Gage R&R Study (Expanded)

ANOVA Table

  

The results displayed in this ANOVA (analysis of variance) tells you if different levels of the factors result in different average values of a response variable.

You want to see if the p-value associated with each source of variation is less than the chosen level of significance. This would indicate that the source contributes significantly to measurement variability.

The ANOVA table lists the following sources of variability:

·    Part, which represents the variability in measurements across different parts.

·    Operator, which represents the variability in measurements across different operators.

·    Nested factors, if you specify them in your model. For example, Part (Operator) indicates that Parts is nested in Operator and represents the variability in measurements across different parts by each operator.

·    Interaction terms, if you specify them in your model. For example, Operator*Part, which represents the variability in measurements across different combinations of operator and part. If an interaction term has a p-value greater than 0.25, the ANOVA will be re-run without it.

·    Error or Repeatability, which represents the variability in measurements that cannot be attributed to parts, operators, or other terms in the model.

The results displayed in this ANOVA table will be used to compute the Gage R&R.

Example Output

ANOVA Table with All Terms

 

Source             DF    Seq SS    Adj SS  Adj MS     F      P

Part               21  1071.303  1071.303  51.014  6.46  0.000

Operator            2    32.178    32.178  16.089  3.27  0.164 x

Station             1    11.247    11.247  11.247  3.50  0.202

Part*Operator      42   331.809   331.809   7.900  1.27  0.189

Operator*Station    2     6.433     6.433   3.217  0.52  0.598

Repeatability      63   390.527   390.527   6.199

Total             131  1843.497

 

x Not an exact F-test.

 

 

α to remove interaction term = 0.05

 

 

ANOVA Table with Terms Used for Gage R&R Calculations

 

Source          DF    Seq SS    Adj SS  Adj MS     F      P

Part            21  1071.303  1071.303  51.014  7.49  0.000

Operator         2    32.178    32.178  16.089  2.36  0.099

Station          1    11.247    11.247  11.247  1.65  0.202

Repeatability  107   728.769   728.769   6.811

Total          131  1843.497

Interpretation

 When the p-value for an interaction is > 0.05, Minitab omits this interaction from the model. For the refraction data, the Part*Operator p-value is 0.189 and the Operator*Station p-value is 0.598  in the top ANOVA Table. Therefore, both of these interactions are omitted from the final model.

The second ANOVA table contains the terms used in the final Gage R&R calculations. Part (0.000) is a significant source of measurement variation at the a = 0.05 level of significance. However, Operator ( 0.099), and Station (0.202) are probably not significant sources of measurement variation.