Have you ever stepped on a scale to weigh yourself, stepped off the scale, and then stepped back on to measure your weight a second time? Did you get two different readings? Whether you are monitoring your weight or trying to improve a process vital to your company’s success, it is imperative that the measurement system you use is adequate.
Most measurement systems contain some variation, and we can use a Gage Repeatability and Reproducibility Study (Gage R&R) to quantify that variation and assess the measurement system.
The total variation in a process is composed of the variation in the parts themselves and the variation due to the measurement system. The measurement system variation can be split into two components: repeatability and reproducibility.
Repeatability is the variation observed when
- the same operator - measures the same part - multiple times - with the same device.
Reproducibility is the variation observed when
- different operators - measure the same part - with the same device.
In a Gage R&R Study, the measurement system variation is compared to the part-to-part variation, which will be the largest component of variation if the measurement system is sufficient.
Follow These Steps to Conduct a Gage R&R Study
- Take a random representative sample of parts to measure.
- Randomly select qualified operators to take the measurements. At least two operators are needed to estimate reproducibility.
- Decide how many measurements each operator should take, typically 2.
- Create the measurement plan and take the measurements.
In this example,
- three operators
- have measured the thickness of 10 parts
- 2 times each
- in random order to minimize external factors.
The first 24 rows are shown below.
5. Run the analysis using crossed Gage R&R.
We can use the Gage R&R results to assess the measurement system. Some of the output of the analysis is below.
The study variation column represents the variation in this sample due to the various components. In a Gage R&R study, we are interested in the percent of the total variation attributed to the measurement system. Therefore, the study variation for the total Gage R&R is divided by the study variation for the Total variation and then multiplied by 100 leading to 33.07% in this example. When looking at the 6-sigma curve for this sample data, the measurement system accounts for 33.07%.
Typically, values for Total Gage R&R %Study Var less than 30% are acceptable. Values under 10% are ideal. In this example, the value exceeds 30% and the measurement system needs improvement. By examining the %Study Variation for Repeatability and Reproducibility, the analyst can determine the largest contributor. Reproducibility contributes more than Repeatability and there is an Operator by Part interaction.
Graphical analysis can be helpful for understanding a poor measurement system.
The Components of Variation graph shows the amount of variation contributed by the Gage R&R combined as well as repeatability, reproducibility, and the part-to-part. The graph shows that the Gage R&R %Study Var is above 30% and that Reproducibility is the larger contributor to the measurement system variation.
We can use the other graphs to figure out why the Gage R&R %Study Var is larger than desired. For example, the Thickness by Part and Part*Operator Interaction plots show a greater amount of variation between the operators’ measurements for part 10, which contributes to the poor reproducibility results. However, the R Chart, which can be used to identify repeatability issues, is in control. In addition, the Xbar Chart is out of control, which is also favorable. This indicates that there is more variation between the parts than when the same operator measured the same part repeatedly.
The Gage Run Chart is another tool that can be used to identify measurement system issues. This graph again shows that part 10 was particularly difficult to measure. The Gage Run Chart will also reveal patterns in the data. For example, we can see that Bill almost always measures the parts smaller the second time, which would have gone undetected if we relied solely on the Gage R&R results.
The Gage R& Study shows that the measurement system used to measure part thickness needs improvement. Perhaps there were certain attributes of part 10 that made it difficult to measure, and the Gage Run Chart indicates that Bill may have used a different procedure when measuring the parts, a second time. There are many causes for inadequate measurement systems, including issues with the measurement device itself, an operator who was not properly trained, or a measurement tool that exhibits wear out after repeated use. Whatever the case may be, evaluating your measurement system is crucial; only then can you uncover measurement system issues and build confidence in your data.