Attribute Agreement Analysis
Tabla de contenidos
Variable datos versus atributo datos
The distinction determines which estudio you can run, and it is decided by what the inspection actually records, not by what is being inspected.
| Aspect | Variable datos | Attribute datos |
|---|---|---|
| Qué is recorded | A measured value on a continuous scale, such as 25.012 mm | A category, such as pass or fail, or a grade such as A, B or C |
| Applicable estudio | R&R del sistema de medición, sesgo, linealidad, estabilidad | Attribute concordancia análisis |
| Headline resultado | Percent GRR and ndc | Percent concordancia and kappa |
A useful test: if you cannot meaningfully subtract one resultado from another, the datos is atributo datos. Pass minus fail is not a quantity, so no varianza can be decomposed and the entire R&R del sistema de medición machinery does not apply.
Por qué you cannot just run a R&R del sistema de medición
R&R del sistema de medición works by splitting the total observed varianza into pieza variación, repetibilidad and reproducibilidad. Every one of those terms is a varianza, and a varianza requires a numeric scale with meaningful distances between values. Category labels have no such scale.
People sometimes code pass as 1 and fail as 0 and feed that into an R and R calculation. Do not do this. The arithmetic will produce numbers, and those numbers will be meaningless, because the distance between the codes is an artifact of the coding rather than a propiedad of the medición. An auditor who understands the método will recognize it immediately.
The three comparisons
A complete atributo estudio has each evaluador inspect the same set of piezas more than once, in a randomized order, without knowing the previous resultado. That design supports three distinct preguntas.
Within evaluador
Does one evaluador reach the same verdict when shown the same pieza again? This is the atributo equivalent of repetibilidad. Poor within-evaluador concordancia means the criteria are ambiguous or the defect is near the limit of what can be seen.
Between evaluadores
Do different evaluadores reach the same verdict on the same pieza? This is the atributo equivalent of reproducibilidad. Poor between-evaluador concordancia usually points at inconsistent training or an unwritten patrón that each person has interpreted differently.
Versus the patrón
Do the evaluadores reach the correct verdict, judged against an independently established referencia decision for each pieza? This is the one that matters most, and the one that requires the most preparation.
Kappa: concordancia corrected for chance
Raw percent concordancia overstates how good a proceso is, because two people guessing randomly will still agree a large fraction of the time. With only two categories, pure guessing produces about 50 percent concordancia. Cohen's kappa removes that baseline.
Cohen's kappa
κ = (Po − Pe) ÷ (1 − Pe)
where Po is the observed proportion of concordancia and Pe is the proportion of concordancia expected by chance alone, calculated from how often each evaluador uses each category.
The numerator is the concordancia above chance actually achieved. The denominator is the concordancia above chance that was available to achieve. Kappa is therefore the fraction of the achievable improvement over guessing that the evaluadores captured. Kappa of 1 is perfect concordancia and kappa of 0 is no better than chance. Negative values are possible and indicate systematic disconcordancia.
Worked example
Illustrative datos. Two evaluadores each classify the same 50 piezas as pass or fail.
- They reach the same verdict on 45 of the 50 piezas, so Po = 45 / 50 = 0.90.
- Both evaluadores call about 80 percent of piezas pass and 20 percent fail, so the chance concordancia is Pe = (0.80 x 0.80) + (0.20 x 0.20) = 0.64 + 0.04 = 0.68.
- kappa = (0.90 - 0.68) / (1 - 0.68) = 0.22 / 0.32 = 0.69.
Ninety percent concordancia sounds strong. Kappa of 0.69 tells a different and more honest story: most of that concordancia was available for free because the proceso rejects few piezas. This gap between raw concordancia and kappa is exactly why the correction exists, and it grows wider as the categories become more unbalanced.
Interpreting kappa
| Kappa | Common interpretation |
|---|---|
| κ ≥ 0.90 | Good concordancia. The inspection is generally considered acceptable on this criterion. |
| 0.70 ≤ κ < 0.90 | Marginal. Usually treated as needing improvement to the criteria, the training, or the inspection conditions. |
| κ < 0.70 | Unacceptable. The inspection is not reliably distinguishing conforming from non-conforming piezas. |
Treat a low kappa as a proceso finding rather than a people finding. It almost always traces back to criteria that were never written down precisely, boundary samples that do not exist, or lighting and fixturing that make the defect genuinely hard to see. Retraining without fixing those conditions rarely moves the number.
Qué you can do in GaugeConnection today
Until that changes, the practical steps are:
- Run the estudio outside this tool against your own documented procedure, and retain the records where your quality system requires them.
- Before running it, write down the acceptance criteria and produce physical boundary samples. Most atributo estudios fail because the patrón was never made concrete, and no statistic will repair that.
- Dónde an atributo check can be replaced by a medición, consider doing so. Variable datos gives you far more information per pieza and supports the full rango of MSA estudios.