Example of Expanded Gage R&R Study

A process engineer wants to evaluate the glass refractive measurement system for a glass manufacturing process. The engineer asks three operators to measure the refractive properties of 22 glass parts at two stations.

Because this study has a fixed factor (station), the engineer performs an expanded gage R&R study to assess the variability in measurements that may be from the measurement system.

  1. Open the sample data, GlassRefraction.MTW.
  2. Choose Stat > Quality Tools > Gage Study > Gage R&R Study (Expanded).
  3. In Part numbers, enter Part.
  4. In Operators, enter Operator.
  5. In Measurement data, enter Measurement.
  6. In Additional factors, enter Station.
  7. In Fixed factors, enter Station.
  8. Click the Terms button.
  9. From Include terms in the model up through order, select 2.
  10. Under Selected terms, remove the Part*Station interaction term from the model.
  11. Click OK in each dialog box.

Interpret the results

The first two-way ANOVA table includes terms for the part, the operator, the fixed factors, and the interactions. If the p-value for an interaction is ≥ 0.05, Minitab omits the interaction from the full model because it is not significant. In this example, the Part*Operator p-value is 0.189, and the Operator*Station p-value is 0.598. Thus, Minitab generates a second two-way ANOVA table that omits these interactions from the final model.

For the refraction data, the measurement system (Total Gage R&R %Contribution, approximately 49%) has as much variability as the parts (Part-to-Part %Contribution, approximately 51%). The Total Gage R&R equals approximately 70% of the study variation. Repeatability is approximately 69% of the study variation, which indicates that the measurement system does not measure the same part consistently.

This process can distinguish only 1 distinct category, which indicates that the measurement system cannot distinguish between parts. For more information, go to Using the number of distinct categories in a gage R&R study.

The graphs also provide the following information about the measurement system:
  • In the Components of Variation graph, you can see that measurement system explains about the same amount of variation as the part-to-part variation. Specifically, most of the variability is from the inaccuracy of the measurement system (Repeatability).
  • In the R Chart by Operator, several of the data points are out-of-control, which indicates that the three operators measure inconsistently.
  • In the Xbar Chart by Operator, only a few points are beyond the control limits for each operator. For this chart, at least 50% of the points should be out of control to indicate an acceptable measurement system. Thus, in this example, the Xbar Chart indicates a measurement system that might not be acceptable.
  • In the By Part graph, the measurements of each part vary noticeably. This variability might be due to the inaccuracy of the measurement system. The averages also vary noticeably, which is desirable because the parts used in the study should represent the entire range of possible parts.
  • In the By Operator graph, the measurements for each operator vary by approximately the same amount. Some variation is always present, but the data indicate that the operators measure similarly.
  • In the Operator*Part Interaction graph, the lines follow each other closely. However, some inconsistencies are present. For example, Operator 3 seems to have different measurements for part 19 than the other two operators.

Gage R&R Study: Measurement versus Part, Operator, Station

ANOVA Table with All Terms Source DF Seq SS Adj SS Adj MS F-Value P-Value Part 21 1071.30 1071.30 51.014 6.46 0.000 Operator 2 32.18 32.18 16.089 3.27 0.164 x Station 1 11.25 11.25 11.247 3.50 0.202 Part*Operator 42 331.81 331.81 7.900 1.27 0.189 Operator*Station 2 6.43 6.43 3.217 0.52 0.598 Repeatability 63 390.53 390.53 6.199 Total 131 1843.50 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-Value P-Value Part 21 1071.30 1071.30 51.014 7.49 0.000 Operator 2 32.18 32.18 16.089 2.36 0.099 Station 1 11.25 11.25 11.247 1.65 0.202 Repeatability 107 728.77 728.77 6.811 Total 131 1843.50