Methods and formulas for method of analysis in Crossed Gage R&R Study

Select the method or formula of your choice.

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ANOVA
Xbar and R

ANOVA

When both Parts and Operators are entered

When you enter Operators and Parts, Minitab analyzes the data using a balanced two-factor factorial design. Both factors are considered to be random. The model includes the main effects of Parts and Operators, plus the Operator by Part interaction. (If you don't enter Operators, the model is a balanced one-way ANOVA with Part as a random factor, as described in the next section.)

Minitab first calculates the ANOVA table for the appropriate model. That table is then used to calculate the variance components.

Note

Some of the variance components could be estimated as negative numbers when the Part by Operator term in the full model is not significant. Minitab displays the full model in the Two-Way ANOVA Table with Interaction. If the p-value for the operator and part interaction is greater than or equal to the significance level, Minitab omits the interaction term to fit a reduced model, and displays that model in the Two-Way ANOVA Table Without Interaction. By default, the significance level is 0.05. This reduced model includes only the main effects of Part and Operator.

Full model

With the full model, the variance component for reproducibility is further broken down into the following sources of variation:

The Operator component is the variation between different operators who measure the same part.
The Part by Operator interaction is the variation between the average sizes of parts that are measured by each operator. This interaction accounts for cases where operator consistency varies significantly across parts. For example, one operator gets more variation when measuring smaller parts, whereas another operator gets more variation when measuring larger parts.

Use the table of variance components to interpret these effects.

Reduced model

With the reduced model, the variance component for reproducibility is simply the variance component for Operator.

When Operators are not entered

When you enter only the parts, the model is a balanced one-way ANOVA, and Part is considered a random factor. Minitab calculates the ANOVA table and estimates the variance components for Part and Gage. The variance component for Gage is the same as Repeatability, and Minitab does not estimate a Reproducibility component. Thus, the variance component for Gage is the error term from the ANOVA model.

Xbar and R

Minitab first calculates the sample ranges from each set of measurements taken by an operator on a part. Then, Minitab uses the sample ranges to calculate the average range for repeatability.

Minitab calculates the variance for reproducibility from the range of the averages of all measurements for each operator. Reproducibility, in this case, is the same as the variance component for operator. Minitab calculates the variance for parts from the range of the averages of all measurements for each part.

Note

All ranges are divided by the appropriate d₂ factor.