Monitoring matrix data has also become increasingly important. Control charts are important tools in the study of statistical process control. Traditional research assumes that the monitored data follows a univariate normal distribution or a vector-valued normal distribution. Matrix sequences can explain the correlations between different row and column variables simultaneously. However, research on the monitoring of such sequences is very limited. In this article, based on the matrix normal distribution, we propose three new matrix control charts. We study the changes in the average run length of three control charts when a matrix normal process shifts. In the application of control charts, the true parameters are rarely known explicitly and are usually obtained through parameter estimation methods. Therefore, estimation errors are inevitable. This article further investigates the effect of parameter estimation errors on control charts. The application of the model and control charts is demonstrated in the example section.