# GRR a case study.

#### Bev D

##### Heretical Statistician
Super Moderator
The line is a 45 degree line so the start and the end point must be equal. Your first graph and the last one are correct.

Now add the spec box with the lower and upper specifications forming vertical and horizontal lines, creating a box

#### New to statistics

##### Involved In Discussions
Also
The choice of the samples must be representative of the variation of the process (like a cherry picking i have read in some posts).
The samples must be between the specification limits also.

Lets say that your process is stable and you don't have so much range between the samples ( e.x USL=9.96 mm USL=10.06mm & your samples are usually among 10.01-10.05) what do you do in this case? you "fabricate" samples to go below 10.00 mm?

How much this will affect the results?

#### Bev D

##### Heretical Statistician
Super Moderator
It’s a stratified sample instead of a random sample. It is NOT cherry picking which is a pejorative for a biased sample used to trick an analysis into he answer one wants rather than the truth….

I would first ask you what effect do you think it will have? The answer lies in understanding how the math works…I’ll give you a hint: there are at least TWO correct answers. I will give you another hint: we have discussed this in many threads over the last 30 years.

#### New to statistics

##### Involved In Discussions
It’s a stratified sample instead of a random sample. It is NOT cherry picking which is a pejorative for a biased sample used to trick an analysis into he answer one wants rather than the truth….

I would first ask you what effect do you think it will have? The answer lies in understanding how the math works…I’ll give you a hint: there are at least TWO correct answers. I will give you another hint: we have discussed this in many threads over the last 30 years.
How is stratified sample if that is your process?
It is NOT cherry picking which is a pejorative for a biased sample used to trick an analysis into he answer one wants rather than the truth….
I do not understand this

I would first ask you what effect do you think it will have?
I believe that for the appraisers will be more easy to catch the bigger differences among the samples and more difficult among the samples that are similar. If that is the case the problem will be bigger that is actually is.
I’ll give you a hint: there are at least TWO correct answers.
Error 1 & 2?

I will give you another hint: we have discussed this in many threads over the last 30 years.
I will check

#### Bev D

##### Heretical Statistician
Super Moderator

1) a sample that isn’t representative of the actual full range of variation will ONLY effect the %study variation as this is the only place that the SD of the parts appears in the mathematical formulas. If the range of parts is too small, then the measurement error/study variation will be excessively large. This will make it look like the gage is not appropriate for SPC. If the range of parts is artificially large (thru creating parts that exceed the natural variation, the measurement error/study variation will be artificially small making it look like the gage is appropriate for SPC when it might not be. You should be able to understand this if you understand the math - it only takes a little effort on your part.

2a) It is possible - tho rare - that a sample that only represents a small portion of the natural variation will enable the operators to ‘fudge’ or cheat the answers (since the parts are all basically the same) artificially reducing the measurement error as the operators can just record the same answers on the second reading of the part. This will affect both %study variation and %tolerance variation. Making the gage look better than it really is.

2b) It is possible - tho even rarer - that an interaction of the gage and the part ‘size’ will be missed when all of the parts have essentially the same value. Interactions tend to occur at the extremes (high and low) of the parts and are most common with visual inspections but I have seen them with CMMs and some hand gages that are effected by difficult to access geometries/features.

Unless the largest component of variation in your process is piece to piece a random sample - especially when as small as 10 pieces - you are likely to get a sample that is not representative of the full range of natural variation of the process. This is basic sampling theory. This is exacerbated by the natural tendency of people to select parts in a short period of time when the process has very little variation. Most processes do experience larger components of variation such as time to time, lot to lot, raw material lot to lot, operator to operator, equipment to equipment and set-up to set-up. A stratified sample allows you to select parts that will span the full range of natural variation. A random sample will only do this if you have a very large population to select from and you actually perform a random sample. But again many people just take the parts from the same place in the population (such as the upper corner of a single pallet). Again this is basic sampling theory. The downside of a stratified sample that is as small as 10 parts is that you may over-inflate the SD of the parts since the sample distribution is ‘flat’ or uniform in nature, when the actual population may have a bell type shape (tall in the middle and longish smaller number of parts in the tails). But again this will only effect the measurement error/study variation ratio.

It is not true that you should only take parts that are within spec. You need to be representative of the full range of natural variation of the process. There are ways around this when the process has a slow drift such as mold or slow tool wear but that is a bit more advanced and again only effects the ratio that is intended to inform you on the appropriateness of the gage for SPC.

It is true that you should not ‘create’ parts at the extremes as these may not be truly representative of the conditions of real parts that might be at the extremes. This is where a Youden plot helps you to extrapolate the gage’s ability to make repeatable measures of extreme parts.

Again, Statistics isn’t about math. It is about understanding variation and then choosing the appropriate mathematical formulas - if necessary. It is not about blindly applying mathematical formulas and thinking that the math will save you.

* and by gage I mean the entire measurement system