Methods and formulas for expected between/within performance in Between/Within Capability Analysis

PPM < LSL for expected "between/within" performance

The expected number of parts per million less than the lower specification limit, based on the variation between/within subgroups, is

Notation

TermDescription
PPMParts per million
LSLLower specification limit
Φ (X) Cumulative distribution function (CDF ) of a standard normal distribution
Average of the observations
Between/within subgroup standard deviation

PPM > USL for expected "between/within" performance

The expected number of parts per million that are greater than the upper specification limit, based on the variation between/within subgroups, is

Notation

TermDescription
PPMParts per million
USLUpper specification limit
Φ (X) Cumulative distribution function (CDF ) of a standard normal distribution
Average of the observations
Between/within subgroup standard deviation

PPM Total for expected "between/within" performance

The expected number of parts per million that are outside of the specification limits, based on the variation between/within subgroups, is

Notation

TermDescription
PPMParts per million
LSLLower specification limit
USLUpper specification limit
Φ (X) Cumulative distribution function (CDF) of a standard normal distribution
Average of the observations
Between/within subgroup standard deviation
By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy