Cumulative sum (Cusum) control chart:

Cumulative sum (Cusum) control chart:

1. Analyze the control material on at least 20 different days, and calculate the mean and SD of those results.
2. Label y-axis cusum. Draw a horizontal line at the midpoint of the y-axis to represent a cusum of zero. Set the range of values above and below to be about 10 times the standard deviation. Label x-axis in terms of time, using day, run number, control observation number or whatever is appropriate.
3.  Introduce control specimens into each analytical run and record the value obtained.
4. Calculate the difference between the value and the expected mean. Obtain the cusum by adding this difference to the cumulative sum of the previous differences. Plot the cusum on the control chart and inspect the plot.I
5. Interpret the charted data by evaluating the slope of the cusum line. A steep slope suggests that a systematic error is present and that the run is out of control.

(Source: Tietz textbook of clinical chemistry, 4th edition)

In figure 19-16, when control values scatter on both sides of the mean, giving both positive and negative differences, the cusum will alternate in sign, and plotted values will wander back and forth across zero line on the control chart. When control values fall mostly on one side of the mean so that most of the differences have same sign, the cusum value increases in magnitude and plotted values will move away form zero line of the control chart. 

The approach to judge the control status in cusum is based on slope of the cusum line. In industry, this is done by constructive templates having a V-shaped section removed from a rectangular sheet of clear plastic. This V-shaped cutout establishes the angle that is the control limit and gives the technique its name of V-mask cusum. The apex of V-mask is positioned on the control chart at a specified distance in front of recently plotted cusum. If all the plotted values are contained within the angle of the V-mask, the method is in control. If any of the plotted values fall outside the angle of V-mask, the method is out of control. 

Sometimes this process is aided by use of special graph paper having an underlying pattern of 45⁰ angles (  <  <  <  ) across the chart. When using this special graph paper, the convention has been to scale the graph so that a change of 2s on the y-axis is the same distance between two points on the x-axis. The 45⁰ angle then represents the slope expected when the observed mean is approximately 2s from the expected mean.