Balanced 2 × 2 × 2 ANOVA screen

Crossed Gage R&R

Inputs

Operator A · Part 1 · Trial 1A11unitFirst raw observation in the fixed balanced study design.

Operator A · Part 1 · Trial 2A12unitSecond raw observation in the fixed balanced study design.

Operator A · Part 2 · Trial 1A21unitThird raw observation in the fixed balanced study design.

Operator A · Part 2 · Trial 2A22unitFourth raw observation in the fixed balanced study design.

Operator B · Part 1 · Trial 1B11unitFifth raw observation in the fixed balanced study design.

Operator B · Part 1 · Trial 2B12unitSixth raw observation in the fixed balanced study design.

Operator B · Part 2 · Trial 1B21unitSeventh raw observation in the fixed balanced study design.

Operator B · Part 2 · Trial 2B22unitEighth raw observation in the fixed balanced study design.

Results

Repeatability variance component

0.005

unit²

Operator variance component

0.02

unit²

Part × operator variance component

unit²

Part-to-part variance component

unit²

Total Gage R&R variance

0.025

unit²

Gage R&R share of observed study variance

0.049975

Repeatability standard deviation

0.070711

unit

Crossed ANOVA: SSPart, SSOperator, SSPart×Operator, SSRepeatability · VarRepeat = MSRepeat · VarOperator = max[(MSOperator−MSInteraction)/(a·n),0]

A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.

Calculation snapshot

Crossed Gage R&R

Formula version 1.0.0

Conditions

Operator A · Part 1 · Trial 1	10.0
Operator A · Part 1 · Trial 2	10.1
Operator A · Part 2 · Trial 1	20.0
Operator A · Part 2 · Trial 2	20.1
Operator B · Part 1 · Trial 1	10.2
Operator B · Part 1 · Trial 2	10.3
Operator B · Part 2 · Trial 1	20.2
Operator B · Part 2 · Trial 2	20.3

Calculated response

Repeatability variance component	0.005 unit²
Operator variance component	0.02 unit²
Part × operator variance component	0 unit²
Part-to-part variance component	50 unit²
Total Gage R&R variance	0.025 unit²
Gage R&R share of observed study variance	0.049975 %
Repeatability standard deviation	0.070711 unit

Method

Crossed ANOVA: SSPart, SSOperator, SSPart×Operator, SSRepeatability · VarRepeat = MSRepeat · VarOperator = max[(MSOperator−MSInteraction)/(a·n),0]

Source

NIST + Minitab crossed Gage R&R ANOVA: https://support.minitab.com/en-us/minitab/help-and-how-to/quality-and-process-improvement/measurement-system-analysis/how-to/gage-study/crossed-gage-r-r-study/methods-and-formulas/anova-table/

Boundaries

Exactly 2 operators
Exactly 2 parts
Exactly 2 trials per cell
User validates study design

This printout is a record of displayed inputs and deterministic formula output. It is not an approval, certification, or engineering conclusion.

Nearby: ISO 286 fits · Tolerance stack · Position deviation · MMC bonus & virtual condition

Method

Formula, when it applies, and when it does not

Calculate crossed-study ANOVA variation components from two operators, two parts, and two trials per operator-part cell.

Crossed ANOVA: SSPart, SSOperator, SSPart×Operator, SSRepeatability · VarRepeat = MSRepeat · VarOperator = max[(MSOperator−MSInteraction)/(a·n),0]

When

Exactly 2 operators
Exactly 2 parts
Exactly 2 trials per cell
User validates study design

Don’t

This is a fixed balanced crossed 2-operator × 2-part × 2-trial ANOVA screen with non-negative component estimates. It does not support other study designs, test significance, assess normality, establish stability, assess bias/linearity/resolution, calculate uncertainty, classify Gage R&R adequacy, or approve a measurement system.

NIST + Minitab crossed Gage R&R ANOVA