Management And Accounting Web

What is Six Sigma?

Provided by James R. Martin, Ph.D., CMA
Professor Emeritus, University of South Florida

Quality Related Main Page | SPC Main Page

Citation: Martin, J. R. Not dated. What is Six Sigma? Management And Accounting Web.

Six Sigma is a continuous improvement methodology developed at Motorola that is designed to systematically reduce defects recognizing two important relationships.1

1. The overall yield of a group of related processes is much lower than the yields of the individual processes. For example, if the individual yields at each of a set of dependent processes is .99, the overall yield for 100 processes or operations would be .99100 = .366.

2. The total cost of a product or service is directly related to the defect rate, i.e., Total cost = (Unit cost)(1+ defect rate).

The six sigma level is where the performance at each function, process, or operation is nearly perfect, generating a defect rate of .000034% or only 3.4 defects per million. For comparison, a three sigma level of performance generates 66,807 defects per million as indicated in the table below.

Sigma* Defects per million Long term yield %
3 66,807 93.32
4 6,21 99.379
5 233 99.9767
6 3.4 99.999966
*A sigma is a statistical unit of measure referred to as the standard deviation.

Areas Under the Normal Curve

Steps in the Six Sigma Methodology

The six sigma methodology includes the following five steps.

1. Define the business.

This step includes defining customer requirements, business goals and objectives, team roles and responsibilities, scope and resources, processes, and performance baselines.

For example, Noritaki Kano's quality analysis is useful in defining the customer's requirements. Kano's approach separates customer requirements into three categories:
Assumed requirements - a given feature or function such as wheels on a automobile.
Specified requirements - the customer's explicitly stated requirements.
Expected requirements - the customer's unstated, but real expectations.

These requirements establish how good work and defective work are defined. Other techniques used in this step include: project charter, stakeholder commitment analysis, affinity diagrams, voice of the customer, force field analysis, Pareto analysis, process mapping, and SIPOC (suppliers, inputs, process, outputs, customers).

2. Measure the processes.

Measure defects per unit, defects per million opportunities and the yield percentage. For example,

Defects per unit = Total number of defects ÷ Total number of units inspected

A unit is the output of a process, e.g., an invoice in accounts payable, a subassembly in an assembly area, a package in a packing department. All defects are counted, not just the number of defective units since a unit may include several defects.

3. Analyze the process to determine the root cause.

Pareto charts or diagrams are used in this step to identify critical factors that have the greatest influence on performance, recognizing that most problems are created by a few causes (Referred to as the 80/20 rule). The analyze step continues with cause and effect, or fishbone diagrams to identify potential causes of problems. Other techniques used in this step include multivary analysis and failure mode and effects analysis. The illustrations below are from MAAW's Textbook Chapter 8.

Pareto Diagram

Fishbone Diagram

4. Improve the process.
This step includes use of two techniques, Design of Experiments and change management.

Design of experiments involves statistically designed experiments where multiple measurements are made of two or more variables are that vary simultaneously. This allows the interactions between many variables to be included in the experiment. After the experiment is designed, data are collected and analyzed with statistical software

5. Control.

Control tools include control charts, precontrol charts, and run charts. The charts below are from MAAW's Textbook Chapter 3. This step includes transforming and maintaining an organizational culture that embraces change and improvement.

X-Bar Control Chart

R Control Chart

Six Sigma DMAIC Roadmap

A somewhat different and more detailed list of steps and tools is provided in the tables below. These tables were adapted from the article "Six Sigma DMAIC Roadmap" found on the Six Sigma web site.

Steps Tools
Define customers and requirements. Project charter
Develop problem statement, goals and benefits. Process flowchart
Identify champion, process owner and team. SIPOC diagram
Define resources. Stakeholder analysis
Evaluate key organizational support. DMAIC work breakdown ...
Develop project plan and milestones. CTQ definitions
Develop high level process map. Voice of the customer ...

Steps Tools
Define defect, opportunity, unit and metrics. Process flowchart
Detailed process map of appropriate areas. Data collection plan/example
Develop data collection plan. Benchmarking
Validate the measurement system. Measurement system analysis
Collect the data. Voice of the customer ...
Begin developing Y=f(x) relationship. Process sigma calculation
Determine process capability & sigma baseline.  

Steps Tools
Define performance objectives. Histogram
Identify value/non-value added process steps. Pareto chart
Identify sources of variation. Time series/run chart
Determine root cause or causes. Scatter plot
Determine vital few x's, Y=f(x) relationship. Regression analysis
Cause and effect/fishbone diagram
5 whys
Process map review and ...
Statistical analysis
Hypothesis testing
Non-normal data analysis

Steps Tools
Perform design of experiments. Brainstorming
Develop potential solutions. Mistake proofing
Define operating tolerances of potential system. Design of experiments
Assess failure modes of potential solutions. Pugh matrix
Validate potential improvement by pilot studies. House of quality
Correct/re-evaluate potential solution. Failure modes and effects ...
Simulation software

Steps Tools
Define and validate monitoring and control system. Process sigma calculation
Develop standards and procedures. Control charts
Implement statistical process control. Cost savings calculations
Determine process capability. Control plan
Develop transfer plan, handoff to process owner.  
Verify benefits, cost savings/avoidance, profit growth.  
Close project, finalize documentation.  
Communicate to business, celebrate.  

For more on six sigma and General Electric's experience using the technique, see the Lucier & Seshadri Summary.


1. Does the six sigma methodology support Juran's approach or Deming's approach to quality? The graphic below is from the constrained optimization summary.

Juran's Zero Defects Quality Model Compared to the Taguchi-Deming Robust Quality Model

Taguchi's and Deming's view is that loss occurs anywhere away form point T in the graphic below.

Taguchi Quality Loss Function

The next graphic shows the Zero Defect Goalpost approach to quality. See the Albrignt and Roth Summary for more information.

Traditional Loss Function

Comparing the Zero Defect Goal Post approach with Taguchi's and Deming's approach.

Taguchi and Deming Quality Loss Function

2. Does the answer to the question above depend on how defects and defective work are defined in the six sigma approach? Discuss.


1 Most of this summary is based on Chapter 2 of Gupta, P. 2004. Six Sigma Business Scorecard: Creating a Comprehensive Corporate Performance Measurement System, and the Six Sigma DMAIC Roadmap from the Six Sigma web site. The graphic illustrations are from MAAW's Chapters and summaries as indicated above.

Related Chapters and summaries:

Deming, W. E. 1993. The New Economics for Industry For Industry, Government & Education. Cambridge: Massachusetts Institute of Technology Center for Advanced Engineering Study. (Deming discusses the concept of variation in several chapters, particularly 8 and 10. (Summary).

Holmes, D. S. and R. E. Hurley. 2003. How SPC enhances budgeting and standard costing - Another look. Management Accounting Quarterly (Fall): 57-62. (Summary).

Lucier, G. T. and S. Seshadri. 2001. GE takes six sigma beyond the bottom line. Strategic Finance (May): 40-46. (Summary).

Martin, J. R. Not dated. Chapter 3: Cost Behavior Analysis & Statistical Process Control - Part II. Management Accounting: Concepts, Techniques & Controversial Issues. Management And Accounting Web.

Martin, J. R. Not dated. Chapter 8: Just-In-Time, Theory of Constraints, and Activity Based Management Concepts and Techniques. Management Accounting: Concepts, Techniques & Controversial Issues. Management And Accounting Web.

Martin, J. R. 1998. Expanding the perspective of performance analysis to include the concepts of SPC, ABCM and REA database systems. Advances in Accounting Education (1): 25-41. (Summary).

Nolan T. W. and L. P. Provost. 1990. Understanding variation. Quality Progress (May): 70-78. (Summary).

Reeve, J. M., and J. W. Philpot. 1988. Applications of statistical process control for financial management. Journal of Cost Management (Fall): 33-40. (Summary).

Reeve, J. M. 1989. The impact of variation on operating system performance. Proceedings of the Third Annual Management Accounting Symposium. Sarasota: American Accounting Association: 75-89. (Summary).

Roehm, H. A., L. Weinstein, and J. F. Castellano. 2000. Management control systems: How SPC enhances budgeting and standard costing. Management Accounting Quarterly (Fall): 34-40. (Summary).

Roth, H. P. and T. L. Albright. 1994. What are the costs of variability? Management Accounting (June): 51- 55. (Summary).

Walter, R., M. Higgins and H. Roth. 1990. Applications of control charts. The CPA Journal (April): 90-93, 95. (Summary).

Some additional articles Books on Six Sigma.

Friedman, M. and H. Gitlow. 2002. Six Sigma primer for CPA's. The CPA Journal (November): 56-59.

George, M. L. 2002. Lean Six Sigma: Combining Six Sigma Quality with Lean Production Speed. McGraw-Hill Trade.

George, M. L. 2003. Lean Six Sigma for Service: How to Use Lean Speed and Six Sigma Quality to Improve Services and Transactions. McGraw-Hill.

George, M. L., D. Rowlands and B. Kastle. 2003. What is Lean Six Sigma. McGraw-Hill.

Gillett, J., R. Fink and N. Bevington. 2010. How Caterpillar uses 6 sigma to execute strategy. Strategic Finance (April): 24-28.

Gupta, P. 2004. Six Sigma Business Scorecard: Creating a Comprehensive Corporate Performance Measurement System. McGraw-Hill.

Hammer, M. 2002. Process management and the future of six sigma. MIT Sloan Management Review (Winter): 26-32.

Hindo, B. and B. Grow. 2007. Six Sigma: So yesterday?: In an innovation economy, it's no longer a cure-all. Business Week (June 11): 11.

Jones, K. T. and C. C. Chen. 2010. The pervasive success of 6 sigma at Caterpillar. Strategic Finance (April): 29-33.

Juras, P. E., D. R. Martin and G. R. Aldhizer III. 2007. Adapting six sigma to help tame the SOX 404 compliance beast. Strategic Finance (March): 36-41.

Kocakülâh, M. C., A. Norris and D. Danko. 2013. How lean and six sigma redesigned an IT department by reducing costs and increasing efficiencies. Cost Management (May/June): 39-47.

Rudisill, F. and D. Clary. 2004. The management accountant's role in six sigma. Strategic Finance (November): 34-39.