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Measure · Tool guide 09 of 40

Gage R&R for discrete (binary) data

For binary pass/fail decisions, an attribute agreement study examines consistency within assessors, between assessors and against an established reference. It is often called attribute Gage R&R, but agreement rates are not the continuous variance components used in numerical Gage R&R.

Expected output: An attribute agreement assessment with error direction and study limitations.

01 · Purpose

Why and when to use it

Use it when the baseline depends on human or automated classifications such as damage/no damage.

Who takes part?

The measurement owner works with people who understand the process and the recorded data. Statistical or measurement-system decisions should involve someone able to check the assumptions and study design.

02 · Application

How to apply it

Start with an agreed measurement purpose, explicit units and trustworthy observations. Identify missing cases and assumptions before calculating.

  1. Define pass/fail rules and establish reference classifications.
  2. Select representative cases including difficult boundary cases.
  3. Have assessors classify the cases in randomised, blinded repeat rounds.
  4. Calculate within-assessor, between-assessor and reference agreement separately.
  5. Examine false accepts and false rejects; clarify the method and repeat the study if needed.

03 · Example

A worked measurement example

Original fictional teaching example. Small datasets illustrate the method; they are not proposed as sufficient study sizes. Supplied parameters are assumptions, not estimates from a real process.

Illustrative resultCalculationMeaning
Reference agreement36 of 40 decisions = 90%Four decisions disagree with the reference
False accepts3 of 10 reference-fail decisions = 30%Three failures incorrectly accepted
False rejects1 of 30 reference-pass decisions = 3.33%One acceptable case incorrectly rejected

04 · Interpretation

What the result tells you

Overall agreement hides the much larger false-accept rate. Check class balance and consequences, not just one combined percentage. Chance-adjusted statistics such as kappa can complement agreement but are sensitive to prevalence.

Completion check: An attribute agreement assessment with error direction and study limitations.

05 · Judgement

Mistakes and limitations

Avoid easy-only cases, unblinded repeats and assuming the reference is infallible. These 40 decisions are arithmetic examples, not an adequate universal study size.

07 · Reading

Sources and further reading

The tool list follows the accepted LeanTrainingLab overview and its reference to Six Sigma+Lean Toolset, second edition (Lunau, editor; Springer, 2013). The book chapters were not available for direct review during this build. Explanations, examples and worksheets are original teaching material. Further reading supplies professional background; local conventions are stated explicitly.