# Measurement Systems Analysis Needs a Stratified Random Sample (Even with Gummi Bears)

Today, we’re going to get ready to do a Gage Linearity and Bias Study with gummi bears. But to do the linearity and bias study, you first have to talk more about how to collect the data. The Gage Linearity and Bias study has a complication that wasn’t present in the Type 1 Gage Study.

The point of the gage linearity and bias study is to assess the bias of a gage across its operating range, not just in one place. That way, we can learn if large measurements or small measurements are harder to get right. The NIST Engineering Statistics Handbook suggests that you need a minimum of 5 standards that you measure multiple times. NIST also suggests that the increments between the standards should be about equal. I’m planning to use 8, 16, 24, 32, 40, and 48 inches.

It’s this shift, from measuring one distance to measuring different distances, that we have to address. You don’t want to do all of the short measurements first and then all of the longest measurements last. We want to know if the measurement system is biased, so we have to make sure that if exhaustion sets in as we measure, it doesn’t only affect the longest measurements. We’ll need to use random assignment  in the order of the measurements. Fortunately, Minitab Statistical Software makes it easy to randomize the setup for gage studies with the built-in Create Gage R&R Worksheet.

Here’s how to start:

1. Choose Stat > Quality Tools > Gage Study > Create Gage R&R Worksheet.
2. In Number of parts, enter the number of standards to measure. I’m planning to use 6 different distances.

3. For the part names, enter the distances to measure. I’m going to use 8, 16, 24, 32, 40, and 48 representing the number of inches where I’ll set the gummi bears to measure.

4. In Number of operators, enter 1. Evaluating different operators is something we’ll look at when we do a Gage R&R Study later.

5. In Number of replicates, enter the number of times that you’ll measure each standard. I’m going to use 12. Click OK.

You now have a worksheet with a column called “Parts” that gives the order that you should take measurements in. (If you do this yourself, you’ll get a different order than I did—that’s the beauty of randomization!)

Have a few more minutes? You can check out a macro that does a stratified random sample, which is what we got from the Create Gage R&R Worksheet command. (And take it from Bruno, macros are pretty cool.)