Example of gage R&R study (Expanded)
main topic     interpreting results     session command     see also     

In this example, ten parts that represent the expected range of the process variation were selected. Additionally, each part is fitted with one of two sub-components (a fixed factor), and you want to determine if this introduces part-to-part variability. Three operators measured the ten parts, four times per part (two times with each sub-component), in random order. You decide to conduct a gage R&R study (Expanded) to determine how much of your observed process variation is due to measurement system variation.

1    Open the worksheet GAGEGENERAL.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 Subcomponent.

7    In Fixed factors, enter Subcomponent.

8    Click Terms. In Include terms in the model up through order, type 2.

9    Click Part-to-Part Variation. In Available terms, click Subcomponent to move it to Selected terms. Click OK twice.

10  Click Options. Under Process tolerance, choose Upper spec - Lower spec and type 8. Click OK.

11  Click Graphs. Under Plots of average measurements by two factors, enter Operator and Subcomponent. Do not change the defaults for the other graphs.

12  Click OK in each dialog box.

Session window output

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

 

 

Factor Information

 

Factor        Type    Levels  Values

Part          random      10  1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Operator      random       3  A, B, C

Subcomponent  fixed        2  A, B

 

 

ANOVA Table with All Terms

 

Source                  DF    Seq SS   Adj SS   Adj MS       F      P

Part                     9   97.8123  97.8123  10.8680  173.10  0.000 x

Operator                 2    3.7413   3.7413   1.8706   10.03  0.038 x

Subcomponent             1    1.7160   1.7160   1.7160   12.17  0.075 x

Part*Operator           18    1.1493   1.1493   0.0638    3.29  0.000

Part*Subcomponent        9    0.1653   0.1653   0.0184    0.95  0.491

Operator*Subcomponent    2    0.2841   0.2841   0.1420    7.31  0.001

Repeatability           78    1.5158   1.5158   0.0194

Total                  119  106.3841

 

x Not an exact F-test.

 

 

α to remove interaction term = 0.25

 

 

ANOVA Table with Terms Used for Gage R&R Calculations

 

Source                  DF    Seq SS   Adj SS   Adj MS       F      P

Part                     9   97.8123  97.8123  10.8680  170.21  0.000

Operator                 2    3.7413   3.7413   1.8706   10.03  0.038 x

Subcomponent             1    1.7160   1.7160   1.7160   12.08  0.074

Part*Operator           18    1.1493   1.1493   0.0638    3.30  0.000

Operator*Subcomponent    2    0.2841   0.2841   0.1420    7.35  0.001

Repeatability           87    1.6811   1.6811   0.0193

Total                  119  106.3841

 

x Not an exact F-test.

 

 

Variance Components

 

                                     %Contribution

Source                      VarComp   (of VarComp)

Total Gage R&R             0.078692           7.92

  Repeatability            0.019323           1.95

  Reproducibility          0.059369           5.98

    Operator               0.042102           4.24

    Part*Operator          0.011132           1.12

    Operator*Subcomponent  0.006136           0.62

Part-To-Part               0.914649          92.08

  Part                     0.900349          90.64

  Subcomponent             0.014300           1.44

Total Variation            0.993341         100.00

 

 

Process tolerance = 8

 

 

Gage Evaluation

 

                                        Study Var  %Study Var  %Tolerance

Source                     StdDev (SD)   (6 × SD)       (%SV)  (SV/Toler)

Total Gage R&R                0.280521    1.68313       28.15       21.04

  Repeatability               0.139006    0.83404       13.95       10.43

  Reproducibility             0.243658    1.46195       24.45       18.27

    Operator                  0.205188    1.23113       20.59       15.39

    Part*Operator             0.105507    0.63304       10.59        7.91

    Operator*Subcomponent     0.078330    0.46998        7.86        5.87

Part-To-Part                  0.956373    5.73824       95.96       71.73

  Part                        0.948867    5.69320       95.20       71.17

  Subcomponent                0.119583    0.71750       12.00        8.97

Total Variation               0.996665    5.97999      100.00       74.75

 

 

Number of Distinct Categories = 4

Graph window output

Gage R&R Study for Measurement

Interpreting the results

Session Window Output

·    Look at the p-value for the Part*Subcomponent interaction in the ANOVA Table. When the p-value for an interaction is > 0.25, Minitab omits this from the full model. Notice there is an ANOVA table without that interaction because the p-value was 0.491. The Part*Operator and Operator*Subcomponent interactions are significant sources of variability and are retained in the model.

·    Note that in the %Contribution column in the Variance Components table the percent contribution from Part-To-Part (92.08) is larger than that of Total Gage R&R (7.92). This tells you that much of the variation is due to differences between parts. Additionally, the sub-component does not add much additional part-to-part variation, only 1.44 percent.

·    Note that in the %Study Var column in the Gage Evaluation table the Total Gage R&R equals 28.15% of the study variation. While the Total Gage R&R %Contribution is acceptable, there is room for improvement. See Guidelines for measurement system acceptability.

·    For these data, the number of distinct categories is 4. According to the AIAG, you need at least 5 distinct categories to have an adequate measuring system. See Number of distinct categories statement.

Graph Window Output

·    The Components of Variation graph (located in the upper left corner) shows that the percent contribution from Part-To-Part is larger than that of Total Gage R&R, telling you that much of the variation is due to differences between parts.

·    The non-level line in the By Part graph (located in upper right corner) shows that there are large differences between parts.

·    The R Chart by Operator (located in middle of the left corner) shows that Operator B measures parts inconsistently.

·    The By Operator graph (located in the middle of the right column) shows that the differences between operators are small compared to the differences between parts, but are significant (p-value = 0.038). Operator C appears to measure slightly lower than the others.

·    The Xbar Chart by Operator (located in the lower left corner) shows that most of the points in the X and R chart are outside the control limits, indicating variation is mainly due to differences between parts.

·    The Operator* Subcomponent graph is a visualization of the p-value for Operator* Subcomponent (0.001), indicating a significant interaction between Operator and Subcomponent. All operators, especially Operator B, tend to measure Parts with Subcomponent B higher than parts with Subcomponent A.