Six Sigma Tools










Six Sigma

Six Sigma Overview

The Six Sigma model is a highly disciplined approach that helps companies focus on developing and delivering near-perfect products and services. It is based on the statistical work of Joseph Juran, a pioneer of quality management who became revered in Japan.
The word "Sigma" is a Greek letter used for a statistical term that measures how far a given process deviates from perfection (standard deviation). The higher the sigma number, the closer to perfection. One sigma is not very good, six sigma means only 3.4 defects per million.
The central idea behind Six Sigma is that if you can measure how many "defects" you have in a process, you can systematically figure out how to eliminate them and get as close to "zero defects" as possible.

Six Sigma History

‘Invented’ in 1986 in Motorola by Bill Smith
Saved Motorola from going out of business
500% growth in sales in 10 years
Savings of $14bn

Taken up by Allied Signal/Honeywell in early 90’s (Larry Bossidy)

Saving $600m per year
6% productivity increase
Profit margin increased to 13%

Taken up by GE in 1995 & publicised by Jack Welch

$750m savings in 3 years
Operating margins increased from 10 to 15%

Six Sigma Statistics

Shown below are the failure rates (defects per million opportunities, or DPMO) for various sigma levels

Sigma level DPMO Sigma (with 1.5σ shift) DPMO Percent defective Percentage yield Short-term Cpk Long-term Cpk
1 317,300 -0.5 691,462 69% 31% 0.33 –0.17
2 45,500 0.5 308,538 31% 69% 0.67 0.17
3 2,700 1.5 66,807 6.7% 93.3% 1.00 0.5
4 63 2.5 6,210 0.62% 99.38% 1.33 0.83
5 0.57 3.5 233 0.023% 99.977% 1.67 1.17
6 0.002 4.5 3.4 0.00034% 99.99966% 2.00 1.5

Note that the failure rate for 'true' 6 sigma is 0.002 ppm. The commonly used headline figure of 3.4 ppm failures arises because a 1.5 sigma mean shift was introduced to take account of process drift over time in typical manufacturing processes, e.g. due to tool wear.

Six Sigma Doctrine

Six Sigma doctrine asserts that:

bulletContinuous efforts to achieve stable and predictable process results (i.e., reduce process variation) are of vital importance to business success.
bulletManufacturing and business processes have characteristics that can be measured, analyzed, controlled and improved.
bulletAchieving sustained quality improvement requires commitment from the entire organization, particularly from top-level management.

Features that set Six Sigma apart from previous quality improvement initiatives include:

bulletA clear focus on achieving measurable and quantifiable financial returns from any Six Sigma project.
bulletAn increased emphasis on strong and passionate management leadership and support.
bulletA clear commitment to making decisions on the basis of verifiable data and statistical methods, rather than assumptions and guesswork. i.e. Evidence based decisions. Often this is accomplished by setting up a hypothesis as to the cause of the problem and the solution and testing that hypothesis to see if it is true. (Statistical hypothesis testing.)

Six Sigma Process

The Six Sigma process follows 5 steps, called DMAIC


Define the system, the voice of the customer and their requirements, and the project goals.


Measure key aspects of the current process and collect relevant data.


Analyze the data to investigate and verify cause-and-effect relationships. Determine what the relationships are, and attempt to ensure that all factors have been considered. Seek out root cause of the defect under investigation.


Improve or optimize the current process based upon data analysis using techniques such as design of experiments, poka yoke or mistake proofing, and standard work to create a new, future state process. Set up pilot runs to establish process capability.


Control the future state process to ensure that any deviations from the target are corrected before they result in defects. Implement control systems such as statistical process control, production boards, visual workplaces, and continuously monitor the process.

Six Sigma Tools

A comprehensive set of tools is available for use in Six Sigma projects. For more information, click here.

Six Sigma Commentary

Typically focussed on Manufacturing Processes

Typically expressed as Defects per ‘Opportunity’ (DPO), rather than overall defects

This means defects per process, or per tolerance etc. Each ‘opportunity’ is a different way something can go wrong, or be out of specification. However, overall defects depend on DPO and number of opportunities

If have 3.4 DPMO (6s on an ‘Opportunity’ basis), but each unit has 1000 opportunities for failure, the customer sees a failure rate of 3400ppm. Is this really a 6s product and company or only a 4s company?

It is characterised by a  hierarchy of qualifications from Yellow Belt to Master Black Belt and this has engendered a huge industry in training and consultancy.

Over time the Six Sigma term has been hijacked by management consultants and applied to almost anything, to the point of becoming meaningless.

Also there has been a coming together with Lean philosophy, resulting in the hybrid Lean Six Sigma, which takes the best elements of both approaches and combines them into one. See Lean Six Sigma.



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