Statistical interference

When two probability distributions overlap, statistical interference exists.

This technique can be used for geometric dimensioning of mechanical parts, determining when an applied load exceeds the strength of a structure, and in many other situations.

A process capability study of actual production, however, may reveal normal distributions with long tails.)

Both the shaft and hole sizes will usually form normal distributions with some average (arithmetic mean) and standard deviation.

This derived distribution can be used to determine how often the difference in dimensions will be less than zero (i.e., the shaft cannot fit in the hole), how often the difference will be less than the required sliding gap (the shaft fits, but too tightly), and how often the difference will be greater than the maximum acceptable gap (the shaft fits, but not tightly enough).