Interpret the key results for Crossed Gage R&R Study

Complete the following steps to interpret a crossed gage R&R study. Key output includes variability estimates, and graphs of the measurements and measurement variability.

Step 1: Use the ANOVA table to identify significant factors and interactions

Use the ANOVA table to identify which sources of variability are significant. The ANOVA table includes the following terms in the Source column:
  • Part: The variation that is from the parts.
  • Operator: The variation that is from the operators.
  • Operator*Part: The variation that is from the operator and part interaction. An interaction exists when an operator measures different parts differently.
  • Error or repeatability: The variation that is not explained by part, operator, or the operator and part interaction.
Note

If you select the Xbar and R option for Method of Analysis, Minitab does not display the ANOVA table.

If the p-value for the operator and part interaction is 0.05 or higher, Minitab removes the interaction because it is not significant and generates a second ANOVA table without the interaction.

Two-Way ANOVA Table With Interaction Source DF SS MS F P Part 9 88.3619 9.81799 492.291 0.000 Operator 2 3.1673 1.58363 79.406 0.000 Part * Operator 18 0.3590 0.01994 0.434 0.974 Repeatability 60 2.7589 0.04598 Total 89 94.6471 α to remove interaction term = 0.05
Two-Way ANOVA Table Without Interaction Source DF SS MS F P Part 9 88.3619 9.81799 245.614 0.000 Operator 2 3.1673 1.58363 39.617 0.000 Repeatability 78 3.1179 0.03997 Total 89 94.6471
Variance Components %Contribution Source VarComp (of VarComp) Total Gage R&R 0.09143 7.76 Repeatability 0.03997 3.39 Reproducibility 0.05146 4.37 Operator 0.05146 4.37 Part-To-Part 1.08645 92.24 Total Variation 1.17788 100.00
Key Result: P

In these results, the p-value is 0.974, so Minitab generates a second two-way ANOVA table that omits the interaction from the final model.

Step 2: Assess the variation for each source of measurement error

Use the variance components (VarComp) and %Contribution to assess the variation for each source of measurement error. The sources are as follows:
  • Total Gage R&R: The sum of the repeatability and the reproducibility variance components.
  • Repeatability: The variability in measurements when the same operator measures the same part multiple times.
  • Reproducibility: The variability in measurements when different operators measure the same part.
  • Part-to-Part: The variability in measurements due to different parts.

Ideally, very little of the variability should be due to repeatability and reproducibility. Differences between parts (Part-to-Part) should account for most of the variability.

Variance Components %Contribution Source VarComp (of VarComp) Total Gage R&R 0.0020816 6.82 Repeatability 0.0011541 3.78 Reproducibility 0.0009275 3.04 Part-To-Part 0.0284585 93.18 Total Variation 0.0305401 100.00
Key Results: VarComp, %Contribution

The %Contribution for part-to-part variation is 93.68%. Minitab divides the part-to-part variance component value, 0.0308455, by the total variation, 0.0329271, and multiplies by 100%. When the %Contribution from part-to-part variation is high, the measurement system can reliably distinguish between parts.

Gage Evaluation Study Var %Study Var %Tolerance Source StdDev (SD) (6 × SD) (%SV) (SV/Toler) Total Gage R&R 0.045625 0.27375 26.11 27.37 Repeatability 0.033972 0.20383 19.44 20.38 Reproducibility 0.030455 0.18273 17.43 18.27 Part-To-Part 0.168696 1.01218 96.53 101.22 Total Variation 0.174757 1.04854 100.00 104.85 Historical standard deviation is used to calculate some values for StdDev, Study Var, and %Study Var. Values for %Process are not displayed because they are identical to values for %Study Var.
Key Results: %Study Var

Use the percent study variation (%Study Var) to compare the measurement system variation to the total variation. The %Study Var uses the process variation, as defined by 6 times the process standard deviation. Minitab displays the %Tolerance column when you enter a tolerance value, and Minitab displays the %Process column when you enter a historical standard deviation.

According to AIAG guidelines, if the measurement system variation is less than 10% of the process variation, then the measurement system is acceptable. Because the %Study Var, the %Tolerance, and the %Process are all greater than 10%, the measurement system might need improvement. For more information, go to Is my measurement system acceptable?.

Key Results: Components of Variation graph

The components of variation graph shows the variation from the sources of measurement error. Minitab displays bars for %Tolerance when you enter a tolerance value, and Minitab displays bars for %Process when you enter a historical standard deviation.

This graph shows that part-to-part variability is higher than the variability from repeatability and reproducibility, but the total gage R&R variation is higher than 10% and might be unacceptable.

Step 3: Examine the graphs for more information on the gage study

The gage R&R graphs provide information about the measurement system.
Components of variation graph
Shows whether the largest of component of variation is part-to-part variation.
In an acceptable measurement system, the largest component of variation is part-to-part variation.
R chart by operator
Shows whether any points fall above the upper control limit.
If the operators measure consistently, the points will fall within the control limits.
Xbar chart by operator
Shows whether most points fall beyond the control limits.
The parts that you choose for a gage R&R study should represent the typical part-to-part variability. Thus, you should expect more variation between part averages, and the graph should show that most points fall beyond the control limits.
Measurements by part graph
Shows whether multiple measurements for each part are close together.
Multiple measurements for each part that are close together indicate small variation between the measurements of the same part.
Measurements by operator graph
Shows whether differences between operators are small compared to the differences between parts.
A straight horizontal line across operators indicates that the mean measurements for each operator are similar. Ideally, the measurements for each operator vary an equal amount.
The operator*part interaction graph
Shows whether the lines that connect the measurements from each operator are similar or whether the lines cross each other.
Lines that are coincident indicate that the operators measure similarly. Lines that are not parallel or that cross indicate that an operator's ability to measure a part consistently depends on which part is being measured. A line that is consistently higher or lower than the others indicates that an operator adds bias to the measurement by consistently measuring high or low.
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