Gauge Bias & Linearity: Accuracy Analysis Online
What Are Bias and Linearity?
Bias is the systematic difference between the measurement average and a reference value (standard or true value), reflecting measurement accuracy; linearity describes how bias behaves across the gauge's operating range. Constant bias is uniform bias; bias changing over the range signals a linearity problem. Along with repeatability and stability, they form the four MSA properties and are the core accuracy indicators in gauge calibration and MSA. Large bias means obvious systematic error and poor linearity means error grows away from the calibration points - both directly threaten measurement reliability.
Running a Type 1 Study
A Type 1 study uses one operator, one gauge and one standard part: measure the same standard part 50 times consecutively in a short period, compute the bias of the measurement mean from the reference value, and derive the capability indices Cg and Cgk from the standard deviation. Cg reflects the gauge's dispersion capability; Cgk removes the bias effect on top of Cg. Cg and Cgk should generally both be at least 1.33, and at least 1.67 in strict applications.
Evaluating Linearity
Select 5 or more reference points covering the full range, measure each repeatedly (e.g., 10 times), compute the mean bias per point, then regress bias against the reference values: a regression slope significantly different from zero indicates linearity error, and linearity% = |slope| x process range / tolerance x 100%. The tool outputs the regression equation, R-squared, slope test, linearity verdict and a bias-versus-reference scatter plot. Uncorrected linearity error makes high- or low-range measurements deviate systematically from true values, affecting tolerance decisions and capability assessments.
How to Use It
First run the Type 1 study to confirm repeatability and bias are acceptable, then run the full-range linearity study; reference values must be traceable to a higher-grade standard. When bias is significant, calibrate first (zeroing, recalibration); if bias remains large after calibration, repair or replace the gauge. The tool works online - paste the data and it outputs bias, Cg/Cgk and the linearity report, including the traceability level and measurement conditions for audit.