Methods and formulas for between/within capability measures in Between/Within Capability Sixpack

Cp

Notation

TermDescription
USLUpper specification limit
LSLLower specification limit
TolerMultiplier of the sigma tolerance (Minitab uses 6 as the default value)
Between/within standard deviation

Cpk

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

Z.LSL Z.USL Z.Bench - B/W

Benchmark Z statistics for between/within capability are calculated by finding the Z value using the standard normal (0,1) distribution for the corresponding statistics.

where:

Notation

TermDescription
LSLLower specification limit
USLUpper specification limit
Φ (X) Cumulative distribution function (CDF) of a standard normal distribution
Φ-1 (X)Inverse CDF of a standard normal distribution
Between/within standard deviation
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