## Wednesday, June 4, 2014

Those who have studied a course in statistics are familiar with a histogram or frequency distribution. In statistical process control or SPC, the Pareto chart is a frequency distribution or histogram of attribute data arranged by categories. For example, suppose we consider defects on an submarine used in a naval application. We can plot the total frequency of occurrence of each type of defect on the y-axis against various types of defects on the x-axis. With this type of chart a user can quickly see which types of defects occur most frequently and less frequently. The cause of the defects that occur most frequently should probably be identified and addressed first.

One must notice that the Pareto chart doesn't list the defect in order of importance, rather just in order of frequency. For example, a certain defect may only occur three percent of the time, but if it's one that could end up in scrapping the submarine. So, in some cases, the defect occurring most frequently may not be the one to take care of first. How do we determine what to take care of first? There are two methods, first you could use a weighted average to modify the frequency counts, meaning that we emphasize the defects that are more significant. You could also have a second chart to consult that lists that has a large cost exposure.

There are variations to the basic Pareto chart I discussed above. Suppose we have components on a circuit board labeled by part number and assume that we know the percentage of defective components. We could have a chart that lists the percentage of defects on the vertical axis and the component number on the horizontal axis.

Suppose we know the components come from three suppliers, A, B and C. We could have a chart with the number of defective components on the vertical axis and the component number listed by supplier on the horizontal axis. For example, suppose for component number 1 that there are 30 overall defects, 20 from supplier A, 8 from supplier B and only 2 from supplier C. The vertical bar above component 1 would extend to 20 (labeled A), from 20 to 28 (labeled B) and from 29 to 30 (labeled C). A chart of this sort quickly enables a used to see which supplier provides a disproportionally large amount of defects.

Another variation that is extremely useful is one that has two scales on the y-axis. On the left side is the number of defects and the right side is total percentage of defects. Suppose there are defects of types A, B, C and D. There are 100 defects total, 35 of which are type A, 30 are type B, 25 are type C and 10 are type D. We have a bar that extends vertically above A up to 35, a bar vertically over B up to 30 and so on. Now we place dots which match the cumulative percent on the right side. For example, 35 is 35 percent of the total defects, so place a dot above defect A which lines up with 35 on the right side. Now B is 30, but since we are doing cumulative, we add it to 35 to get 65 and place a dot that lines up with 65 above B. With C, the dot will go at 90 since (65 + 25 = 90) and the final dot goes above D at 100. Connect the dots to complete the chart.

Generally speaking, the Pareto chart is a very useful SPC problem solving tool. There are five others tools which I may discuss in future articles on statistical process control.