MSA / 004OFFLINE

Gage R&R (crossed)

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

Input

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

Paste measurements to start.

ColumnsDecimal

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

—%Study var · Total Gage R&R

—Distinct categories (ndc)

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 text at the end of this file).