SC QUALITY GUILDLinearity study
SCQUALITYGUILD.COM/CALCULATORS/LINEARITY-STUDY.HTML
Certified references across the operating range. %EV at each and pooled against the tightest tolerance, then whether bias stays constant end to end.
%EV AT EACH REFERENCE · POOLED · LINEARITY ACROSS THE RANGE · FREE · NOTHING YOU TYPE LEAVES YOUR BROWSER
Q-BotClick for an explanation of this calculator.Linearity study
%EV AT EACH REFERENCE · POOLED · LINEARITY ACROSS THE RANGEOne appraiser, several certified references spread across the operating range, repeated readings on each. The result to read is %EV — how much of the part tolerance the gauge’s own scatter consumes, at each reference and pooled across the range. The linearity test below asks a second question: whether the bias stays the same from one end of the range to the other.
One row per reference. Specification limits are per reference because each block stands for a different product band; leave them blank and the %EV columns read “n/a”. Blank readings are ignored.
k decides how much of the gauge’s scatter is charged against the tolerance, and the two values are conventions rather than choices: 6.00 covers 99.73 percent and is the MSA 4th edition default, 5.15 covers 99 percent and appears in older customer agreements. Switching knocks about fourteen percent off every %EV figure, so state which you used.
Repeatability at each reference
Linearity across the range
Linearity plot
Band check
For educational use. This page is a study aid. The method behind it has far more depth and detail than one page and one tool can cover, and what you see here is not everything the method offers or everything this site offers. For full understanding and application, use the governing standards and texts, and seek further education, training or qualified advice. Results depend on the data you enter, so check them before relying on them.
Bias at one point is not accuracy
A bias study takes one reference, measures it repeatedly, and reports how far off the average sits. A linearity study asks a harder question: does that bias stay the same across the whole range the gauge is used over?
Often it does not. Bias drifts with size — because of how the instrument was calibrated, wear in a screw, a probe that deflects more on a larger part, a fixture that is not square. The gauge is accurate where somebody checked it and steadily less accurate away from that point.
A gauge that passes at the midpoint and fails at both ends
| Certified reference | Bias | As % of tolerance |
|---|---|---|
| 2.00 | −0.012 | 12.0% |
| 4.00 | −0.005 | 5.0% |
| 6.00 | +0.001 | 1.0% |
| 8.00 | +0.008 | 8.0% |
| 10.00 | +0.017 | 17.0% |
The fitted slope is +0.00355 of bias per unit of reference, and the bias swings 0.029 across the range — twenty-nine percent of the whole tolerance, purely as a function of where in the range you happen to be working.
A single-point check at 6.00 would have reported a bias of 0.001 and passed without comment. That is the entire argument for doing linearity rather than bias alone.
A linear bias is the good case. When bias drifts smoothly with size you can at least see it, model it and often correct it. A study that comes back scattered — bias jumping about with no pattern — is usually telling you something worse: the measurement is not repeatable enough for the question to even be meaningful, and gauge R&R is the study you needed first.
Reading the result
- Slope near zero, small scatter. Bias is constant across the range. A single correction handles it, and a single-point verification is genuinely adequate.
- Clear slope. The gauge reads progressively high or low with size. Recalibrate across the range rather than at one point, and check what the instrument is doing mechanically.
- No slope but wide scatter at each point. Repeatability is the problem, not linearity. Stop here and run a gauge R&R.
Where linearity studies go wrong
- References that do not span the working range. Five standards clustered near the middle cannot detect end-of-range drift, which is where it lives.
- Standards no better than the gauge. The references need to be meaningfully more accurate than the instrument under test, and traceable. Otherwise you are comparing two unknowns.
- One reading per reference. Without repeats you cannot separate bias from noise, and the slope you fit may be entirely imaginary.
- The operator knows the reference value. If the study is not blind, the numbers have a way of landing where everybody expects them to.