There’s an old saying that history repeats itself. Someone long ago modified that to, “History repeats itself; historians repeat each other.” When it comes to guidelines for gauge r&r studies, there’s a lot of repetition going on. Search for information about gauge r&r studies online and you’ll find a lot of material merely referencing other material without any objective commentary. It’s kind of like a mutual admiration society for measurement systems analysis, but we can do better.
Several guidelines have been suggested and documented over the years to help people decide whether or not a measurement system is capable. Three common guidelines read like this:
1) The precision-to-tolerance ration (PTR) should be less than 10%, and if greater than 30% the system is unacceptable.
2) The percentage gauge r&r (%GRR) should be less than 10%, and if greater than 30% the system is unacceptable.
3) The number of distinct categories (ndc) should be 5 or greater, and a value of 0 or 1 implies the system is unacceptable.
Let’s take a closer look at these guidelines and see how they might fit into your measurement systems analysis.
PTR = 6 times stdev(gauge)/tolerance — The PTR guidelines are based on the notion that a measurement device should be calibrated in units 1/10 as large as the final required measurement accuracy. This notion may hold for your measurement system, but it may not. We know that you may have guidelines established by internal or external customers, but we recommend determining your own guidelines based on your data and experience. Note that if you blow open your limits for whatever reasons, PTR can look quite impressive but not be meaningful. Or, if you have great repeatability and reproducibility, you might consider tightening your limits and fighting back against pesky defects.
Remember that 6*sigma is obviously going to give you a bigger value than 5.15*sigma. 6*sigma represents 99.73% of a normal distribution, while 5.15 sigma represents 99% of a normal distribution. You might ask, What’s 0.73% among friends?, but 6/5.15 is about 1.165. Most mentions of the PTR guidelines ignore this fact. To put it another way, reducing measurement error is harder than merely changing a multiplier from 6 to 5.15.
%GRR = stdev(gauge)/stdev(total) — In terms of round numbers, the %GRR guidelines are generally the same as the PTR guidelines. BTW, a %GRR of 30% is the same as saying that the measurement system variance is 9% of the total variance (in other words, less than 10%).
Note that if the part-to-part variation increases, %GRR goes down. This does not mean you should ask your friends in the fab to increase part-to-part variability. Ratios are just that – ratios. If your part-to-part variability is extremely low than your %GRR doesn’t compare directly with someone else’s %GRR where there is considerable part-to-part variability. If you’re going to do a gauge r&r study, don’t just pick two or three parts. You’re either going to underestimate part variability or over estimate it, neither of which is helpful.
Also note that if you use 6 as your sigma multiplier for PTR, then %GRR divided by PTR (approximately) equals Cp.
Again, use your data and experience to determine how the %GRR metric can help you decide whether your measurement system is capable.
NDC = square-root