Method (AIAG MSA)
For every measurement the bias is x − reference. A straight line bias = a + b · reference is fitted by least squares. Linearity is |b| · process variation, %linearity is 100 · |b|. The average bias over all measurements is tested against zero with a t-test, and so is the bias at each reference value.
Interpreting the plot
Blue squares are the average bias per reference part. The red line is the regression and the shaded band its 95 % confidence interval. If the green zero line stays inside the band, the gauge has no significant linearity problem. Results are validated against SciPy linregress, see the validation report.
Frequently asked questions
›What is gauge linearity?
Linearity is the change of the bias over the operating range of the gauge. A gauge can read correctly at the bottom of the range and too high at the top. The slope of the regression of bias on reference value measures it.
›How many parts and measurements are needed?
AIAG MSA recommends at least 5 reference parts covering the operating range, each measured at least 10 times (12 is common) by one operator.
›When is linearity acceptable?
If the slope is not significantly different from zero (p ≥ 0.05) and the zero line lies inside the confidence band over the whole range, linearity is acceptable. If the bias at single reference values is significant, the gauge needs recalibration at those points.
›What do I enter as process variation?
Six times the process standard deviation, or the tolerance if the gauge is used for inspection. It is only used to express linearity and bias as a percentage.