# Linearity

Linearity is the difference in the bias values through the expected operating range of the gauge.

Linearity can be determined by choosing parts throughout the operating range of the measurement instrument. The bias of each one of those chosen parts is determined by the difference between the reference value and the observed average measurement. The slope of the regression line that best fits the bias average versus reference values multiplied by the process variation (or tolerance) of the parts is an index that can represent the linearity of the gauge. To convert gauge linearity to a percentage of process variation (or tolerance), multiply by 100 and divide by the process variation (or tolerance).

As in the bias study, the reference values of the parts can be determined with tool room or layout inspection equipment. Appraiser measures the parts chosen throughout the operating range and the observed average for each part is determined. The difference between the reference value and the observed average is the bias; this is determined for each part chosen. The linearity graph is plotted between biases and reference values throughout the operating range. If the graph shows that a straight line could represent the plotted points, then a best fit linear regression line between biases and reference values represents the linearity between those two parameters. The goodness of fit (R2) of the linear regression line will determine whether the biases and reference values have a good linear relationship. Linearity and percent linearity of the system are calculated from the slope of the regression line and the process variation (or tolerance) of the parts. If the regression line has a good linear fit, then the magnitude of the linearity and percent linearity can be evaluated to determine whether linearity is acceptable. If the regression line does not have a good linear fit, then it is possible that the bias has a nonlinear relationship. This requires further analysis to judge whether the measurement system’s linearity is acceptable.

Study to find Linearity is divided into three parts - Linearity Mapping, Linearity Measurement and Linearity Data Analysis.