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# What are Pareto Diagrams

Pareto diagrams, named after the Italian economist Vilfredo Pareto (1848-1923), provide a method by which causes of a problem can be arranged by their relative importance. The diagram has as its basis the idea of the “vital few” and the “trivial many.” Very often more than half of all quality problems are the result of one cause. It is a much better tactic to locate the most important cause and eliminate it rather than attempt to eliminate all causes at once. Eliminating the one important cause will result in a dramatic quality improvement with the greatest payback and, possibly, the least amount of effort.

## Where Pareto Diagrams Can Be Used

Pareto diagrams can be used with either variable data or attribute data, but they are used most often with attribute data. Usually, the data is expressed in percentages or the number of occurrences in each category. For example, inspection data can be broken down by the number rejected due to various causes. Table 2.3.1 lists some sample inspection data. The first step in making a Pareto diagram is to identify the categories of data we wish to display. Often, we will have previously collected data to place on our diagram. If not, we will have to collect data using methods outlined in the following sections.

Next, draw a left vertical axis and label it with a scale going up to the total number rejected. See Figure 2.3.1. Draw a horizontal axis and mark off equal lengths to be labeled with each of the causes. Put the most frequent cause to the left, and the rest in descending order. If there is an “other” category, put it on the right side, even though it may not be the smallest. The “other” category can be used to group lesser causes and reduce the width of the diagram. Now draw vertical bars of equal width for each cause, each at a height that matches its frequency to the total scale.

## What Alternative Measures Do We Have

An alternative measure is to put an additional scale on the left side, which represents the cost of defectives. On the right side, draw a second vertical axis and label it with the percent defective. Finally, if desired, draw a segmented line, which represents the cumulative percentage, starting at the bottom left corner and ending at the upper right. The completed diagram will be similar to Figure 2.3.2. The segmented line simply totals each defect, but it also provides a way to quickly estimate percentages. Draw two horizontal lines to the percent scale and subtract to get the percent due to any one cause.

### Pareto Diagrams have these characteristics:

• They highlight the few most important causes. If we were to try to reduce scratches by one-half in Figure 2.3.2, it would not impact total defects as greatly as reducing plating flaws by one-half. The effort expended to reduce either flaw might be equal, but the payoff is much different. Pareto diagrams help focus on effective solutions to problems.

• They highlight the results of improvements. Diagrams drawn side by side will illustrate the overall results of quality improvements in a before/after context. Figure 2.3.3 shows the results of improving the main cause of circuits failing a power-on test.

• They use numbers, not percentages, of defects or costs of defects on the left-hand scale of the diagrams. If percentages were used, the causes in the second diagram would look larger in comparison to the first. Repetitive audits of this problem’s causes should show the main cause shifting to second or third position if attempts at improving the main cause are successful. If repetitive audits show the causes shifting their order without an overall reduction in the magnitude of the problem, then attempts to solve the problem are insufficient. A daily control system that effectively focuses on all aspects of the process should result in a reduction of all causes without much shifting of order.
• Often, personnel involved in the process will have a good idea of the major defects or problems but will lack the data to prove those ideas. Pareto diagrams provide an effective, yet simple, tool to clarify problem areas. When used with cause and effect diagrams, Pareto diagrams become an instrument for plotting the course of activity, noting progress, and gaining perspective on a problem at any point during the process.

After a cause and effect diagram is made, data must be collected to determine the relative importance of causes. The Pareto diagram can be the first useful document produced after initial data collection.