# Methods and formulas for expected overall performance in Nonnormal Capability Analysis for Multiple Variables

## PPM < LSL for expected "overall" performance

The expected number of parts per million that have measurements less than the lower specification limit is calculated as follows:

PPM < LSL = 1,000,000 * F(LSL)

### Notation

TermDescription
F(X)The cumulative distribution function (CDF) of the distribution used in the analysis based on estimated or specified parameters
PPMParts per million
LSLLower specification limit

## PPM > USL for expected "overall" performance

The expected number of parts per million that have measurements greater than the upper specification limit is calculated as follows:

PPM > USL = 1,000,000 * (1 – F(USL))

### Notation

TermDescription
F(X)The cumulative distribution function (CDF) of the distribution used in the analysis based on estimated or specified parameters
PPMParts per million
USLUpper specification limit

## PPM Total for expected "overall" performance

The expected number of parts per million that are outside of the specification limits is calculated as follows:

PPM Total (Exp. Overall) = PPM < LSL (Exp. Overall) + PPM > USL(Exp. Overall)

PPM Total (Exp. Overall) = [1,000,000 * F(LSL)]+ [1,000,000 * (1 – F(USL))]

### Notation

TermDescription
F(X)The cumulative distribution function (CDF) of the distribution used in the analysis based on estimated or specified parameters
LSLLower specification limit
USLUpper specification limit
PPMParts per million