Input
Sigma = 6
Alpha = 0.05
Tolerance = NULL
dat = read.csv("~/Desktop/Vendors/ICT B591/IQC/newGRR.csv", header = TRUE)## 'data.frame': 90 obs. of 3 variables:
## $ Part : Factor w/ 10 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
## $ Operator : Factor w/ 3 levels "A","B","C": 1 1 1 1 1 1 1 1 1 1 ...
## $ Measurement: num 0 -0.047 0 -0.033 -0.053 -0.015 -0.065 -0.08 -0.05 -0.055 ...## Operators: 3
## Parts: 10
## Trails: 3Interpret the key results for Crossed Gage R&R Study
Step 1: Use the ANOVA table to identify significant factors and interactions
Step 2: Assess the variation for each source of measurement error
Step 3: Examine the graphs for more information on the gage study
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.
## Analysis of Variance Table
##
## Response: Measurement
## Df Sum Sq Mean Sq F value Pr(>F)
## Operator 2 0.000013 0.0000067 1.9534 0.1707
## Part 9 0.061101 0.0067890 1985.9404 <2e-16 ***
## Operator:Part 18 0.000062 0.0000034 1.5539 0.1033
## Repeatability 60 0.000132 0.0000022
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1If the p-value for the operator and part interaction is 0.05 or higher, removing the interaction because it is not significant and generates a second ANOVA table without the interaction.
## Analysis of Variance Table
##
## Response: Measurement
## Df Sum Sq Mean Sq F value Pr(>F)
## Operator 2 0.000013 0.0000067 2.6914 0.07408 .
## Part 9 0.061101 0.0067890 2736.1694 < 2e-16 ***
## Repeatability 78 0.000194 0.0000025
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Step 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
## VarComp %Contribution
## Total Gage R&R 0.0000026 0.35
## Repeatability 0.0000025 0.33
## Reproducibility 0.0000001 0.02
## Operator 0.0000001 0.02
## Operator*Part 0.0000000 0.00
## Part-to-Part 0.0007541 99.65
## Total variation 0.0007567 100.00Key Results: VarComp, %Contribution
The %Contribution for part-to-part variation is 99.65%. Divides the part-to-part variance component value, approximately 7.54110^{-4}, by the total variation, approximately 7.56710^{-4}, and multiplies by 100%. When the %Contribution from part-to-part variation is high, the measurement system can reliably distinguish between parts.
## StdDev Study Var %Study Var
## Total Gage R&R 0.0016190 0.0097139 5.89
## Repeatability 0.0015752 0.0094511 5.73
## Reproducibility 0.0003740 0.0022441 1.36
## Operator 0.0003740 0.0022441 1.36
## Operator*Part 0.0000000 0.0000000 0.00
## Part-to-Part 0.0274601 0.1647603 99.83
## Total variation 0.0275077 0.1650464 100.00## *Number of Distinct Categories (truncated signal-to-noise-ratio) = 23Key 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. Displays the %Tolerance column when you enter a tolerance value.
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.