Pareto Diagrams

Pareto Diagrams

11.1 Purpose

In most systems, quality related problems are owing to numerous factors, but the vast majority of the problems are the result of only a small subset of those factors. A Pareto diagram is used to separate the few significant factors from the trivial many. Identification of the most important sources of problems can help managers to prioritize and allocate resources.

11.2 Strengths, weaknesses, and limitations

The Pareto diagram has proven to be a very quick and easy graphical method to identify when the Pareto principle holds, and to identify the significant factor or factors at play. When used correctly, the Pareto diagram is an important tool in quality improvement efforts because of its ability to help focus attention on the area or areas where attention is warranted. Practice has shown that the Pareto principle holds in many different situations, thus the Pareto diagram can be quite useful in a large range of applications.

The most common mistake when constructing Pareto diagrams is not categorizing the data correctly. If categories are defined too broadly, then too few categories are present in the diagram. If categories are defined too narrowly, then too many categories are present. In both cases, little or nothing is learned by constructing the diagram. The process of collecting data and constructing the diagram can often lead to better definitions. At any time during the process, one can redefine the categories and then reclassify the data. If the diagrams are being constructed by hand or with software not specifically tailored to produce Pareto diagrams, a common mistake is not to rank order the categories from left to right. The resulting diagrams are misleading and not of great interest.

The greatest weakness of the Pareto diagram is the subjectivity inherent in using categorical data. In many situations, the definitions of the categories are quite subjective and the measurement process of placing observations into the correct category is subjective as well. Furthermore, like all graphical methods, the information relayed by a Pareto diagram is subject to personal interpretation.

11.3 Inputs and related ideas

Brainstorming is a useful tool when developing a list of categories to be used in a Pareto diagram. Once the Pareto diagram is drawn, it is often helpful to use cause-and-effect diagrams (Chapter 18) to study the cause-and-effect relationships associated with the significant factors. In general, the seven tools for quality improvement (Pareto diagram, cause-and-effect diagram, control chart, process flow diagram, check sheet, scatter diagram, and histogram) serve as a complimentary tool set that has been proven to be effective in improving many systems.

11.4 Concepts

In most systems, quality related problems are due to numerous factors, but the vast majority of the problems are the result of only a small subset of those factors. This phenomenon is called the Pareto principle. The concept is named after the Italian economist Alfredo Pareto who recognized that a large proportion of the wealth in Italy was in the hands of a small number of people. A Pareto diagram is used to separate the few significant factors from the trivial many. Identification of the most important sources of problems can help managers to prioritize and allocate resources.

A Pareto diagram can help to identify the important factors leading to a specific event. For example, consider a systems analyst interested in evaluating the causes of downed servers. The first step in the construction of the diagram is to collect data pertaining to past episodes of downed servers, and then categorizing the factor responsible for each event. Categories must be selected so that each observation of the downed server is in one and only one category. For example, Table 11.1 lists six factors causing a downed server and the count associated with each. Count simply refers to the number of times, or frequency, a particular factor is deemed responsible. The table also lists the percent of times a certain factor is responsible for a downed server.

A Pareto diagram is a specialized bar chart. The horizontal axis lists the categories of interest, the left-hand vertical axis represents counts, and the right-hand vertical axis represents percent. Note that the categories must be rank ordered left to right according to the count for each category. As you can see in Figure 11.1, the most common factor associated with a downed server is that the server is out of memory.

Across the top of the bars in Figure 11.1 is a line (the cum-line) identifying the cumulative count and the cumulative percentage. In our example, over 88 percent of the time a server went down the cause was an error with the server software or a lack of server memory. All of the other factors leading to a downed server resulted in less than 12 percent of the problems. Thus the Pareto principle holds and the systems analyst should focus attention on the two significant factors identified in the diagram. Note that in situations where the Pareto principle holds, the cum-line will have a very pronounced bend between the few significant factors and the trivial many. In situations where the principle does not hold, the cum-line will take on the appearance of a piece-wise arc. In all cases, the cum-line will reach 100 percent in the final category.

Selecting the appropriate number of categories to include in the diagram is critical. In general, at least five categories should be used. In cases where there are a large number of factors, the maximum number of categories actually charted is usually determined by when the cumulative percent reaches 95 percent. At this point, all the remaining categories are typically combined together in an “other” category.

In some situations it is helpful to use multiple levels of Pareto diagrams. In our example it might be helpful to produce two more diagrams, one addressed at server software problems and one addressed to the memory problems. Consider the server memory problems. The systems analyst will need to critically examine all of the 28 cases categorized as out of memory problems. A new Pareto diagram and analysis can then take place with the event of interest being memory problems and the factors being the underlying reasons for the memory shortages. It may very well be that even though there are many possible factors leading to memory errors, the vast majority of those errors can be traced to a few significant factors.

Figure 11.1  A Pareto diagram produced by Minitab for Windows.

11.5 Key terms

Count —

The number of observations in a category.

Cumulative count —

The total number of observations in all the categories up to and including the category of interest; for example, the cumulative count corresponding to the third category is the sum of the counts for categories one, two, and three.

Cumulative percent —

The combined percentages of all the categories up to and including the category of interest; the cumulative percent for the last category will always be 100 percent.

Pareto principle —

In many different situations, the majority of outcomes are the result of a few significant factors. The remainder of the outcomes is owing to a large number of less important factors. This concept is named after the Italian economist Alfredo Pareto who recognized that a large proportion of the wealth in Italy was in the hands of a small number of people.

11.6 Software

Most statistical or quality improvement software has the ability to produce Pareto diagrams. Construction of Pareto diagrams using Minitab for Windows is very easy and flexible. In SAS, use the Pareto procedure. Statistical add-ins for Excel and Lotus are available which have the capability to produce Pareto diagrams. By not including the cumulative frequency line, a simplified version of a Pareto diagram can be easily produced in spreadsheet packages by constructing a bar chart.

11.7 References

1.  Gitlow, H., Oppenheim, A., and Oppenheim, R., Quality Management: Tools and Methods for Improvement, 2nd ed., Irwin, Burr Ridge, Illinois, 1995, chap. 9.

2.  Ozeki, K. and Asaka, T., Handbook of Quality Tools: The Japanese Approach, Productivity Press, Cambridge, MA, 1990, chap. 11.