The natural tolerance in manufacturing systems is defined as 6*σ* where *σ* is the standard deviation of the observed data.

Being 6 times of standard deviation would mean that natural tolerance includes 99.73% of observed variability in dimensions. Take a look at the graph below.

Each band has a width of 1 standard deviation. The nominal dimension lies at the crest of the wave, and the parts touching the horizontal lines would be the max and min allowable dimensions.

Imagining a specification of 20±0.5mm, the crest would be at 20mm and the parts touching the horizontal lines would be at 20.5mm and 19.5mm.

And with *σ* being the standard deviation, 6*σ* would include most (99.73%) of the variability.

This variability is called Natural Tolerance.

**Where is Natural Tolerance used?**

Natural tolerance is used in the statistical analysis of dimensional variability. Most notably in C_{pk} calculations. They form a very important part of Process Capability Analysis and have direct impact on part quality.

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