Methods and formulas for overall capability measures in Nonnormal Capability Analysis

Pp

Pp is calculated using the parameter values that you specify or is estimated using maximum likelihood method for a distribution used in the analysis. Minitab calculates the Pp statistic using either the Minitab method (default) or the ISO method, depending on the settings that are selected in Tools > Options > Control Charts and Quality Tools > Capability Analysis. The following formulas are based on the default tolerance of K = 6, which is 6 standard deviations wide (3 standard deviations on each side of the process mean).

Minitab method

Notation

TermDescription
ZlslΦ–1(p1)
Zusl Φ–1(p2)
Φ–1(p)p * 100th percentile of a standard normal distribution
p1 Prob (X ≤ LSL)
p2Prob (X ≤ USL)
XX follows the distribution used in the analysis

ISO method

Notation

TermDescription
USLUpper specification limit
LSLLower specification limit
X0.99865The 99.865th percentile for the specified distribution
X0.00135The 0.135th percentile for the specified distribution

PPL

PPL is calculated using the parameter values that you specify or is estimated using maximum likelihood method for a distribution used in the analysis. Minitab calculates the PPL statistic using either the Minitab method (default) or the ISO method, depending on the settings that are selected in Tools > Options > Control Charts and Quality Tools > Capability Analysis. The following formulas are based on the default tolerance of K = 6, which is 6 standard deviations wide (3 standard deviations on each side of the process mean).

Minitab method

Notation

TermDescription
Φ–1(p)p * 100th percentile of a standard normal distribution
p1 Prob (X ≤ LSL)
XX follows the distribution used in the analysis

ISO method

Notation

TermDescription
LSLLower specification limit
X0.5The 50th percentile for the specified distribution
X0.00135The 0.135th percentile for the specified distribution

PPU

PPU is calculated using the parameter values you specify or is estimated using maximum likelihood method for a distribution used in the analysis. Minitab calculates the PPU statistic using either the Minitab method (default) or the ISO method, depending on the settings that are selected in Tools > Options > Control Charts and Quality Tools > Capability Analysis. The following formulas are based on the default tolerance of K = 6, which is 6 standard deviations wide (3 standard deviations on each side of the process mean).

Minitab method

Notation

TermDescription
Φ-1(p)p * 100th percentile of a standard normal distribution
p2 Prob (X ≤ USL)
XX follows the distribution used in the analysis

ISO method

Notation

TermDescription
USLUpper specification limit
X0.5The 50th percentile for the specified distribution
X0.99865The 99.865th percentile for the specified distribution

Ppk

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