# Absolute to Relative Uncertainty - Expressing the U as a percent of the reading

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#### edge540

##### Guest
I am working on my uncertainty budget for a 1m long calibration device for testing machine crosshead travel and long stroke extensometers. Basically I want to express the U as a percent of reading. So far everything is absolute in um... so I'm a bit stuck.

I have had the instrument calibrated and they give a +/- 5um uncertainty to the device.
Resolution is 1um.

I calculated through a repeatability study appx 15um for the std dev. and then introduced a cosine error and came up with appx 23um for that std. dev.

In the end I calculate about a 27um Uncertainty... but I would rather express it as a % of reading.
I'm not too clear on how to do that though.

If this question has been asked (and it is probably buried here somewhere) I apologize in advance.

Any help is appreciated.

#### Stijloor

##### Super Moderator
Staff member
Super Moderator
I am working on my uncertainty budget for a 1m long calibration device for testing machine crosshead travel and long stroke extensometers. Basically I want to express the U as a percent of reading. So far everything is absolute in um... so I'm a bit stuck.

I have had the instrument calibrated and they give a +/- 5um uncertainty to the device.
Resolution is 1um.

I calculated through a repeatability study appx 15um for the std dev. and then introduced a cosine error and came up with appx 23um for that std. dev.

In the end I calculate about a 27um Uncertainty... but I would rather express it as a % of reading.
I'm not too clear on how to do that though.

If this question has been asked (and it is probably buried here somewhere) I apologize in advance.

Any help is appreciated.
Any calibration/uncertainty experts who can help?

Thank you!

Stijloor.

#### Mike Boothe

##### Inactive Registered Visitor
Convert each item in your uncertainty budget to % of reading then your result will be in % of reading.

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#### edge540

##### Guest
Convert each item in your uncertainty budget to % of reading then your result will be in % of reading.
Yes, I was thinking about it last night and decided to do that.

I have 10 set points and ten readings each but its in excel now so it should be easy to take care of that.

Should I then combine all to use in my Type A uncertainties or should I take each one individually in there?

Once in % I suppose I only need to take the Std Dev of all and use one Type A.

What about resolution? it is abs. 0.001mm
And the calibration report UnC is 0.005mm (the range will be 50mm to 999mm)
Should I use the 50mm point for those (since they are the worst case so to speak)

Resolution is then 0.002% and the Cal Cert Unc is then 0.01% (k=2)

Does that make sense? (that is the one question that I remember from my Uncertainty training course back about 10 years ago,,, problem is that some of this makes sense but I'm not so sure I know if that is me wanting for it to make sense or if it really does)

#### dv8shane

##### Inactive Registered Visitor
What about resolution? it is abs. 0.001mm
And the calibration report UnC is 0.005mm (the range will be 50mm to 999mm)
Should I use the 50mm point for those (since they are the worst case so to speak)

Resolution is then 0.002% and the Cal Cert Unc is then 0.01% (k=2)
Using the worst case is in my opinion OK but not preferred, as the customer will inherit your transfer uncertainty. Therefore at the points where your uncertainty is much better you are providing a lesser service to them.

I think the resolution contribution is lower than stated as the distribution of resolution is determined at a 100% level of confidence by dividing by root 12.
Question Do you also include degrees of freedom in your budgets?

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#### edge540

##### Guest
I do field service and am pretty conservative with my budgets. In this case, the parameter need not be super critical so I would rather take a higher uncertainty as I know that there will be setup issues and other contributors in reality once this is in service.

In I do use DOF in my calculations (normally using the Unc 3.2 calculator).