The S chart with variable charting statistic to control bi and trivariate processes

- Monitoring one variable per time is better than monitoring all of them all the time.
- Univariate S chart with the VCS policy performs better than the |S| chart.
- Univariate S chart with the VCS policy performs better than the VMAX chart.
- Monitoring one variable per time does not require the knowledge of the correlations.

In this article, we propose the S chart with variable charting statistic to control the covariance matrix as an alternative to the use of the bivariate |S| chart and the trivariate VMAX chart. As usual, samples are regularly taken from the process, but only one of the two quality characteristics, X or Y, is measured and only one of the two statistics (Sx,Sy) is computed. The statistic in use and the position of the current sample point on the chart define the statistic for the next sample. If the current point is the standard deviation of the X values and it is in the central region (warning region), then the statistic for the next sample will be the standard deviation of the Y values (X values). If the current point is the standard deviation of the Y values and it is in the central region (warning region), then the statistic for the next sample will be the standard deviation of the X values (Y values). For the trivariate case, when the sample point falls in the central region, the charting statistic for the next sample changes from Sx to Sy, or from Sy to Sz, or yet, from Sz to Sx. The VCS chart is not only operationally simpler than the bivariate |S| and trivariate VMAX charts but also signals faster even with less measurements per sample.