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

## 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

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 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

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 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

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