Methods and formulas for overall capability measures in Normal Capability Sixpack

Pp

Notation

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

Ppk

Cpm

Cpm is available only when a target is specified. Minitab calculates Cpm based on known values of LSL, USL, and T.

Known value Cpm
LSL and USL only *
LSL, USL, and T = m
LSL, USL, and T ≠ m
USL and T only
LSL and T only
Either LSL or USL only *

Notation

TermDescription
*Missing value
USLUpper specification limit
LSLLower specification limit
mMidpoint between USL and LSL
TTarget value
Xijjth observation in the ith subgroup
niNumber of observations in the ith subgroup
TolerMultiplier of the sigma tolerance (Minitab uses 6 as the default value)

PPM Total for expected overall performance

The expected number of parts per million that are outside of the specification limits, based on the overall variation of the process, 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
Overall standard deviation

Z.LSL, Z.USL, and Z.Bench for overall capability

Benchmark Z statistics for overall 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
Overall standard deviation
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