Gauge repeatability and reproducibility

In a crossed Gage R&R study, repeatability concerns repeats of the same part by the same operator. Reproducibility concerns differences associated with operators. The procedure and setup are part of the study. Minitab: crossed-study data considerations

In the example, repeatability SD 0.003 mm and reproducibility SD 0.004 mm give GRR SD 0.005 mm. With part SD 0.020 mm, %Contribution is 5.88% of total variance and %Study Variation is 24.25% of total SD. %Tolerance is 30.00% at six SD and 0.100 mm tolerance width. Each percentage answers a different question.

NIST treats precision, bias, stability, resolution and configuration as separate study questions. NIST: important issues for a gauge study

Define the process and study population

Identify the characteristic, units, inspection method, fixture, software, operators, part family and intended decision. Record normal preparation and repositioning. If production requires removing and reclamping a part, an experiment that leaves it clamped throughout does not evaluate that setup variation. Define whether different days, instruments or configurations are in scope rather than assuming the word “reproducibility” includes them all.

NIST explicitly treats artifacts, operators, gauges, parameter levels and configurations as design choices. Its own reproducibility analysis includes between-day effects. That scope differs from the familiar crossed operator-by-part model, so state exactly which changing conditions the reported component represents. NIST: study design, NIST: reproducibility analysis

Crossed, nested and destructive studies

In a crossed study, every selected operator measures every selected part repeatedly. Minitab recommends randomized order within each replicate, representative operators and parts spanning the actual or expected process range. Its guidance suggests at least ten parts when suitable historical process variation is available, and considering more when the study must estimate that variation. These are study-design recommendations, not a universal contractual sample size. Minitab: data collection and sampling

For example, ten parts × three operators × three replicates produces 90 measurements. That arithmetic does not establish adequacy for every application. Keep part and operator identities, replicate and actual collection order. Avoid letting operators simply copy or recall previous readings. A collection order that coincides with warming, drift or fatigue can confound those effects with the study factors.

Destructive testing requires a different design argument because the same physical specimen cannot be tested again. Minitab describes crossed designs using sufficiently homogeneous substitute specimens and nested designs where different operators receive different part groups. The assumption that specimens within a group are effectively equivalent is critical: uncontrolled within-group variation can be absorbed into the apparent measurement variation. Relabeling different specimens with one part ID does not create homogeneity. Minitab: destructive-testing study design, January 31, 2013

Understand the variance model

For Minitab's crossed ANOVA analysis, the full model includes part, operator and part-by-operator interaction. Interaction means that the operator differences depend on the part—for example, operators may handle small and large features differently. With interaction included, reproducibility combines operator and interaction variance components; total GRR combines reproducibility and repeatability. Variances add, and the combined standard deviation is the square root of the combined variance. Minitab: variance-component formulas

Minitab's ANOVA implementation can fit a reduced model when the interaction does not meet its significance criterion. Its Xbar-and-R analysis treats reproducibility differently, and entering parts without operators does not estimate an operator reproducibility component. Report the analysis method, model and software settings so two reports with the same “GRR” label can be compared meaningfully. Minitab: methods of analysis

Keep the percentage denominators explicit

For a conventional variance decomposition, let σGRR be measurement standard deviation and σtotal include both measurement and part-to-part variation. With a two-sided tolerance width T and study multiplier k:

Minitab normally uses k = 6 but permits another multiplier. Variance contributions add to 100%; standard-deviation percentages generally do not. A report must also identify whether total variation came from the selected parts or a historical estimate. Minitab: statistics and interpretation

Original reconciled example: assume estimated repeatability SD is 0.003 mm, reproducibility SD is 0.004 mm and part-to-part SD is 0.020 mm. Assume the reproducibility estimate already includes any retained interaction. Then:

GRR variance = 0.003² + 0.004² = 0.000025 mm²
GRR SD = 0.005 mm
total variance = 0.000025 + 0.020² = 0.000425 mm²
total SD = 0.020616 mm
%Contribution = 100 × 0.000025 / 0.000425 = 5.88%
%Study Variation = 100 × 0.005 / 0.020616 = 24.25%
%Tolerance, for T = 0.100 mm and k = 6, = 30.00%

The part-to-part contribution is 94.12%, which reconciles with the GRR contribution to 100%. The three GRR percentages describe the same assumed estimates; none is a transcription error. If the selected part spread increases, %Study Variation may improve without any reduction in measurement SD. If only the tolerance widens, %Tolerance improves while the instrument remains unchanged. Neither denominator should be manipulated to obtain approval.

Interpret uncertainty and act on causes

Examine repeatability, operator and interaction patterns alongside the summary. Confidence intervals matter: Minitab provides intervals for variation metrics, and broad intervals can limit a decision. Number of distinct categories is related to the part variation represented in the study; it is not the number of display digits or a complete uncertainty statement. Minitab: intervals and distinct categories

Investigate causes appropriate to the observed pattern: fixturing, alignment, procedure ambiguity, operator technique, surface condition or environmental variation. Define the acceptance basis through the customer or quality system and intended use. A percentage threshold is not by itself a guarantee of correct decisions on parts close to a limit. Following corrective action, verify performance under the revised operating conditions rather than reusing the earlier study conclusion.

Reporting and source scope

Retain raw readings, part-selection basis, operator population, equipment and procedure revisions, collection order, study dates, model, variance components, SDs, percentage denominators, multiplier, confidence intervals and decision basis. State omitted conditions and avoid presenting a short-term study as proof of stability over an unexamined service period.

Sources were reviewed November 1, 2026. The Minitab support pages and NIST handbook pages cited here did not display article revision dates. Software formulas and defaults are identified as Minitab behavior; they are not represented as universal requirements from an automotive or metrology standard.

Inspection and quality documents