Methods and formulas for within capability measures in Normal Capability Sixpack

Cp

Notation

TermDescription
USLUpper specification limit
LSLLower specification limit
TolerMultiplier of the sigma tolerance (Minitab uses 6 as the default value)
Within-subgroup standard deviation

Cpk

PPM Total for expected "within" performance

The expected number of parts per million that are outside the specification limits, based on the variation within the 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
Within-subgroup standard deviation

Z.LSL, Z.USL, and Z.Bench for potential (within) capability

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

where:

Notation

TermDescription
Φ (X) Cumulative distribution function (CDF) of a standard normal distribution
Φ-1 (X)Inverse CDF of a standard normal distribution
Within-subgroup standard deviation
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