### Author Topic: Developing a CMC and calculations  (Read 2372 times)

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#### moosebiscuit

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##### Developing a CMC and calculations
« on: April 16, 2024, 03:28:59 pm »
Good morning everyone. I am developing a CMC template for my calibration lab. We plan to adhere to 17025 requirements, but I am having some difficulties. I figured I would start with a Calibration and Measurement capability sheet. I am using a template that I obtained online for uncertainty calculations. I am starting with DCV - Source with a 5560A Multiproduct Calibrator.

This is my current understanding: The CMC format should disregard uncertainty values from the UUT. Aim to have the lowest uncertainties as possible, so when performing repeatability or reproducibility tests I am using an 8588A DMM. Possible sources of uncertainty for the CMC are Repeatability, Reproducibility, Ref standard stability, ref standard uncertainty, resolution, and bias. These are what I am using, anyway. I took a look at the specifications of the 5560A:

"The specifications include stability, temperature, and humidity; within specified limits,
linearity, line and load regulation, and the reference standard measurement uncertainty. The
product specifications are provided at a level of confidence of 99 %, k=2.58, normally
distributed. In some cases, additional specifications with a level of confidence of 95 %, k=2,
normally distributed are also listed. Fluke Calibration guarantees product performance to the
99 % level of confidence."

We send this unit in for calibration annually, I am using the 1 year spec @ 95% confidence. I would like to format the CMC with ranges for example 120mV, 1.2V, 12V, 120V and 1020V.  I am using a 100mV test point for reference for this first range. The uncertainty value published and calculated is 0.0000938000V. I took repeatability measurements with the DMM and calculated a STDEV (another uncertainty value) of 0.0000000316V. This is rather insignificant in comparison to the published uncertainty I mentioned. For my Bias check all I did was transfer over the error obtained from the 5560's latest certificate which was 0.0000001900V. Again, extremely insignificant compared to that first value.

Is it safe to say that I can just use these published specifications in my CMC for sourcing DCV? I am very new to this, any help would be greatly appreciated

#### mendip_discovery

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##### Re: Developing a CMC and calculations
« Reply #1 on: April 16, 2024, 05:14:40 pm »
Until you have some history you are limited to just published specifications.

Did you take into account the thermal EMF caused by the material contacts?

I would avoid having your UoM written as 0.0000938000V, first, there needs to be a space between the number and the V. But I would refer it as 93.8 µV but you need round to two digits so 94 µV.

I just looked at my UoM for my Transmille and I have 7.5 µV at 100 mV. I will double-check this once I have cooked dinner.

EDIT:
Now that dinner has been dealt with.

Taking assumption,
9.3 µV/V + 0.8 µV for 1yr 95% spec.
0.01 µV Resolution
0.0316 µV Repeatabilty
1.2 µV to cover 0.3 µV/°C over a ± 2 °C swing of temp

I don't know your Imported UoM so I can take a stab at 4.9 µV/V from Fluke's Schedule in the UK

I get an Uncertainty of 2 µV at 100 mV. But it would be best to quote yours at FS, so 2.2 µV.

Remember it is fine having a low number but you have to prove you can achieve this and maintain it. So it is advisable to add a bit extra at first just so you have room to move if it starts to drift out.

Start doing a monthly cross-check between the multimeter and calibrator. Having some data will help you.

« Last Edit: April 16, 2024, 06:04:41 pm by mendip_discovery »
Motorcyclist, Nerd, and I work in a Calibration Lab :-)
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So everyone is clear, Calibration = Taking Measurement against a known source, Verification = Checking Calibration against Specification, Adjustment = Adjusting the unit to be within specifications.

#### moosebiscuit

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##### Re: Developing a CMC and calculations
« Reply #2 on: April 16, 2024, 06:36:17 pm »

Quote
Did you take into account the thermal EMF caused by the material contacts?

What would your recommendation be? For most general applications we use the Pomona banana leads, is this characteristic published anywhere?

Thank you for your input regarding the two digits. I wanted to play with the full numbers straight before making that conversion if that makes sense.

Quote
1.2 µV to cover 0.3 µV/°C over a ± 2 °C swing of temp

I am curious as to how you came up with these numbers. Referring to my quote in the original post, isn't temperature already accounted for here: 9.3 µV/V + 0.8 µV? Or am I misinterpreting it? Also, when you mention importing UoM, are you referring to taking the expanded uncertainty from my certificate's 100mV point? If so, should I divide it by their coverage factor of 2 and then simply add it to my values?

#### mendip_discovery

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##### Re: Developing a CMC and calculations
« Reply #3 on: April 16, 2024, 07:20:05 pm »
Quote
Did you take into account the thermal EMF caused by the material contacts?
Quote
1.2 µV to cover 0.3 µV/°C over a ± 2 °C swing of temp

I am curious as to how you came up with these numbers.

