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Unequal Bilateral Size Tolerances

This is a topic that arises frequently.

The figure below shows two common ways to specify size tolerances.  On the left is a max/min direction, and on the right is an equal bilateral tolerance.
Picture
Parts will be produced with sizes between the Upper Spec Limit and the Lower Spec Limit.  There are two common distributions for these sizes.  The first is the Uniform Distribution as shown below.
Picture
The other common distribution is the Normal Distribution as shown below
Picture
The questions arise when the size tolerance is expressed as an unequal bilateral tolerance as shown below.
Picture
Many people believe that the unequal bilateral tolerance means that the distribution should be skewed to the large size
Picture
or skewed to the small size
Picture
However, there is no standard that specifies a skewed distribution for an unequal bilateral tolerance.   If a skewed distribution is required, the drawing should specify a skewed distribution and specify how skewed the distribution must be.

Unless a skewed distribution is clearly specified, there is no reason to assume anything other than a uniform distribution or a normal distribution.
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