Methods and formulas for overall capability measures in Nonnormal Capability Analysis for Multiple Variables

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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 Z-Score method (default) or the ISO method, depending on the settings that are selected in File > 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).

Z-Score method

Notation

Term	Description
Zlsl	Φ^–1(p₁)
Zusl	Φ^–1(p₂)
Φ^–1(p)	p * 100^th percentile of a standard normal distribution
p₁	Prob (X ≤ LSL)
p₂	Prob (X ≤ USL)
X	X follows the distribution used in the analysis

ISO method

Notation

Term	Description
USL	Upper specification limit
LSL	Lower specification limit
X_0.99865	The 99.865^th percentile for the specified distribution
X_0.00135	The 0.135^th 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 Z-Score method (default) or the ISO method, depending on the settings that are selected in File > 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).

Z-Score method

Notation

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

ISO method

Notation

Term	Description
LSL	Lower specification limit
X_0.5	The 50^th percentile for the specified distribution
X_0.00135	The 0.135^th 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 Z-Score method (default) or the ISO method, depending on the settings that are selected in File > 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).

Z-Score method

Notation

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

ISO method

Notation

Term	Description
USL	Upper specification limit
X_0.5	The 50^th percentile for the specified distribution
X_0.99865	The 99.865^th percentile for the specified distribution

Ppk