Resources

Interpretation of CuSum charts

On a CuSum chart, significant changes in the QC results compared to the target value are indicated by changes in the gradient of the plot. A CuSum chart cannot therefore be interpreted using warning and action limits as in the case of Shewhart charts. Instead, a mechanism is required to make it possible to detect significant changes in the gradient. Typically, changes in gradient are monitored using a V-mask. An example of a V-mask is shown in the figure below.

V-mask for the interpretation of CuSum charts

The mask is usually made of transparent material so that it can be placed of the points on the chart. To test whether QC results remain in control, the mask is placed on the chart with the cross placed over each point in turn (the horizontal line in the centre of the mask is always kept parallel to the x-axis). If all of the preceding points fall within the arms of the ‘V’ the results are consider to be in control. If one or more of the preceding results fall outside of the V, this indicates a significant change in the gradient of the plot and therefore a significant deviation from the target value.

The ability to detect changes in the gradient that represent a significant change in the QC results will obviously depend on the dimensions of the V-mask; specifically the distance, d, and the angle Θ. Unfortunately, selecting these values is not as straightforward as calculating the 2s and 3s values for the warning and action limits on a Shewhart chart. The aim is to be able to spot quickly when the measurement method has gone out of control but to avoid too many ‘false alarms’. The dimensions of the mask are often chosen by trial and error or by examining historical QC data. A common starting point is to use d = 2 x-axis units and Θ = 22^o. Once the chart has been in use for a while, the dimensions can be fine-tuned if required.

CuSum chart with V-mask for the determination of cholesterol in milk fat

(Click here for a pdf version of the chart)

The figure above was constructed using the data used to construct the Shewhart and moving average charts. The CuSum was calculated using a target value of 269.3 mg/100 g. The standard deviation (used to calculate the warning and action limits on the Shewhart charts shown elsewhere in this section) was 1.7 mg/100 g. Each division on the y-axis is equivalent to 2σ = 3.4. The figure above illustrates how a V-mask can be used to determine when the measurement results deviate significantly from the target value. When the V-mask is placed over the CuSum value for run 16, all the preceding values fall within the arms of the V. This indicates that the measurement system is under control. However, when the mask is used at point 29, some of the preceding values fall outside of the V. This indicates a significant change in the gradient of the plot and therefore a change in the mean of the QC results compared to the target value. The CuSum plot confirms the problem identified using the moving average chart.