# Gage R&R graphs

## Components of variation chart

The components of variation chart is a graphical summary of the results of a gage R&R study. The sources of variation that are represented in the graph are:
Total Gage R&R
The variation due to the measurement system including multiple operators using the same gage.
Repeatability
The variability in measurements obtained when the same part is measured multiple times by the same operator.
Reproducibility
The variability in measurements obtained when the same part is measured by different operators.
Part-to-Part variation
The variability in measurements across different parts.
Separate colored bars represent:
% Contribution
The percentage of process variation from that source. % Contribution is calculated as the variance component for that source multiplied by 100 and then divided by the process variation.
% Study Variation
% Study Variation is calculated as 100 times the study variation for that source divided by the total study variation.
% Tolerance
% Tolerance is calculated as 100 times the study variation for that source divided by the process tolerance. Minitab calculates this value when you specify a process tolerance or specification limit.
% Process
% Process is calculated as 100 times the study variation for that source divided by the process variation. Minitab calculates this value when you specify a historical standard deviation.

## R chart

Use an R chart to determine whether operators measure parts consistently. A point that is higher than the upper control limit (UCL) indicates that the operator does not measure parts consistently. The calculation of the UCL includes the number of measurements by an operator of a part, and part-to-part variation. If the operators measure parts consistently, then the difference between the highest and lowest measurements is small, relative to the study variation, and the points should be in control.

The R chart contains the following elements:
Plotted points
For each operator, the difference between the largest and smallest measurements of each part. The R chart plots the points by operator; therefore, you can see how consistent each operator is.
Center line (Rbar)
The grand average for the process (that is, average of all the sample ranges).
Control limits (LCL and UCL)
The amount of variation that you can expect for the sample ranges. To calculate the control limits, Minitab uses the variation within samples.
###### Note

If the subgroup size is greater than 9, Minitab displays an S chart instead of an R chart.

## Xbar chart

Use an Xbar chart to determine whether the measurement system is acceptable. Because the parts chosen for a Gage R&R study should represent the entire range of possible parts, this graph should ideally show lack-of-control. Lack-of-control exists when many points are higher than the upper control limit and/or lower than the lower control limit.

The Xbar chart contains the following elements:
Plotted points
The average measurement of each part. The Xbar chart plots the points by operator; therefore, you can see how consistent each operator is.
Center line (Xbar)
Tthe overall average for all part measurements by all operators
Control limits (LCL and UCL)
The control limits are based on the repeatability estimate and the number of measurements in each average.

## By Part chart

Use the By Part chart to display all the measurements taken in the study, arranged by part. Ideally, the multiple measurements for each individual part vary as minimally as possible (the dots for one part will be close together), and the averages vary enough that differences between parts are clear.

The By Part chart shows all the measurements that were taken in the study, arranged by one factor. This graph helps you visualize the differences between factor levels. Gage R&R studies traditionally arrange measurements by part and by operator. However, Gage R&R Study (Expanded) lets you graph other factors.

###### Note

If there are more than 9 observations per level, Minitab displays a boxplot instead of an individual value plot.

## By Operator chart

Use the By Operator chart to display all the measurements taken in the study, arranged by operator. Ideally, the measurements for each operator vary an equal amount and the part averages vary as minimally as possible.

###### Note

If there are more than 9 observations per level, Minitab displays a boxplot instead of an individual value plot.

## Operator*Part Interaction chart

Use the Operator * Part Interaction chart to display the average measurements taken by each operator on each part in the study, arranged by part. Ideally, the lines follow the same pattern and the part averages vary enough that differences between parts are clear.

Interaction plots display the interaction between two factors. An interaction occurs when the effect of one factor is dependent on a second factor. This plot is the graphical analog of the F-test for an interaction term in the ANOVA table.

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