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Cumulative Sum Charts vs. U-Type Attribute Charts

Cumulative Sum charts, or Cusum charts, are an alternative to Shewhart control charts. While Shewhart control charts are widely used and the control violations well documented, there may be conditions to which they are insensitive. This technique determines an average value for the subgroups and determines the expected variability about the mean. These charts are good at detecting distinct, steady and intermittent shifts in the process.

Cusum charts are better suited to detecting small, sustained shifts in a process. These charts measure a cumulative deviation from the mean or a target value. The chart, therefore, displays the deviation from the target instead of the rate or mean value of the subgroup size, which is what is plotted on a Shewhart chart. If the process remains in control, then the deviations will scatter around the target or average value. On the Cusum chart, this will produce a straight line or a random shift around the target with a mean of zero.

There is another significant difference in a Cusum chart, which is the accumulation of the deviations. This is what gives this technique its name. Each point on a Cusum chart is based on information from all samples, including the current sample. The plotted points represent the cumulative deviations from the target value. If the deviations from the target fluctuate in opposite directions about the target, including large fluctuations, the Cusum chart may not provide adequate indication of process problems. This is due to the fact that it is charting cumulative deviations. If the deviations are both above and below target, it will not result in an increasing or decreasing trend. Instead, it will show that the process is centering around the mean or target. However, if there is a consistent increasing or decreasing trend, the Cusum chart will be much more sensitive to this than Shewhart charts. The detection of trends holds true even with small shifts. Cusum charts are better at detecting trends in process shifts between .5 and 2 sigma. Shewhart techniques typically identify larger shifts in the process. The larger shifts are more likely to be identified by Shewhart charts regardless of whether they are sporadic or a trend.

Here is a comparison of a U-Chart and a Cusum chart for data on medication errors. In this example, medication errors are charted against total doses administered. Since multiple errors could occur during the administration of a single dose, it is appropriate to use a U-chart rather than a P-chart. A single dose could be a combination of the incorrect amount, the wrong medication, administered improperly, administered to the wrong patient, etc. Although this distinction is subtle, it is important. However, chart choice is a subject for another article. This purpose here is to illustrate the value of Cusum charts.

The U-type Cusum chart for this data is show below. The last 13 months of 24 months of medication errors are plotted. The first 5 months of this period show that there is little cumulative deviation from the target value of 0. After that period, however, there appears to be an increasing trend in medication errors. What does this look like on the U-chart?

The U-chart for the same time period shows a control violation in the 22nd month. Although the control violation would need to be investigated, there is no substantial indication of an upward trend in medication errors in this chart. With the exception of 1point, this chart describes a process that is experiencing normal variation.

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In conclusion, there may be multiple tools that should be employed to more completely characterize a process. Any chart should be used with discretion. Even in the absence of control violations, charts should be scrutinized to determine if the results are reasonable. In the U-chart example, perhaps the variability is an issue that warrants further investigation. The cumulative variability does show a trend when viewed in the Cusum context.