Gage Repeatability and Reproducibility (GR&R) studies are designed to show the amount of variation certain portions of the measurement system contribute to the total variation in measurement, often expressed in percent. There are many ways and products available to help you calculate these numbers, which range from a piece of graph paper to full blown software packages costing 1000s of dollars.
So let’s take a look at the values produced by a typical G R&R study and then see how they could fit with the data produced by the OvenRIDER® or OvenCHECKER™ software:
Appraiser Variation (AV%) – This is the percent of the total variation which we humans introduce because the measurement method may vary due to physical or subjective interpretation issues. Things like value interpolation between two tick marks on a ruler or how hard they squeeze a caliper around a part. This is the "Reproducibility" part of a measurement. The lower the measurement variation caused by the appraiser, the better its reproducibility and so almost anyone can do it and get the same or very close answer. If it is more than 30%, then there is too much variation from one person's measurements to another's. You will want to make sure they are following the procedure and not taking some shortcut.
Equipment Variation (EV%) – This is the percent of the total variation which is caused by the measurement equipment or tools used to make the measurement, like a ruler for length or thermometer for temperature. This is the "Repeatability" part of a measurement. The lower the variation caused by the equipment, the better its repeatability. Again, more than 30% means a good portion of the variation lies with the measurement tools.
Reproducibility and Repeatability (R&R%) – This is the combination of the AV and EV and is the percent of the total variation due to the tools and the people used to measure the parts. The measurement system, people and tools should produce a percent of less the 10% to know you have a good measurement system. Between 10% and 30% and you should work to improve the component(s) contributing the majority of the variation.
Part Variation (PV%) – This is the percent of the total variation which is caused by the parts being measured. This is where most of the variation should be found no matter how small the variation. After all, the part variation is what you are trying to measure, no matter how small. So expect to see this number in the 90% range, which means your parts are what is varying.
Total Variation (TV) – The TV is typically not given in percent and is a “standard deviation” like number where one can expect 99.73% of all the measurements to fall between +/-3 times the TV.
The form shows a typical example of a GR&R with sample data one way the values can calculated. How the numbers are calculated is not too important at this point. What they mean and how one can apply them to the data captured from an OvenRIDER® or OvenCHECKER™ is the real question.
So what does it take to do a GR&R?
- Two or more Appraisers – These are the people who are going to use the measuring tools to measure the parts.
- At least 5 sample parts – These are the things the manufacturing process is designed to produce.
- At least two trials measurements – This means measuring the same value from the same part at least two times.
How do these three things map into to the data produced by the OvenRIDER® or OvenCHECKER™:
- We have two or more appraisers, no problem!
- How about at least 5 sample parts? Well, what is the “part” we are making? We have an oven, and the oven has a recipe which was characterized to melt solder without killing the parts on your boards. So, the oven is set up to make … thermal profiles, or time vs. temperature graphs of a specific shape. We assess the shape in many ways, just like we could assess a bolt made by a screw machine. On the bolt we could measure its length, diameter, thread pitch, hardness, etc. On a profile, we measure the initial ramp slope, soak time, time above liquidous, peak temperature, etc. So the profile is the sample part, and one of the profile measures is the value we want to study. Let’s say, peak temperature. Then you run the RIDER through the oven at least five times to make at least 5 sample parts (profiles). So far so good.
- Now each appraiser is to take at least two trial measurements of the same value off the sample parts. So for a given profile, instruct each appraiser to measure the same value off the part (profile) at least two times. How? The software, which takes the data out of the profiler which was recorded from the RIDER, extracts that data from the profiles automatically. No matter how many times or who you instruct to ask the software to give you the peak temperature for a given profile, it will produce the exact same value. If you wanted to do it the hard way, and have each appraiser look at the profile graph using a straightedge and pen, and interpolate the peak value from the graph, you would likely get some appraiser caused variation. But no one in their right mind would do this.
What does this mean? It means that no matter what version of GR&R you use to run the math, the AV and EV will be 0%, leaving all the variation in the parts, which does not make for a very practical GR&R study.
But wait, could you just run the RIDER through the oven again to take a second trial measurement of the SAME profile (or part)? That is NOT a second measure of the same part. That would be producing another new sample part, not a second trial measure of the same part.
This is a typical problem with over half of the measurements we are asked to take in industry these days. It can only be measured once, and then it’s gone. If you want to pull to failure test a bolt as the GR&R studied value, you can only do it once, and then the bolt is broken. You can’t put it back together to make a second or third trial measure. It is the same with a profile. It happens in time and once the profile is produced, that specific profile at that instant in time cannot be measured again. It’s gone! You can only produce another profile (or part), which is not the same as measuring the same profile value twice.
So GR&R is not really the best method of assessing a RIDER product’s variation. The real question is, what is the accuracy of the instrument (the MOLE® thermal profiler), which is stated in the specification, and the variation in the RIDER sensors?
Great care is taken to manufacture sensors to a tight tolerance and tested to show that they have consistent response time to temperature changes. That, coupled with the fact that the materials do not break down or alter properties with use, makes it reasonable to accept any variation measured by the RIDER products lies most completely with the machine producing the profiles.
DataMyte HandBook Sixth Edition – A practical guide to computerized data collection for Statistical Process Control" by DataMyte Business, Allen-Bradley Company, Inc.
Understanding Gage R&R by Rick Sloop, Quality Magazine, September 2009