Minding your g’s and t’s

Charting rare events effectively

Signs in factories or on the back of long-range trucking rigs sometimes proclaim “X days since our last accident” or “No on-the-job injuries since 1964.” Extending the stretch between such accidents may be motivated by this announcement alone, but there are better ways to diminish or prevent rarely-occurring events by using data analysis and process improvement tools.

Simply keeping track of tragic but rarely-occurring events may seem like an ineffective way to prevent future tragedies. In fact, however, data analysis that focuses on the intervals between such events can help to diminish their recurrence by analyzing special cause and common cause variation. It can also help to evaluate whether an improvement step that has been taken is working. A statistical approach includes the use of g-charts and t-charts, control charts that are enjoying expanded application in healthcare and crisis management organizations.

Rare-event charting was developed in response to the limitations of p-charts, which might sample 20 items week after week, for example, and continually find no defective items. T- and g-charts, on the other hand, provide information about the number of normally-occurring events between nonconforming or rarely-occurring incidents.

Recalling that control charts are meant to minimize the chance of making one of two types of mistakes when acting on a system, such charting makes sense. Reacting to single occurrences as if they are trends (over-control) or ignoring them because they occur infrequently (under-control) can both be minimized by utilizing the power of g- charts and t-charts.

A g-chart is a chart for attributes data. It is used to count the number of events between rarely-occurring errors or nonconforming incidents. In a hospital or other healthcare environment, these rare events might include patient falls, infection rates, or accidental needle-sticks. Nonconforming events might be a failed procedure, an incomplete record, or a death. While p-charts show the proportion of errors or of nonconforming events, g-charts track the count of events that occur between occurrences. For example, the number of admissions between errors in admissions processed, or the number of surgeries between surgical errors would be accurately charted on a g-chart. The “g” in “g-chart” stands for “geometric,” since data relating to events between occurrences represents a geometric distribution.

In the following pairs of charts, the first, a u-chart, shows the number of harmful medications per 1000 doses (Figure 1), and the second, a g-chart (Figure 2), indicates the number of doses between harmful administrations of medications:

Figure 1

Figure 2

A t-chart is also used for rarely-occurring events, but it analyzes time data—that is, the hours, days, weeks, or months between these events—rather than the number of intervening events between incidents, so its information may be more useful for certain kinds of incidents.

A t-chart allows each nonconformity or non-conforming unit to be evaluated, rather than having to wait to the end of a time period before the data is plotted. Some examples of non-conforming units include infections, falls, deaths, injuries, and complaints.

Figure 3 (a c-chart) and Figure 4 (a t-chart) indicate two approaches to data related to cardiac arrests. The t-chart shows changes after certain improvements have been made, giving insight into the effects of those improvements.

The t-chart identifies the two types of variation present in a system, special and common cause variation, so that appropriate improvement action can be taken. Using the t-chart to assess stability first will determine which kind of action to plan next. Once the improvement action has been sufficiently tested and then implemented, a t-chart can be used to monitor the system to assure that the improvement is sustained.

Figure 3

Figure 4

In this case, it is clear from the t-chart that there has been improvement in the process, and the steps taken for the improvement have been noted on the chart.

With the panoply of charting approaches available, one should identify the objective of the chart that is selected, asking what data will be most useful in improving this process. In the case of t-charts and g-charts, it is hoped that their approach to rarely-occurring events will help to render these events even more rare in their occurrence.

Originally published in the November 2009 edition of Quality eLine, our free monthly newletter.

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