The PARETO Procedure

Overview: PARETO Procedure

The PARETO procedure creates Pareto charts, which display the relative frequencies of quality-related problems in a process or operation. The frequencies are represented by bars that are ordered in decreasing magnitude. Thus, you can use a Pareto chart to decide which subset of problems you should solve first or which problem areas deserve the most attention.

Pareto charts provide a tool for visualizing the Pareto principle,[26] which states that a small subset of problems tend to occur much more frequently than the remaining problems. In Japanese industry, the Pareto chart is one of the "seven basic QC tools" that are heavily used by workers and engineers. Ishikawa (1976) discusses how to construct and interpret a Pareto chart. Examples of Pareto charts are also given by Kume (1985) and Wadsworth, Stephens, and Godfrey (1986).

You can use the PARETO procedure to do the following:

  • construct Pareto charts from unsorted raw data (for example, a set of quality problems that have not been classified into categories) or from a set of distinct categories and corresponding frequencies

  • construct Pareto charts that are based on the percentage of occurrence of each problem, the frequency (number of occurrences), or a weighted frequency (such as frequency that is weighted by the cost of each problem)

  • add a curve that indicates the cumulative percentage across categories

  • construct side-by-side Pareto charts or stacked Pareto charts

  • construct comparative Pareto charts, which enable you to compare the Pareto frequencies across the levels of one or two classification variables. For example, you can compare the frequencies of problems that occur on three different machines for five consecutive days.

  • highlight the "vital few" and the "useful many"[27] categories by using different colors for bars that correspond to the n most frequently occurring categories or the m least frequently occurring categories.

  • restrict the number of categories that are displayed to the n most frequently occurring categories

  • create charts whose bars are oriented vertically or horizontally

  • highlight special categories by using different colors for specific bars

  • display sample sizes and other statistics on Pareto charts

  • label the bars with their frequency values

  • create charts as ODS Graphics output or as traditional graphics

  • annotate traditional graphics charts

  • save traditional graphics output in a graphics catalog for subsequent replay

  • save information that is associated with the categories (such as the frequencies) in an output data set

  • create variations on traditional Pareto charts, as described by Wilkinson (2006)

A Pareto chart has three axes, whose display depends on whether the Pareto chart is a traditional vertical Pareto or a horizontal bar chart. A horizontal bar chart that is produced by the PARETO procedure is essentially a vertical Pareto chart that is rotated 90 degrees clockwise. Table 15.1 shows how the three axes are displayed on the two types of Pareto charts.

Table 15.1: Pareto Chart Axes

 

Displayed on a Vertical

Displayed on a Horizontal

Axis

Pareto Chart

Pareto Chart

Category axis

Horizontally at the bottom of the chart

Vertically at the left side of the chart

Frequency axis

On the left (also called the primary vertical axis)

At the top of the chart (also called the primary horizontal axis)

Cumulative percentage axis

On the right (also called the secondary vertical axis)

At the bottom of the chart (also called the secondary horizontal axis)



[26] Both the chart and the principle are named after Vilfredo Pareto (1848–1923), an Italian economist and sociologist. His first work, Cours d’Économie Politique (1895–1897), applied what is now termed the Pareto distribution to the study of income size.

[27] Juran originally referred to these categories as the "trivial many"; however, because all problems merit attention, the term "useful many" is preferred (Burr 1990).