Bias and Linearity Explained
Tabla de contenidos
The exactitud side of MSA
Repeatability and reproducibilidad are precisión propiedades. They describe spread. Bias, linealidad and estabilidad are exactitud propiedades. They describe location, significado cómo close your readings sit to the true or accepted valor.
These are independent. A gauge can be extremely precise and consistently wrong, and a R&R del sistema de medición estudio will not detect it, because every operador and every repeat reading is shifted by the same amount. The estudio measures concordancia, and a uniformly shifted set of readings still agrees perfectly with itself.
Bias: the definition and the arithmetic
Bias is the difference between the average of repeated mediciones of a single pieza and that pieza's referencia valor. The referencia valor comes from a higher-order fuente: a calibrado master, a gauge block, or a medición made on a system with substantially better exactitud.
Bias
bias = x̄ − reference
The convention is to take at least 10 repeated readings of the same referencia pieza, taken by one evaluador under normal operating conditions. More readings give a more trustworthy estimate. Because sesgo is an average, a single reading tells you nothing useful about it.
Worked example
Illustrative datos. One evaluador measures a calibrado master 15 times with a micrometer.
| Quantity | Value |
|---|---|
| Reference valor of the master | 25.000 mm |
| Average of the readings (x-bar) | 25.012 mm |
| Bias (x-bar minus referencia) | +0.012 mm |
| Standard deviation of the readings (s) | 0.008 mm |
| Number of readings (n) | 15 |
Is the sesgo real, or is it noise?
Any set of readings will produce a sesgo figure that is not exactly zero, purely from random scatter. The question is whether the offset you observed is larger than the scatter can reasonably explain. That is a one-sample t-test against a sesgo of zero.
t statistic for sesgo
t = bias ÷ (s ÷ √n)
t = 0.012 ÷ (0.008 ÷ √15) = 0.012 ÷ 0.00207 = 5.81
With n = 15 there are 14 grados de libertad, and the two-sided critical t valor at 95 percent confidence is about 2.145. The calculated t of 5.81 is well beyond that, so the sesgo is statistically significant. It is not an artifact of the scatter, and the gauge is genuinely reading high by roughly 0.012 mm.
Statistical significance is not the same as practical importance. A sesgo can be statistically significant and still be trivially small next to your tolerancia, and it can be practically serious while failing the t-test simply because you took too few readings. Always compare the sesgo against the tolerancia you are trying to control, not only against its own uncertainty.
Linearity: does the sesgo change across the range?
Linearity asks whether the sesgo is the same everydónde in the gauge's operating range. You measure several referencia piezas spanning the range, calculate the sesgo at each one, and then look at cómo sesgo behaves as the referencia valor increases. A gauge might read accurately at 10 mm and read high by 0.02 mm at 100 mm.
Linearity as a regression of sesgo on referencia valor
bias = a + b × (reference value)
Fit a least-squares line through the sesgo valors plotted against the referencia valors. Three outputs matter.
| Term | What it tells you |
|---|---|
| b (pendiente) | How much the sesgo changes per unit of measured size. A pendiente that is statistically different from zero means a linealidad problem: the error depends on qué you are medir. |
| a (intercepto) | The fitted sesgo at a referencia valor of zero. Useful for characterizing the offset, but often outside the range you actually measure, so treat it as a model parameter rather than a physical claim. |
| R² | How much of the variación in sesgo the straight line explains. A high valor means sesgo changes predictably with size; a low valor means the sesgo is erratic rather than trending, which is a different and usually harder problem. |
A gauge with good linealidad has a pendiente near zero and small sesgo at every referencia point. A gauge with a significant pendiente can often be corrected, because the error is predictable. A gauge with erratic, non-trending sesgo usually cannot be corrected by adjustment and needs repair or replacement.
Interpreting the resultadoados
Acceptable
- Bias is not statistically significant, or is significant but negligible against the tolerancia.
- The regression pendiente is not statistically different from zero across the working range.
Needs action
- Bias is significant and large relative to the tolerancia: recalibrate or adjust.
- The pendiente is significant: the gauge errs differently at different sizes, so a single correction factor will not fix it.
- Bias varies erratically with no trend: investigate the gauge, the fixture, or the method before trusting any medición from it.
Acceptance limits for sesgo and linealidad are not universal. They come from your tolerancia, your customer requirements and your own procedures. Any threshold quoted in general training material, including this page, is a convention rather than a rule you can cite as compliance.
What you can do in GaugeConnection today
What you can do today with the existing features:
- Use calibración certificate as-found and as-left readings. When a certificate records the reading obtained against a known patrón, the difference is a sesgo observation at that point, and a certificate covering several points across the range gives you a coarse linealidad picture.
- Use the Stability Tracker on a master pieza. Charting repeated mediciones of the same referencia over time detects drift, which is sesgo that is changing rather than constant.
- Use the Uncertainty tool. A documented sesgo that you have chosen not to correct should be carried as a contribution in the uncertainty budget rather than ignored.
None of these substitute for a properly designed sesgo or linealidad estudio. If your customer or your quality system requires one, run it against your own procedure and record it outside this tool.