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

摘要

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 (S_x,S_y) 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 theX 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 S_x to S_y, or from S_y to S_z, or yet, from S_z to S_x. The VC5 chart is not only operationally simpler than the bivariate |S| and trivariate VMAX charts but also signals faster even with less measurements per sample.