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Using the Cumulative Line

How a Pareto chart can help you keep track of the progress of your corrective efforts

by Bart P. Hamilton

The Pareto chart is usually thought of as a problem identification tool, and it is. Once used to identify the potential causes of a problem, it can also report the progress of the corrective efforts. This is where the cumulative line in the chart shows its worth.

The cumulative line is based on the total number of defects in the initial study and plotted using a scale of cumulative percentages on the right-hand side of the y-axis. As the corrective actions take place and the incidents are reduced, you can create Pareto charts based on the current status. To do so, keep the scale for comparison the same as in the initial study so any reduction in the cumulative percentage will indicate the amount of improvement made.

Example

In this study, there are eight categories of potential causes, plus a miscellaneous category. The charts measure the dollars lost in each category (see Table 1).

Figure 1 is an example of a typical Pareto chart based on the results, and it is the basis for future reports and comparisons. The results of the initial study are listed and sorted in descending order, except for the miscellaneous category, which is always on the right.

The cumulative line on the chart is a graphical representation of the contribution of each cause to the total number of defectives. The contributions cumulate from cause to cause and are plotted. The cumulative line in the initial study represents the total of all the causes. The data for status studies and reports are gathered under conditions similar to those in the initial study. Any changes should, therefore, reflect the efforts for improvement.

Figure 1 is based on Table 1. The total dollar loss numbers are found on the left-hand side of the y-axis and the cumulative percentage on the right-hand side of the y-axis. Between Figure 1 and Table 2, some time has passed and work has been performed to try to improve the process. Table 2 results from a study done under the same conditions used to collect the initial data.

For the purpose of this article, the figures are assumed. The highest dollar loss category was reduced by 50%, and the second highest dollar loss category was reduced by 25%. This represents the work accomplished (see Table 2).

The order of the categories is different in the status report (Table 2) than it is in the initial report (Table 1). This change in order makes reporting progress difficult and sometimes confusing.

The second part of the status report uses the cumulative line (see Figure 2). The chart maintains the same scale as the initial chart and uses the initial total dollars for calculating the cumulative percentage. Figure 2 shows a cumulative percentage loss of 79%. This means there has been a 21% improvement in reducing causes of dollars lost by the work performed.

Using the cumulative line in the status report chart (Figure 2) is a good way to summarize the results to inform management of the progress you have made.

BART P. HAMILTON is a retired senior manager at Uniroyal Goodrich Tire Co. in Akron, OH, and a part-time instructor at the University of Akron. He earned a master's degree in industrial management from the University of Akron. Hamilton is a certified quality engineer, certified quality manager and a Senior Member of ASQ.

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