# Calibration Report Uncertainty Budget - Discussion and Spreadsheets Attached

K

#### Knowledge seeker

Hi

Calibration report aren't really complete without providing the uncertainty statement.

However, deriving uncertainty budget is an headache

My intention of putting up this post is to hope that you guy could share any of your Uncertainty Budget here (as an attachment) for us as an reference. Although there is no fixed budget, but it would provide a good reference.

Anyone here is an expert in Uncertainty calulation would like to share?

R

#### Ryan Wilde

Give us a clue as to what type of equipment budget you are looking for, such as dimenesional, electrical, etc. I can whip up an example of a dimensional uncertainty budget off the top of my head in excel without much of a problem, but the electrical budgets tend to be much more involved, and very specific to your location, equipment, and accessories (such as leads).

Ryan

K

#### Knowledge seeker

Right, Electrical budget are much more complex.
May you could provide those dimension like micrometer; Mechanical like Digital balance; conductivity meter calibration using standard solution etc.

By the way, can you show me in more detail how to calculate the type B uncertainty when calibrating a balance with combined weight or microemeter with combined gauge block (as an attachemnt to make this post shorter)

For example, calibrating a balance with a load of 9g by using 3 standard weight together (2g, 3g and 4g)with uncertainty of 0.00007g each (stated in their calibraion report), coverage factor = 2.
Is it :
{square root [Square of(0.00007) x3] }/ 2?

R

#### Ryan Wilde

Knowledge seeker said:

By the way, can you show me in more detail how to calculate the type B uncertainty when calibrating a balance with combined weight or microemeter with combined gauge block (as an attachemnt to make this post shorter)

For example, calibrating a balance with a load of 9g by using 3 standard weight together (2g, 3g and 4g)with uncertainty of 0.00007g each (stated in their calibraion report), coverage factor = 2.
Is it :
{square root [Square of(0.00007) x3] }/ 2?
Close, but the weights would be: SQRT([0.00007/2]² + [0.00007/2]² + [0.00007/2]² = 0.00006 (k=1)

The same would go for the gage blocks, except that you must also include the error of ringing blocks together (usually in the 0.25 to 0.5 µm area, depending on the quality, grade and condition of your blocks. This actually becomes a Type A uncertainty if done correctly.

I will develop a few budgets in Excel (if that is okay) at home so that you can see the formulae at work(except for the conductivity meter - I haven't done enough of them to give you a competent budget, and I don't want to steer you wrong).

Ryan

K

#### Knowledge seeker

Hi Ryan, really appreciate you professional advice. By the way, still have some doubt:

Close, but the weights would be: SQRT([0.00007/2]² + [0.00007/2]² = 0.00006 (k=1)
But why K=1 when the calibration report shows the coverage factor for the respectively weights is 2 (K=2)

The same would go for the gage blocks, except that you must also include the error of ringing blocks together (usually in the 0.25 to 0.5 µm area, depending on the quality, grade and condition of your blocks. This actually becomes a Type A uncertainty if done correctly.
If i am not wrong, the way of doing is to the ringing block together and take the measurement. Repeat this a few time and get the Standard deviation ( This will be contribute to the type A uncertainty)

(Pardon me as i am not really familiar with all these techincal stuff, but still learning)

Thanks you in advance for the budget in excel format.

R

#### Ryan Wilde

Knowledge seeker said:

Hi Ryan, really appreciate you professional advice. By the way, still have some doubt:

But why K=1 when the calibration report shows the coverage factor for the respectively weights is 2 (K=2)
Because this uncertainty is a component of the total uncertainty, not the whole budget. Generally a component is best left as a single standard deviation (k=1), and the final result of the budget is multiplied by 2 for the total estimated uncertainty figure. You must still add scale resolution, atmospheric condition, gravitational variables, etc into the budget.

If i am not wrong, the way of doing is to the ringing block together and take the measurement. Repeat this a few time and get the Standard deviation ( This will be contribute to the type A uncertainty)
Your method gives you part of the uncertainty, but cannot show a bias, only a repeatability. There are amounts of oil residue, dust, flatness/parallelism errors, etc in there that have to be quantized. Bias must be part of the equation, and you must determine it. An easy way is to measure a 25 mm block, then using as many different combinations of blocks you can make (20 mm and 5 mm, 10 mm and 15 mm, etc) determine the bias of your rung blocks versus the non-rung block, as well as the repeatability. You can then either compensate for the mean of the error and use a Type A for the repeatability, or if it is sufficiently small for your process, take the worst case and use it as a single component.

Regards,
Ryan

A

#### AlbertPaglinawan

Hi!

<i>Coverage factor
In general, the value of the coverage factor k is chosen on the basis of the desired level of confidence to be associated with the interval defined by U = kuc. Typically, k is in the range 2 to 3. When the normal distribution applies and uc is a reliable estimate of the standard deviation of y, U = 2 uc (i.e., k = 2) defines an interval having a level of confidence of approximately 95 %, and U = 3 uc (i.e., k = 3) defines an interval having a level of confidence greater than 99 %. </i>

and they made an example of...
<i>The following are examples of uncertainty statements as would be used in publication or correspondence. In each case, the quantity whose value is being reported is assumed to be a nominal 100 g standard of mass ms.
Example 1
ms = 100.021 47 g with a combined standard uncertainty (i.e., estimated standard deviation) of uc = 0.35 mg. Since it can be assumed that the possible estimated values of the standard are approximately normally distributed with approximate standard deviation uc, the unknown value of the standard is believed to lie in the interval ms ± uc with a level of confidence of approximately 68 %. </i>

having said that, um, i would like to know where the 68% come from. and what exactly is a coverage factor? is this the equivalent of the coverage factor, like k=2=xx%

Plus, on an entirely different matter, I would like to know how we estimate the errors on leads used in electrical measurements.

cheers!

M

#### M Greenaway

Isn't 68% the portion of the normal distribution curve between +/- 1 standard deviation ?

R

#### Ryan Wilde

Okay, the story behind the 68%, 95%, k=1, k=2, etc.

It's statistics. Statistics state that a single standard deviation of a bell curve (gaussian curve, whatever you like to call it) is such that approximately 68% of a population will fall within the range specified. If you multiply that range by 2 (coverage factor of 2, k=2, 2 standard deviations, etc.) then 95.45% of the population will fall within the range.

The international calibration community has settled on 95% (k=2) as the default.

I've attached a very simple illustration in Excel that I threw together to illustrate this. It should help.

Ryan

#### Attachments

• 16 KB Views: 392
K

#### Knowledge seeker

Hi Ryan,

Still looking forward to some of your uncertainty budget in excel format..

Regard

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