Gage Linearity and Bias Study Calculator

Use this calculator to evaluate whether a measurement system has a consistent systematic error across its operating range. A bias study compares measurements with known reference values. A linearity study determines whether that bias changes as the reference value increases or decreases.

How to calculate gage linearity and bias

1. Measure several reference parts repeatedly. The parts should cover the measurement system's intended operating range.
2. Enter one row per measurement with columns for the measured value, part identifier, and known master or reference value.
3. Select Linearity and bias study, then assign the Measurement, Part, and Master columns in the calculator above.
4. Optionally enter a process variation greater than zero to express linearity and bias as percentages, then review the regression, bias table, and chart.

What are gage bias and linearity?

Bias is the difference between an observed measurement and its accepted reference value. Positive bias means the gage reads high; negative bias means it reads low. The calculator reports the average bias overall and for each reference value, together with p-values for testing whether the bias differs from zero.

Linearity describes how bias changes across the measurement range. The calculator fits a regression with bias as the response and the reference value as the predictor. A slope near zero indicates that the bias is relatively consistent across the range. A meaningful nonzero slope indicates that the measurement error depends on the size of the measured value.

Required data for a linearity and bias study

Use reference parts whose accepted values are known from a suitable standard or a more accurate measurement method. Include multiple distinct reference values and repeated measurements for each part. Each part must have exactly one reference value in the data. The references should span the range in which the measurement system will be used.

How to interpret the results

First inspect the bias at each reference value and the overall average bias. Then inspect the regression slope and its p-value to determine whether bias changes systematically across the range. The bias chart helps reveal trends, isolated reference levels, and variation among repeated measurements. Statistical significance alone does not determine whether an error matters in practice; also compare its magnitude with process variation, engineering requirements, and the intended use of the measurement system.

Linearity and bias evaluate measurement accuracy across a range. They do not replace a Gage R&R study, which separates repeatability, reproducibility, and part-to-part variation.