Standardized U Statistic

The U Statistic, used in U Charts, can be standardized for use in Short Run Processes as follows:

where n is the sample size, and u-barr is a constant, based on prior data or a desired value.

When based on prior data, u-barr may be calculated as:

Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).