Quality & Metrology calculator

Gauge Reproducibility Calculator

Separate operator differences from repeat noise on one master. Enter three operator means, equal repeat counts, pooled within-operator deviation and your permitted operator deviation.

What this calculator does

  • Estimate the between-operator standard deviation from a balanced three-operator study on one stable master.

Formula used

  • Mean variance = sum((operator mean − grand mean)²) ÷ 2
  • Untruncated operator variance = mean variance − within-operator deviation² ÷ repeats
  • Operator deviation = sqrt(max(untruncated operator variance, 0))
  • Operator range = maximum operator mean − minimum operator mean
  • Limit margin = allowed operator deviation − estimated operator deviation

Inputs explained

  • Operator 1 Mean: Mean of equal-count repeats on the common stable master.
  • Operator 2 Mean: Second operator’s mean using the same gauge and master.
  • Operator 3 Mean: Third operator’s mean under the same controlled study conditions.
  • Pooled Within-Operator Deviation: Pooled repeatability standard deviation from these balanced operator groups.
  • Repeats per Operator: Equal number of actual readings behind each operator mean.
  • Maximum Operator Deviation: Approved maximum between-operator standard deviation for this master.

How to use the result

  • Best suited to Single-Master operator Comparison, balanced measurement trial.
  • Only two between-operator degrees of freedom support this estimate. Part interaction, operator bias against truth and long-term changes are excluded.

Current U.S. benchmarks

  • U.S. manufacturing runs at 75.7% of capacity (Federal Reserve, Aug 2026). New factory orders are up 8.5% year over year (Census).

Common questions

  • Why subtract repeatability from the operator means? Averaging reduces, but does not remove, within-operator noise. Subtracting its variance divided by repeats isolates the estimated between-operator component.
  • Why show a negative untruncated variance? Sampling can make operator means closer than expected from repeat noise. The physical component is reported as zero, while the raw estimate exposes that uncertainty.
  • Can this replace a crossed gauge study? No, a study across multiple parts can reveal operator by part interaction. One master does not provide that information.
  • Can the three operators use different repeat counts? No, the variance correction assumes equal group sizes. Analyze unbalanced study data with a suitable variance-component method.

Last reviewed 2026-10-06.