ARTICLES
# Gauge Performance Curve

A Gauge Performance Curve is used to determine the probability of accepting or rejecting a part whose value is equal to some reference value. For example, if the lower and upper specification for bags of confectionery with a declared weight of 100g are 100g and 110g respectively, then what is the probability of the scales displayed weight of an actual 102g bag falling inside the specification limits. The displayed weight, depending on the scales error will be less or greater than 102, due to weighing error. In fact, the displayed weight, due to weighing error, may fall outside the specification limits, even though the actual weight falls within the specification limits.

To calculate the probabilities of acceptance requires an assumption that the measurement system consists predominantly of repeatability, reproducibility and bias, measured with a Gauge R&R analysis. A second assumptions is that the measurement error is normally distributed.

The assumptions do not always hold. More advanced technology, such as machine powered algorithms must be used if violation of these assumptions are significant. Fortunately, this is rarely the case.

Probability of acceptance is computed from Normal Cumulative Probabilities as follows for two double specifications.

Pa = Probability (Measured Value < UL )-Probability (Measured Value < LL)

where

LL = Lower Limit

UL = Upper Limit

Measured value is the value of a part with some reference value.

Referring to the image below, the white curve shows the probability of accepting a part at various reference (actual values).

For this example, where the lower specification limit is .6 and upper 1.0, if a part whose actual measured value is .50 then there is a 16% chance of accepting the part, even though it clearly falls below the lower specification limit. The reason is measurement error. 16% of measured values, where the true value is 0.5, will fall above the lower specification limit even though the true value is below the lower limit.

**NOTE:**

Machine powered algorithms are able to determine the effect of measurement error on process capability and reported non-conformance which some find more useful information.

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