ANOVA practical application

I think that we are struggling with language differences and perhaps a theoretical statistical education that focused on mathematical calculations rather than the fundamentals of study designs and how the math works. My advice is to stop asking random isolated questions and take the time to read and understand what I and Miner have posted here on MSA and other statistical analyses. Then begin practicing by starting a study design from scratch.

That said, I agree 10,000% with Miner that having the operators measure different parts is NOT an MSA. In MSA you need to be able to separate the contribution of 3 factors (or components of variation):

(1) the ability of the measurement system to measure the same value of the same location on the same part. This is repeatability variation. So each operator must measure the same place on the same part at least 2 times. This creates a crossed study. If the measurement is non-replicable as in many profilometers or is destruct then you must use a nested study design. Both Miner and I cover this distinction in our posted papers in the resources section.
(2) the ability of different operators to measure the same location/part and get the same value as every other operator. This is Reproducibility; operator to operator variation.
(3) the contribution of the part variation itself. Sometimes this includes within part variation as well.

Is the profilometer a contact or non-contact instrument. This really, really matters. I have worked with both. A non-contact one can in fact measure the exact same location on a part multiple times and will allow you to perform a crossed study. If it is a contact instrument then you are stuck with a nested design. Then you will need to program the thing to measure specific not random locations.


A proper study design will allow for the math to separate and quantify the contribution of these 3 factors.

No offense but it seems that your advanced knowledge of statistical calculations (MS) has not prepared you for understanding the mechanics of statistical study designs. This is not uncommon by the way. No engineering or scientific discipline prepares the graduate for the real world application of their discipline. The graduate needs mentoring and coaching in the real world.

A few other things to ponder that can affect your analysis. First is the feature that is being measured. Is it a geometric shape or a surface finish?
Often, the data that is provided and used for the specification is the result of a calculation of some sort. A radius or a height might be calculated for a geometric shape. Surface finish can be peak to peak differences or peak to valley differences and the max or average is reported.
Surface finish is notoriously non repeatable as the finish will change by location. You will need to understand the specification and ho exactly the measurement is made and calculated; I have seen such things as measure 5 places and the average of the 5 measurements is wah hte specification is trying to control…

A surface Finish Tale:
We had a plastic part that slid across a metal part. At one point in time, we began seeing that the plastic part was shedding small particles of plastic on the metal part. We traced the immediate cause to a change in surface finish on the metal part. We jokingly referred to the bad parts as “cheese graters”. We couldn’t pass a surface finish MSA with a traditional profilometer; we couldn’t even distinguish between good parts and bad parts although we could feel the difference with our finger nails. We then used a non contact method and three things stood out: one was that we could see the actual geometry of the surface (the instrument took pictures of the surface) and the bad parts had very sharp curved shapes (like a wave or ironically an actual cheese grater). The second thing was that the sharpness had a dependency on location and direction. This was actually a great clue as to cause…This led us to the third thing - we figured out how to best calculate the ‘sharpness’ based on direction and location on the part and could then distinguish between good and bad parts. It wasn‘t great or cheap but we were able to determine cause, set a specification and create a solution to the problem. We eventually used a standard profilometer for the supplier and for our incoming inspection (because of cost), using multiple measurements per part in specific locations and path direction on the part yet we could only distinguish between good and bad with some over lap in the middle.

Statistical analysis in an industrial setting isn’t about generating tables of statistics. It is about helping the engineers and scientists gain insight, solve problems, develop solutions, and control processes. One of my favorite quotes: Statistics without physics is gambling; Physics without statistics is psychics…

What I usually like to do is to take a single part and to measure it many time -- say 40 or 50 times. If the measurements are very homogeneous (=small within subgroup/part standard deviation), we conclude that the part is homogeneous. Therefore, it does not matter that we don't control the exact measurement location and all the discussion "crossed vs nested" becomes academical. Thus, try to pick some homogeneous parts and you can evaluate it as crossed gauge RR.
Nevertheless, I agree that it is very important to have a clear goal. Without this clear goal you never know how to define the acceptance criteria, and asking three different people you will get five different answers/suggestions.

Just a grammatical clarification: a small standard deviation or small within part variation does not indicate homogeneity but consistency…in teh English language anyway.