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
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