Bias & linearity calculator
Enter your reference standards and the repeated readings at each one to get the bias at every level, the AIAG linearity slope and percent linearity, and a plain verdict on whether your gage reads consistently across its range. Uses the AIAG MSA bias and linearity method. Everything runs in your browser.
Study setup
Adds the percent of range at each point and the absolute AIAG linearity value. Enter your tolerance width instead if you prefer to judge against the spec.
Measurements
One reference value per row, then the repeated readings taken at that reference. Tab through the grid; results update live.
Paste your data from Excel or a spreadsheet directly into the grid, or import a CSV with the downloadable template. Use the arrow keys or Enter to move between cells.
Result
Method: AIAG MSA 4th ed. bias and linearity. Linearity fits the individual biases against the reference value by least squares; %Linearity = 100 × |slope| and Linearity = |slope| × process variation. Slope significance is a two-sided t-test at α = 0.05 (df = N − 2).
Bias and linearity, in plain terms
What bias and linearity tell you
Gage R&R asks whether your measurements are repeatable and reproducible. Bias and linearity ask a different question: are they correct, and are they correct across the whole range? You take a few reference standards whose true value you know, measure each one several times, and look at the error. Bias is the average error at one reference level. Linearity is whether that error stays put as you move from the low end of the range to the high end. A gage can be perfectly repeatable and still read high at the bottom and low at the top, and only a linearity study exposes that.
Bias, point by point
At each reference level the bias is simply the mean of the repeated readings minus the reference value. Positive means the gage reads high there, negative means it reads low. To make the number comparable across instruments you scale it: AIAG divides the bias by the 6σ process variation to get a percent, and many teams divide by the tolerance width instead to see it against the spec. This tool shows the mean, the bias, and, when you enter a range, the percent of range at every point you measured.
Linearity across the range
Linearity fits a straight line through the individual biases plotted against the reference value, using ordinary least squares. The slope is the heart of it: a flat line (slope near zero) means the bias does not change across the range, while a tilted line means the error grows or shrinks as the value climbs. AIAG turns the slope into two figures. Percent linearity is100 × |slope|, which needs no other input at all. The absolute linearity value is |slope| × process variation, which is why the tool asks for your 6σ process variation before it reports it. The intercept, the bias the line predicts at a reference of zero, comes along for free.
The method and its limit
The verdict here is the transparent one: a two-sided t-test of the slope atα = 0.05 with df = N − 2. If the slope is statistically significant, the bias really does change across the range and the gage has a linearity problem worth correcting. If it is not, the bias is steady within the noise of your data. AIAG has a fuller graphical acceptance too, that the zero-bias line stays inside the confidence band of the fitted line across the whole range. That check leans on how you model your process, so it stays your call rather than a number this tool invents. References: AIAGMeasurement Systems Analysis (MSA), 4th edition.
Common questions
What is an MSA bias and linearity study?
A bias and linearity study checks whether a gage reads the true value correctly and whether that error stays the same across its range. You measure several reference standards of known value, several times each, then compare. Bias is how far the average reading sits from the reference at one level. Linearity is how much that bias changes as you move across the range. Both come from AIAG Measurement Systems Analysis (MSA), 4th edition.
How is bias calculated?
At each reference level, bias is the average of the repeated readings minus the reference value. A positive bias means the gage reads high, a negative bias means it reads low. To put it in context you divide by the process variation (6 sigma) or the tolerance width to get a percentage: percent of range = 100 times the absolute bias divided by that range. This tool reports the average, the bias, and the percentage at every reference point you enter.
How is linearity calculated?
Linearity fits a straight line to the individual biases (each reading minus its reference) plotted against the reference value, using ordinary least squares. The slope of that line is the key number: a slope near zero means the bias is steady across the range, while a steep slope means the error grows or shrinks as the value changes. AIAG expresses it two ways: percent linearity = 100 times the absolute slope, and linearity = the absolute slope times the process variation. This tool reports the slope, intercept, R-squared, and both linearity figures.
What counts as a good linearity result?
The cleanest sign of good linearity is a slope that is not statistically significant: the bias does not change meaningfully across the range. This tool runs a two-sided t-test of the slope at alpha = 0.05 and tells you whether the slope is significant. AIAG also has a fuller graphical check, that the zero-bias line stays inside the confidence band of the fitted line across the whole range. That fuller check depends on how you model your process, so it stays your call. Either way, a statistically significant slope is a signal to investigate or apply a linearity correction.
How many reference points and readings do I need?
AIAG suggests choosing at least 5 reference parts that span the normal operating range, and measuring each one several times (often around 10). This tool accepts 3 to 5 reference levels with 2 to 6 readings each, which is enough to see the trend. You need at least 3 total readings across 2 or more distinct reference values for the regression to run. More points spread across a wider range give a more trustworthy slope.
Do I enter a tolerance or the process variation?
Either works, and it is optional. AIAG expresses bias and linearity as a percentage of the 6 sigma process variation, so entering your process variation gives you the AIAG percentages and the absolute linearity value. If you would rather judge against the specification, enter the tolerance width instead. Without it, the tool still gives you the raw bias at each point and percent linearity, which is just the absolute slope as a percentage and needs no range at all.
This calculator applies the AIAG MSA bias and linearity method to the readings you enter and reports the per-point bias, the regression slope and intercept, percent linearity, and a slope-significance verdict. It does not run AIAG's fuller confidence-band acceptance (that depends on your process model), does not replace the AIAG Measurement Systems Analysis manual, and is not your quality system. Treat the result as a working estimate and validate it against your documented MSA procedure before acting on it.
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