Gauge Bias and Linearity Study Calculator
Bias against a reference with its t test and interval at every master, and a linearity regression across the operating range with slope and intercept intervals and a confidence band on the fit — because a gauge can read high at one end and low at the other and still pass a single-master bias study.
Why one master is not enough
The study this page loads on first visit is the argument. Five masters at 7, 9, 11, 13 and 15; ten readings on each. The gauge reads 0.49 high at the bottom of its range and 0.61 low at the top — both unmistakably significant — and its average bias over the whole range is −0.044, which cannot be distinguished from zero at any sample size you would run.
A bias study at a single master, especially one taken from the middle of the range, passes this gauge. Fitting bias against reference value and asking whether the slope is zero is the test that does not.
Data
Live preview — unlock to use your own data
The sample dataset below is real and the chart beside it is live: change any option and watch the limits move, then export the figure. Entering your own measurements into Bias & Linearity needs a licence — a one-time payment, no account, no subscription.
This is the sample dataset, shown in full. The chart beside it is live — change any option and watch it redraw.
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Enter data on the left to chart it
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Options
This plot has no adjustable options yet.
Your measurements are processed entirely in this browser tab. Nothing you type here is uploaded, so confidential production data stays confidential.
What is computed
Bias is reading minus reference. At each master that is a one-sample t test: bias ÷ (s/√n) on n − 1 degrees of freedom, with an interval at your chosen confidence level. The table marks a master whose interval excludes zero.
Linearity is ordinary least squares of bias on reference value across every reading, giving a slope and intercept with standard errors, t statistics and intervals, and the residual standard deviation on n − 2 degrees of freedom. The shaded band is the interval for the fitted line — narrowest at the centre of the reference range, widest at its ends — not a prediction interval for a future reading.
%Linearity does not need a process variation
Linearity = |slope| × process variation, and %Linearity = 100 × Linearity ÷ process variation. The process variation cancels, so %Linearity is exactly 100 × |slope|. That falls out of the published definitions and it is worth knowing: a reader who has been asked for "%linearity" and cannot find a denominator is hunting for something that is not needed.
%Bias does need one — it is 100 × |bias| ÷ process variation — and the denominator is supposed to come from a separate variation study of the parts, not from the repeated masters this study measures. There is no default here. Leave it empty and the tool reports the bias in measurement units and says why the percentage is missing.
Reading the two panels
The left panel is the linearity study: every reading as its bias, a heavy tick at each master’s average bias, the fitted line, and the band. Where the band clears the zero-bias rule, the bias over that part of the range is real rather than sampling noise.
The right panel is the bias study: one interval per master, so the pattern across the range is legible without reading a slope off a chart. A master drawn in the violation colour is one whose interval excludes zero.
The zero-bias line is drawn in the specification colour rather than as a control limit, because it is a statement about what the measurement system ought to do — not a limit estimated from the data.
What a non-significant slope does and does not mean
If the slope is not significantly different from zero, the tool says so — and says, in the same sentence, that this is an absence of evidence for a linearity problem at your sample size rather than evidence that the gauge is linear. With five masters and ten readings each, a slope small enough to hide is still large enough to matter on a tight tolerance.
The published procedure asks for at least five masters spanning the operating range and at least ten readings on each. Below either, the tool computes and warns: a slope fitted through three masters is dominated by wherever the two extremes happen to sit.
Common questions
- What is the difference between bias and linearity?
- Bias is the gap between the average reading and the reference value at one point. Linearity is how that gap changes across the operating range. A gauge with a large constant bias is miscalibrated and easy to correct; a gauge with a linearity problem reads differently depending on the size of the part, and no single offset fixes it.
- How many masters and how many readings?
- At least five masters spanning the range the gauge actually measures, and at least ten readings on each. Fewer of either still computes here, with a warning naming what is thin — but the slope is the whole result of a linearity study, and a slope through three points is a line through the two extremes.
- Where does the process variation come from?
- From a separate study of the parts — typically the total variation of the Gage R&R study, or 6σ of a stable process. Not from the masters measured here: they were chosen to span the range, not to represent production. Because the number changes %Bias and does not change %Linearity, the tool asks for it rather than assuming one.
- The band on the chart — is that where future readings will fall?
- No. It is the confidence interval for the fitted line, which is a statement about where the true average bias lies, not about where an individual reading will land. A prediction interval for a single future reading is several times wider. The figure says which one it is drawing, under the chart.
- Can I check the numbers?
- Yes. The validation page reproduces a published worked example on this exact dataset — the fitted line, the residual standard deviation, the t statistic, the t multiplier and a confidence interval on the fit — recomputed at render time by the same code this tool runs. It also records one printed value in a sibling article that does not reproduce, and what was checked before concluding that.
- Is my data uploaded anywhere?
- No. The whole calculation runs as JavaScript in this browser tab, and nothing on this site accepts a measurement.