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- Index
Z-Score
Measure of how close the process average is to the specification relative to the variation. For a single specification limit its formula is:
where USL is the upper specification limit, LSL is the lower specification limit, m is the average and s is the standard deviation. In the 1-sided spec case the Z-Score is 3 times Cpk. Z-score is independent of the units of measure.
Assuming the normal distribution, the Z-score can be used to calculate the defect rate as follows:
where F[x] is the cumulative normal distribution function.
For two specification limits, the Z-score is calculated in order to maintain the same relationship between the Z-score and defect rate shown above. Its formula is:
where 
is the inverse of the cumulative normal distribution function.
The Z-score is closely related to the sigma level.