Multivariate control charts for mean vector and covariance matrix with supplementary runs rules

Abstract

The Shewhart control chart developed to statistically control the production process is not implemented in the actual process. It is simple and has the advantage of effectively detecting large shifts. But it is not effective in small shifts. To compensate for this, there are many several methods. In 1956, Western Electric Company presented a control chart with runs-rules added. In this paper, to compensate for the shortcomings of traditional Shewhart charts, we propose a chart for monitoring the mean vector and covariance matrix using runs rules proposed by Western Electric Company. In the run length distribution of the control chart to which the finite Markov chain embedding method and run rule were applied, it was confirmed that the mean of the run length rapidly decreased even with a small shift of the mean vector and covariance matrix. It is sensitive to small shifts. Therefore, it can be seen that the Shewhart control chart using runs rules in the production process is effective in detecting small fluctuations.