"Watch Out for Those Thermoelectric Voltages!" by Martin L. Kidd of Fluke using the Copper > Gold value of 0.3 µV per °C

Quote
Referring to my quote in the original post, isn't temperature already accounted for here: 9.3 µV/V + 0.8 µV? Or am I misinterpreting it? Also, when you mention importing UoM, are you referring to taking the expanded uncertainty from my certificate's 100mV point? If so, should I divide it by their coverage factor of 2 and then simply add it to my values?

Yes temp is, but the emf of the leads isn't included. It's worth noting in any procedures to watch out for issues if using the current features and then trying to do 120 mV measurements.

If the budget is for the range then pick the worst values from the range. With imported it gets divided by two in the maths anyway.

Do a screenshot of your maths and I will take a squint at it.
Motorcyclist, Nerd, and I work in a Calibration Lab :-)
--
So everyone is clear, Calibration = Taking Measurement against a known source, Verification = Checking Calibration against Specification, Adjustment = Adjusting the unit to be within specifications.

#### moosebiscuit

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##### Re: Developing a CMC and calculations
« Reply #4 on: April 16, 2024, 08:01:12 pm »
I attached the document I am using for this. Here is what I know -

-Sensitivity coefficient stays as 1 because units are all the same here

-I believe my Type's are correct

-Distribution.. I'm about to make everything Normal because this topic seems to always go over my head

-Divisor kind of makes sense, it is dependent on the distribution.

-Degrees of Freedom, I believe this value is just a representation of how many measurements were taken?

-(c^4*u^4)/v <---- I am not sure what this column is, does this look familiar?

#### mendip_discovery

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##### Re: Developing a CMC and calculations
« Reply #5 on: April 17, 2024, 02:13:09 am »
Safer to go rectangular if you are ever unsure.

There are commonly two types of Normal,  Normal (95%) and Normal (68%). The first is for things like Imported Uncertainty as that is K=2 95.45% and will have a divisor of 2. The latter is for things like repeatability so has a divisor of 1.

Not sure what Bias is. Why is it being included?

Its 3am here in the UK, so this is just a quick reply. I will have a look at your other questions a bit later.
Motorcyclist, Nerd, and I work in a Calibration Lab :-)
--
So everyone is clear, Calibration = Taking Measurement against a known source, Verification = Checking Calibration against Specification, Adjustment = Adjusting the unit to be within specifications.

#### EC8010

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##### Re: Developing a CMC and calculations
« Reply #6 on: April 17, 2024, 04:03:43 pm »
-Degrees of Freedom, I believe this value is just a representation of how many measurements were taken?

Not quite. The number of degrees of freedom is the number of variables involved. So if you calculated a result from variables of V, C, and T, you would have three degrees of freedom. The significance comes when you calculate the standard error of your fit from plotting a load of measured points and fitting them. Standard error is calculated very similarly to standard deviation. For standard deviation, you calculate an average value. Then you calculate individual deviations from that average, square them (to stop negative deviations cancelling positive), sum them and divide by the number of values to get the mean, then take the square root (Root of the Mean of the Squares, familiar?). For standard error, you calculate individual proportionate deviations from the fitted value at that point (measured/fitted -1), square them, sum them and divide by the number of values less the number of degrees of freedom, then take the square root of the result. The result is usually expressed as a percentage.

If you only have half a dozen points the number of degrees of freedom becomes very important.

And all of the above assumes normal distributions. If you have popcorn noise, that is not a normal distribution, but random switching between two normal distributions. I'm afraid that's where I hit my statistical limit.
« Last Edit: April 17, 2024, 04:08:22 pm by EC8010 »

#### mendip_discovery

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##### Re: Developing a CMC and calculations
« Reply #7 on: April 17, 2024, 05:43:56 pm »
I attached the document I am using for this.

That helps. I have a basic Excel sheet I can upload that might be a bit neater.

Quote
-Sensitivity coefficient stays as 1 because units are all the same here

Yup though you could add 4°C as a value, then 0.3 is sensitivity and that will do cover the EMF.

Quote
-I believe my Type's are correct

Yup they seem ok.

Quote
-Distribution.. I'm about to make everything Normal because this topic seems to always go over my head

I think this is where you went a little wrong. You have some Normal 1 which should be normal 2, and some that would be best suited to rectangular. Often when in doubt it's considered safer to go for Rectangular.

Quote
-Divisor kind of makes sense, it is dependent on the distribution.

True. Though when I went through the budget I inherited I found a few that were wrong.

Quote
-Degrees of Freedom, I believe this value is just a representation of how many measurements were taken?

Yup, most of yours will be infinite except for the repeatability. Which will be n-1 where n is the number of readings you took during the repeatability.

Quote
-(c^4*u^4)/v <---- I am not sure what this column is, does this look familiar?

Not off the top of my head, but will look to see if I have seen it elsewhere.

I was hoping to be home tonight but I am now in a pub in Neath, Wales. So apologies if my typing is a little rubbish. I am on da phone.
Motorcyclist, Nerd, and I work in a Calibration Lab :-)
--
So everyone is clear, Calibration = Taking Measurement against a known source, Verification = Checking Calibration against Specification, Adjustment = Adjusting the unit to be within specifications.

Smf