# Which Six Sigma Metric Should I Use?

by Frank Rudisill and Steve Druley

This article was featured in January 2016’s Best Of Back to Basics edition.

Since its inception at Motorola in the early 1980s, Six Sigma has helped large and small companies solve problems, improve processes, delight customers and increase profits. Its define, measure, analyze, improve and control (DMAIC) approach is accepted as an industry standard in the United States, and many foreign companies are also adopting it.

Six Sigma uses several common quality metrics to emphasize the consistency of products, services and their associated processes:

• Defects per million opportunities (DPMO): (1,000,000 x number of defects)/(number of units x number of opportunities per unit).1
• Cpk: distance from the process average to the nearest specification limit/3, where represents the process standard deviation.2
• Cost of poor quality (COPQ): a percentage of sales; poor quality costs are those associated with rework, scrap, solutions, prevention and appraisal.3
• Sigma level: number of standard deviations, , from the process average to the nearest specification.4

These metrics are well understood by quality practitioners, but many in the Six Sigma arena are confused by them. For this reason, RBX Industries created a nomograph (see Figure 1) to help it apply the Six Sigma tools with a directional purpose.

The nomograph has been useful in explaining the relationship among these commonly used performance indexes. The lower horizontal axis represents the sigma levels from zero to six. The left vertical axis portrays Cpk values from zero to two. The upper horizontal axis indicates the expected DPMO, and the right vertical axis shows the typical industry standard values for the COPQ.5

The diagonal line indicates the graphic equivalency of these metrics. For example, a sigma level of three equals a Cpk of one, which equals a DPMO of 66,811, which equals an estimated COPQ of 30%. The line contains several reference points that help users better understand these relationships and provide a common perspective for evaluation. If known, metric values for an individual company, its industry, suppliers, customers and competitors can easily be added for comparative purposes.

A nomograph is an effective way to introduce and explain these metrics to all levels of an organization, from operations to upper management. It facilitates understanding and interpretation of these basic quality metrics and moves the focus away from arguing for or against a particular measurement system. It is simple to create using spreadsheet software or by hand. At RBX, we enlarged our nomograph to a 24 by 36 inch poster and placed it in strategic locations throughout the building.

This nomograph has allowed RBX to enhance communication regarding Six Sigma objectives, improve the prioritization of projects and set more realistic goals.

REFERENCES

1. Peter Pande, Robert Neuman and Roland Cavanagh, The Six Sigma Way, McGraw-Hill, 2000, p. 396.

2. D.R. Boothe, Measuring Process Capability, McGraw-Hill, 1997, p. 219.

3. Pande, The Six Sigma Way, see reference 1.

4. Forrest W. Breyfogle III, Implementing Six Sigma, Wiley, 2003, p. 1090.

5. Mikel J. Harry and Richard Schroeder, Six Sigma, Doubleday, 2000, p. 17, and experiential data from RBX Industries.

FRANK RUDISILL is an associate professor of management at the University of South Carolina, Spartanburg. He earned a doctorate in management science from Clemson University and is a member of ASQ.

STEPHEN DRULEY is the corporate director of quality at RBX Industries Inc. in Roanoke, VA. He is a Master Black Belt with 38 years of industrial experience in quality management.