# Two Gauges (Gages) - Two measurements correlation I do not know how to explain

D

#### Devlin

Hi,

I have two gauges, A and B, and I used them to measure 31 samples. Attached is the results. However, as I calculate the correlation between L1-L1, L2-L2, L3-L3 and L4-L4 of A and B, the correlations of them are interesting which I have no knowledge. For example, L1-L1 correlation is around 60% and L2-L2 is about 30%. However, as I checked the raw data of L2-L2, I feel that the data measured by A and B are pretty close or nearly same. Did I use wrong formula? I use Correl() in the Excel.

Thanks,

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#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: Two gauges - Two measurements correlation I do not know how to explain

A quick look at the scatter diagrams (aka Youden Plots) shows that you don't have much variation in teh parts you measured vs the measurement error this can lead to misinterpretation of any statistical test.

A few points: correlation and regression are not appropriate statistical tests for measurement error. (You can use them but they must be interpreted with caution as they are not designed to assess measurement error directly.)

The intraclass correlation coefficient was designed to assess measurement error; the Youden plot was designed to display measurement error including comparisons of two or more gauges; the Bland -Altman and paired t tests are also applicable for method comparison.

I have attached a document briefly describing each of these as well as a spreadsheet that perfroms the calculations and plots the data.

Did you assess the repeatability of the individual guages first? without knwoing if the guages themselves are repeatable, any analysis of gauge to gauge performance is tenous at best.

can you describe what L1, L2 L3 and L4 refer to?

did your samples span the full range of known variation? what are the spec limits?

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D

#### Devlin

Re: Two gauges - Two measurements correlation I do not know how to explain

Hi,

I summarised what your suggestion as follow,
1. Do repeatability for each gauge first to understand the repeatability of each gauge is good before compare them.
2. Plot "Youden plot" to understand the bias and use "Bland -Altman" to understand the bias magnitude.

I have some further questions,
1. To do the repeatability for a gauge, I need to sample a full process variation. What about the data for "Youden plot" and "Bland - Altman"?
2. Our company's product is glass sheet and we are planning to buy a laser cutter to cut the glass sheet to the right dimension. After the cutter, we would like to install a gauge, called Dimension Gauge, to measure glass sheet dimension including X, Y and squareness. Our cutting dimension spec. is 2500.30 +/- 0.10mm. Here are the questions
a) As you mentioned, we have to do repeatability with 30 samples which cover the full process variation for our gauge. It means that I have to collect samples which dimension is from 2500.20~2500.40. Is this correct?
b) The laser cutter and Dimension Gauge are new for our process. Can I qualify them together? What I mean is that set the cutting size to 2500.20 for laser cutter and cut the glass sheet, and then measure the glass sheet by the Dimension Gauge. Repeat the same process, set the laser cutter to 2500.21~2500.40, until we collect 30 samples. Or should I qualify one by one?
3. Our Dimension Gauge vendor proposes that the gauge has 30um repeatability. Can I use the way you suggested to qualify this gauge?
4. People in this fourm told me that I have to calculate the gauge measurement uncertainty, is it the same as yours?
5. In my company, we use GRR to qualify a new gauge, here is the way we do, collect 30 samples which cover the product tolerance and calculate the GRR by Minitab, and if the % Total Variation is < 10%, then this gauge is acceptable. What is the difference between our GRR and your suggestion, repeatability?
6. I put L1 and L2 data in the column on A and B in "Discrimination Plot" spread sheet, however, I do not see the Measurement Discrimination Plot shows points. Did I make mistakes? Please see the attachment.

P.S: L1, L2, L3 and L4 refer to our glass dimensions.

Regards,

A quick look at the scatter diagrams (aka Youden Plots) shows that you don't have much variation in teh parts you measured vs the measurement error this can lead to misinterpretation of any statistical test.

A few points: correlation and regression are not appropriate statistical tests for measurement error. (You can use them but they must be interpreted with caution as they are not designed to assess measurement error directly.)

The intraclass correlation coefficient was designed to assess measurement error; the Youden plot was designed to display measurement error including comparisons of two or more gauges; the Bland -Altman and paired t tests are also applicable for method comparison.

I have attached a document briefly describing each of these as well as a spreadsheet that perfroms the calculations and plots the data.

Did you assess the repeatability of the individual guages first? without knwoing if the guages themselves are repeatable, any analysis of gauge to gauge performance is tenous at best.

can you describe what L1, L2 L3 and L4 refer to?

did your samples span the full range of known variation? what are the spec limits?

#### Attachments

• 299 KB Views: 279

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: Two gauges - Two measurements correlation I do not know how to explain

Hi,

I summarised what your suggestion as follow,
1. Do repeatability for each gauge first to understand the repeatability of each gauge is good before compare them.
2. Plot "Youden plot" to understand the bias and use "Bland -Altman" to understand the bias magnitude.
Plot both the repeatability data for each guage and the gauage to gauge comparison on a Youden plot...

I have some further questions,
1. To do the repeatability for a gauge, I need to sample a full process variation. What about the data for "Youden plot" and "Bland - Altman"?
yes - all methods need the full range of variation.

2. Our company's product is glass sheet and we are planning to buy a laser cutter to cut the glass sheet to the right dimension. After the cutter, we would like to install a gauge, called Dimension Gauge, to measure glass sheet dimension including X, Y and squareness. Our cutting dimension spec. is 2500.30 +/- 0.10mm. Here are the questions
a) As you mentioned, we have to do repeatability with 30 samples which cover the full process variation for our gauge. It means that I have to collect samples which dimension is from 2500.20~2500.40. Is this correct?
basically yes. If you are using the guage for product acceptance you need to understand the repatability and bias in relation to the tolerances. If you are using it for SPC you need to understand the actual range of variation. well behaved processes will have less variation than the tolerances...much has been written here and elsewhere on this topic. I recommend you google Donald Wheeler for his article "An Honest Guage R&R Study" for starters. it's free.
b) The laser cutter and Dimension Gauge are new for our process. Can I qualify them together? What I mean is that set the cutting size to 2500.20 for laser cutter and cut the glass sheet, and then measure the glass sheet by the Dimension Gauge. Repeat the same process, set the laser cutter to 2500.21~2500.40, until we collect 30 samples. Or should I qualify one by one?
Yes you can combine the qualifications, in fact I recommend it.

3. Our Dimension Gauge vendor proposes that the gauge has 30um repeatability. Can I use the way you suggested to qualify this gauge?
yes. remember that vendors typically only claim perfect repeatability where nothing else changes; they simply measure teh same thing in the exact same location over and over...tehy do not include all other factors in the measurement system.

4. People in this fourm told me that I have to calculate the gauge measurement uncertainty, is it the same as yours?
Marc covered uncertainty in another thread. Uncertainty is a very specific characteristic. for your application repeatability and reproducibility and stability are most likely sufficient.

5. In my company, we use GRR to qualify a new gauge, here is the way we do, collect 30 samples which cover the product tolerance and calculate the GRR by Minitab, and if the % Total Variation is < 10%, then this gauge is acceptable. What is the difference between our GRR and your suggestion, repeatability?
As covered in other posts and in Wheelers' articles the use of 10/20/30% total variation usign Minitab's version of the AIAG calculations is not mathematically sound and can lead to misinterpretation of the results. Unfortunately although humans, managers and customers tend to demand simple yes/no answers, there really are no yes/no answers in physics (perhaps in the spiritual world there is). I recommend you start with Wheeler and some of the many threads here to begin understanding how to use MSA to guide you in understanding your measurement systems and what you can and can't do with them.

6. I put L1 and L2 data in the column on A and B in "Discrimination Plot" spread sheet, however, I do not see the Measurement Discrimination Plot shows points. Did I make mistakes? Please see the attachment.
You have to manually adjust the scales: double right clik on the axes and a window will open to allow you to set the min/max valeus of the axes...

B

#### BrQ

Re: Two gauges - Two measurements correlation I do not know how to explain

"The differences between measurement methods appears to be random, and so the calculated 2 σd limits can be considered a good estimation for future results. "
Does this mean that you can expect this much error in any future measurements?

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