TECHNOLOGY OVERVIEW
# Extreme Value Distribution

The extreme value distribution is a two-parameter distribution where the random variable is either the maximum, or minimum of the data sets

The probability density function for the minimum is equal to 1-exp(-exp[(x-a)/b})/ Reversal of the sign of x gives the distribution for the maximum.

Where a is the location parameter and b the scale parameter, which is >0

There are many applications for the extreme value distribution. One tempting example that comes to mind is maximum and minimum daily temperatures. However, because the average temperature changes throughout the year, affecting the extremes, this would not be a good application. A better example is in the proverbial ‘nuts and bolts industry’. Extreme dimensions are critical to fitting nuts on bolts. Provided the process average is on target control charts based on the extreme distribution can be set up. Process Capability analysis can then be based on the extreme value distribution

The BIS.Net Process Performance APP uses a machine powered algorithm to obtain the parameters subject to minimizing the Anderson Darling statistic.

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