parent nodes: Anderson Darling normality test | Cp Cpk % out of tolerance | Distribution fitting | non parametric | t-test | What to do with not normally distributed Data


Normal Distribution

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The normal distribution is a widely used probability density function to describe data. The distribution is defined by two parameters formula (Mean) and formula (STDEV). The curve is also called bell curve due to it shape. This distribution is widely used in statistics because data is often normally distributed.

Influence of the Mean
the
Red
curve has a higher mean
Influence of the STDEV
The
Red
curve has a bigger STDEV

The formula probably density function of the normal distribution is:
formula

Central limit theorem

The sum of a large amount of independent distributions results in a approximately normally distributed data. Even if the independent distribution are not normally distributed. Below are 5 uniform distributions combined and after every extra data-set that is added the result of the Anderson Darling normality calculation is higher (0.00, 0.06, 0.18, 0.29).

Due to the Central limit theorem many data is normally distributed because the data is affected by many different factors.


Data file

Sigma level

A sigma level of 1 is one time the STDEV.
Two sided table
Cpk Sigma level % out of tolerance PPM out of tolerance
0.33 1.0 31.73 317310.508
0.50 1.5 13.36 133614.403
0.67 2.0 4.55 45500.264
0.83 2.5 1.24 12419.331
1.00 3.0 0.27 2699.796
1.17 3.5 0.05 465.258
1.33 4.0 0.01 63.342
1.50 4.5 0.001 6.795
1.67 5.0 0.0001 0.573
1.83 5.5 0.000004 0.038
2.00 6.0 0.0000002 0.002


Example

Sigma level of 2 => 100-(34.1 + 13.6 + 34.1 + 13.6) = 4.6%

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