Statistical interference

When two probability distributions overlap, statistical interference exists. Knowledge of the distributions can be used to determine the likelihood that one parameter exceeds another, and by how much. When two probability distributions overlap, statistical interference exists. Knowledge of the distributions can be used to determine the likelihood that one parameter exceeds another, and by how much. This technique can be used for dimensioning of mechanical parts, determining when an applied load exceeds the strength of a structure, and in many other situations. This type of analysis can also be used to estimate the probability of failure or the frequency of failure. Mechanical parts are usually designed to fit precisely together. For example, if a shaft is designed to have a 'sliding fit' in a hole, the shaft must be a little smaller than the hole. (Traditional tolerances may suggest that all dimensions fall within those intended tolerances. 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. With two such normal distributions, a distribution of interference can be calculated. The derived distribution will also be normal, and its average will be equal to the difference between the means of the two base distributions. The variance of the derived distribution will be the sum of the variances of the two base distributions.