6 Sigma - Chapter4

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© Copyright 2004, All Rights Reserved. Edutech Dimensions Pvt. Ltd.
Chapter 4: Statistic Definition of Six Sigma
Aim
The previous chapter aimed to introducerefresh concepts on process statistics. With
a clear understanding, we now venture into the statistical aspect of Six Sigma.
Learning Objectives
On completing this chapter you will be able to:
1. Define Six Sigma
2. Relate process capability to Six Sigma
3. Explain how Six Sigma covers Process Shift Concept
4. Explain the benefits of Six Sigma over three or four sigma
Introduction
We know that process outputs vary. This variation follows some pattern known as
Distribution.
Tchebyeff’s Theorem states that: “No matter what the shape of the distribution is, at
least 75 percent of the values will fall within ± 2 standard deviations from the mean
of the distribution, and at least 89 percent of the values will lie within ± 3 standard
deviations from the mean.”
For a normal distribution, the following relationships hold good:
Mean ± 1 sigma covers 68.27% of the items
Mean ± 2 sigma covers 68.45% of the items
Mean ± 3 sigma covers 99.73% of the items
Most output processes have output that follows a normal distribution as shown by
curve X in the diagram. A process that is naturally centered at O will have a natural
spread around O of plus or minus three-sigma standard deviation.
In the case of Six Sigma, this process variation is only half the width of the design
tolerances for the process, that is to say, the difference between the upper
specification limit (USL) and lower specification limit (LSL). Since, 99.9973 per cent
of the process output is contained by this natural spread, a process running at O is
highly capable of meeting the design specifications and only 0.002 defects per million
opportunities will arise since only 0.002 parts per million are outside this curve.

2. Page 2 of 2
© Copyright 2004, All Rights Reserved. Edutech Dimensions Pvt. Ltd.
Six Sigma and Process Capability
We have seen that all processes will have some variation. In a stable process, this
variation will be equal to Plus or Minus 3 Sigma from its own average.
This plus or minus 3 Sigma (six Sigma) is called Process Capability.
If process capability is less that the tolerance or expectations then the process will
produce lesser defects.
Six Sigma and Defect per million opportunities
Six Sigma brings about process improvement by reducing Defects per million
opportunities in the process.
Process Shift Concept
Regulating processes so that they always remain on target may not be feasible in the
long term. In practical scenarios the process is likely to deviate from its natural
centered position by approximately one and a half standard deviations.
Under these circumstances, one side will be 7.5 Sigma and the other side will be 4.5
Sigma.
Under Six Sigma we focus on the long-term capability, which means that we have to
account for a 1.5 Sigma shift in the process average.
Summary
• Mean ± 1 sigma covers 68.27% of the items
• Mean ± 2 sigma covers 68.45% of the items
• Mean ± 3 sigma covers 99.73% of the items
• If process is operating well; 3.4 million effects per million opportunities
• Process Capability: Variation seen in a stable process
• Process average shift in real life is 1.5 over any period of time
• The Higher the sigma level, the more accurate the process