Six Sigma Process

According to ISO (International Standards Organization), a process is defined as "a set of interrelated activities that transforms inputs into outputs".

Process could be manufacturing, designing, offering services etc.

And in any process variation is inevitable.

Lesser the variation - better the process would be.

Any step towards process improvement should be welcomed.

Six Sigma (6σ) is a set of techniques and tools for continuous improvement.

As statistical methods are used, it is of interest to us here.

The concept of Six Sigma was first introduced at Motorola in the 1980s and deployed as business strategy at General Electric in the 1990s.

The main advantages of implementing 6σ process are:

it minimizes the variations in a process
it identifies and eliminates the causes of defects
it improves the quality of output/product

Why is it called 6σ ?

You know that σ represents standard deviation.

And that in a normal distribution, 99.7% of the data is within the limits "mean ± 3σ".

But 99.7% is not good enough!

In a world at "Three Sigma" (3σ)

105 false arrests would be made by police every hour
964 flights would be cancelled every day
5,390 newborns would be accidentally dropped each year
47,283 long distance telephone calls would be disconnected in one hour

Would the above be acceptable to any one ?

Let us consider the process of manufacturing a product.

A product has specifications with tolerances.

Ex :

Resistor value : 100Ω ± 5%.

Sol:

So the upper specification limit (USL) is 105Ω and the lower specification limit (LSL) is 95Ω.

Now consider the mean (μ) as 100Ω and 'σ' as the S.D. of the process.

If the difference between the mean and the nearest specification limit (95 or 105 in this case) is six standard deviations (6σ),

then 99.99966% of resistors produced will meet the specification.

This translates to only 3.4 defective parts per million (ppm) resistors produced.

So, the standard deviation of the resistor manufacturing process should be

(105 – 100) ≥ 6σ

⇒ σ ≤ 0.83

(If σ = 1, then it is only a "5σ process" since (105 – 100)/1 = 5)