Calculating Contributors to MU - Developing MU budgets for in house calibrations

[Benjamin28]

Good day friends, I wanted to see if anyone could provide some insight into developing MU budgets for in house calibrations.

First, let me start by giving some background here. I have been tasked with creating initial MU budgets for various in house calibrations we perform. I do not have formal training in MU calculations, in fact I'd never even heard of MU until about a month ago. That being said, I have read fairly extensively on MU calculations and I think am making reasonable progress on learning this via book work, trial and error, and the valuable information supplied on these forums.

What I could use more information on is the calculation of type B contributing uncertainty. For example, a micrometer...I know parallelism of anvils should be included, however, I am uncertain how to calculate this value, the same goes for environmental conditions such as thermal expansion. Another stumbling block would be assigning a distribution to the uncertainty values...what determines if you use a student t, normal, u shape, rectangular, etc...

I need to determine these MU budgets for various calibrated tools, micrometers, calipers, extensometers, calibrated weights, flare cones, flowmeters and density cups....there is an extensive list....however, we are a materials testing lab, not a cal lab...as such we do not have the experience or means to do instrument studies to determine uncertainties in thermal expansion...air bouyancy..or such...

Well as you can imagine, jumping into MU budget calculations with no official training makes this a difficult and painful process, I would definately appreciate any advice given.

[HotRog]

Try the reference documents on A2LA's website www.a2la2.org
If your master instruments are sent to a 17025 accredited lab, they will have the master gauges uncertainty on the certificate, that is your starting point. That uncertainty, along with R&R of your tech performing the calibrations combine to be a large part of your MU budget. This is all good information but if you are not a 17025 accredited lab, MU is nt mandatory.

[Benjamin28]

We are ISO17025 accredited through NADCAP PRI, actually the entire reason we are calculating MU is for a CAR issued by our registrar.

I'll use a micrometer MU budget as an example.

I have done the calculations utilizing gage repeatability as my type A value and the reported MU on my master gage blocks as a type B. Is it enough to only use these values, or must I include instrument resolution, parallelism of anvils, and thermal expansion in this budget? If I do need to include these factors...I am at a loss as how to calculate an uncertainty value for them...

[Hershal]

Yes, those influences and possibly more.....

Resolution is typically half of the least resolution; thermal expansion is typically 6.7 microinches per inch per degree C and is the difference between what the gage block(s) are calibrated at and what the block(s) are used at; don't forget ringing.....if more than one block is used to effect a specific measurement (e.g., 0.1 inch couple with 0.2 inch) you have ringing, which is generally accepted at 0.00005 inch per ringing; and don't forget parallax if using analog mics.

Hope this helps.

Hershal

[Benjamin28]

Wanted to post a thank you for all the valuable information supplied on the topic of MU, the continual conversation on this topic and terrific feedback to my questions have really been a great source of information and assistance.

As a newcomer to the forums I have been absolutely delighted to read the many different topics posted in these forums and astounded at what a great resource these have proven to be.

[Benjamin28]

Wanted to post this attachment. It contains a measurement uncertainty budget for a caliper and some of the data from which it's derived. If anyone would care to look at this I would appreciate any feedback as to whether it looks correct.

One area I'm interested in is the Repeatability portion. From reading a number of guides I understood that you take the std deviation and divide this by the square root of the number of readings taken...thus finding the standard deviation of the mean. However, my boss believes that the repeatability data should use the direct standard deviation. I wondered which is correct.

Anyhow, here it is, any feedback is appreciated.

[Hershal]

The budget does not look too out of line.....but the thermal effects are rectangular distribution as that effect could occur anywhere is the distribution.....the block uncertainties if taken from the calibration certificate (and already reported at k=2) will be divided by two to return them to standard uncertainty.....also, if there was any wringing (putting two blocks together to obtain a different value) the standard figure is 0.00005" per wringing.

The overall budget may go up a bit.....

Hope this helps.

Hershal

[Benjamin28]

Well, I've reviewed, revised, researched, revised, calculated, recalculated, and revised....and now, I'm finally relatively comfortable with the results of this caliper budget.

You were correct Hershal, the gage block was reported at k=2 therefore requiring a division by two and entry into the MU calculator software as std uncertainty. I also changed the thermal effects calculations to account for the 10% variation between materials of the same nominal coefficient and taking into account the offset from 20C. Both diff in coefficients, and diff in temp I calculated at full range of the caliper @6" and adjusted the distribution to rectangular as you suggested.

I also decided to use the experimental standard deviation for repeatability based on the tn1297 Nist Technical note equation. The revisions seem to reflect an appropriate result. Still I wish I could find more examples of uncertainty budgets for common devices, that would be more beneficial than 25 different guides all stating the same equations in different formats!

At least I now have 15 of 22 budgets completed and looking decent, thanks again for all the help