LIVE TOOL

Gage R&R (crossed)

Measurement system analysis from parts, operators and trials pasted from Excel or CSV: ANOVA or X̄-R.

Input

Example dataReplace with your own measurements

Data

Paste, open a CSV, TSV, TXT or XLSX file (up to 20 MB), or drop it on the field. Files are read in this browser only.

ColumnsPartOperatorMeasurement

Found by the header names, or in the order Part, Operator, Measurement. Change them if they are wrong.

Part  Operator  Measurement
1     A         0,29
1     A         0,41
1     B         0,08

Long format
1 row = 1 measurement

Columns: tab, ; or ,
Decimals: 12,5 or 12.5

Read as: tab-separated · decimal comma · 90 rows · header row skipped
Study: 10 parts × 3 operators × 3 trials

ColumnsDecimal

Data as understood — first 10 of 90 rows
#	Part	Operator	Measurement
1	1	A	0,29
2	1	A	0,41
3	1	A	0,64
4	1	B	0,08
5	1	B	0,25
6	1	B	0,07
7	1	C	0,04
8	1	C	-0,11
9	1	C	-0,15
10	2	A	-0,56

+80 more rows

Crossed study: every operator measures every part the same number of times (trials).

MethodANOVATwo-way ANOVA with the Operator × Part interaction (Minitab default method).X̄-R (AIAG)Average and range method of the AIAG MSA manual; needs at least 2 trials and cannot estimate the interaction.

Study variationAlpha to remove interaction

The interaction is removed when its p-value is at least alpha. 0.05 is the current Minitab default; 0.25 is the AIAG MSA rule (also the default of older Minitab, version 16 and earlier).

Optional

Tolerance (USL − LSL)

Process σ (historical)

Tolerance adds %Tolerance, process σ adds %Process.

Runs in this browser. Data is not uploaded or stored.

Results

27,86%%Study var · Total Gage R&R

4Distinct categories (ndc)

Conditionally acceptable — %StudyVar 27,86% (10–30%)
ndc < 5 — 4 distinct categories: the gage cannot tell enough part groups apart

10 parts × 3 operators × 3 trials · ANOVA · alpha 0,05 · StudyVar = 6 × SD

The Operator × Part interaction was removed from the model (p = 0,974 ≥ alpha 0,05); variance components use the table without interaction.

% Contribution% Study variation

Part in one operator's blockCenter lineUCL / LCLOutside the limitsR chart: points inside the limits mean consistent repeats. X̄ chart: most points should fall outside, because parts should differ more than the measurement error.

MeasurementAverage

ABCParallel lines: no Operator × Part interaction.

Two-way ANOVA table with interaction
Source	DF	SS	MS	F	P
Part	9	88,3619	9,81799	492,3	0,000
Operator	2	3,16726	1,58363	79,41	0,000
Operator × Part	18	0,358982	0,0199435	0,4337	0,974
Repeatability	60	2,75893	0,0459822
Total	89	94,6471

Two-way ANOVA table without interaction (used)
Source	DF	SS	MS	F	P
Part	9	88,3619	9,81799	245,6	0,000
Operator	2	3,16726	1,58363	39,62	0,000
Repeatability	78	3,11792	0,0399733
Total	89	94,6471

Variance components
Source	VarComp	%Contribution
Total Gage R&R	0,0914285	7,76
Repeatability	0,0399733	3,39
Reproducibility	0,0514553	4,37
Operator	0,0514553	4,37
Operator × Part (not in model)	—	—
Part-to-part	1,08645	92,24
Total variation	1,17788	100,00

Gage evaluation
Source	StdDev (SD)	Study var (6 × SD)	%Study var
Total Gage R&R	0,302372	1,81423	27,86
Repeatability	0,199933	1,1996	18,42
Reproducibility	0,226838	1,36103	20,90
Operator	0,226838	1,36103	20,90
Operator × Part (not in model)	—	—	—
Part-to-part	1,04233	6,25396	96,04
Total variation	1,0853	6,5118	100,00

Number of distinct categories
Statistic	Value
ndc = ⌊1.41 · SD part / SD gage⌋	4

Download offline versionSingle HTML file · v1.6 · 566 KB · works without internet

Method

Data: long format, one measurement per row with Part, Operator and Measurement columns (Minitab's layout). The study must be crossed and balanced: every operator measures every part the same number of times. Missing or extra combinations are listed.
ANOVA (Minitab default method): two-way ANOVA with parts and operators as random factors. Part and Operator are tested against Operator × Part, the interaction against repeatability. When the interaction's p-value is at least alpha (0.05 by default, as in current Minitab; enter 0.25 for the AIAG MSA rule, also the default of older Minitab), it is pooled into repeatability and the table without interaction is used.
Variance components from the expected mean squares: repeatability = MS_E, Operator × Part = (MS_OP − MS_E) / r, operator = (MS_O − MS_OP) / (p·r), part = (MS_P − MS_OP) / (o·r); without interaction MS_E takes the place of MS_OP. Negative estimates are set to 0 and reported.
X̄-R (AIAG MSA 4th ed.): EV = R̄̄ · K1, AV = √((X̄diff · K2)² − EV² / (parts · trials)), PV = Rp · K3, with K1 = 1/d2(trials) and K2, K3 = 1/d2* for one range of the operator or part averages. It cannot estimate the interaction.
Study var = 6 × SD (Minitab) or 5.15 × SD (older AIAG). %Study var = SD / SD total; %Contribution = variance / total variance; %Tolerance = Study var / (USL − LSL); %Process = SD / process σ.
ndc = ⌊1.41 · SD part / SD gage⌋, at least 1 (Minitab).
AIAG criteria: %Study var of Total Gage R&R below 10% acceptable, 10–30% conditionally acceptable depending on the application, above 30% unacceptable; ndc should be at least 5.
Charts by operator use R̄ with the usual constants for the number of trials: R chart D3·R̄ to D4·R̄, X̄ chart X̄̄ ± A2·R̄.
With one operator reproducibility cannot be estimated; with one trial the interaction cannot be separated from repeatability and the model without interaction is used.
Results use the decimal sign of the pasted data. The results CSV follows it too: decimal comma gives “;” between columns.
Files: CSV, TSV and TXT are read as if pasted (UTF-8, UTF-16, otherwise Windows-1257). XLSX: choose the sheet and the columns or a cell range; formula cells use the value Excel last saved, dates are kept as text. Files up to 20 MB are read in this browser only and never uploaded.
XLSX files are read with SheetJS Community Edition 0.20.3, Apache License 2.0 (license), loaded only when an Excel file is opened or created.