# Component Calibration - Overall TUR for a loop? ANSI/NCSL Z-540 Standard Section 10.2

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#### John McIntosh

I am looking for clarification on the following statements from the ANSI/NCSL Z-540 Standard and Handbook :
Section 10.2 "…if such techniques or analyses are not used, then the collective uncertainty of the measurement standards shall not exceed 25% of the acceptable tolerance (e.g., manufacturer's specification) for each characteristic of the measuring and test equipment being calibrated or verified."

"A TAR of 4:1 means that the tolerance of a parameter (specification) being tested is equal to or greater than four times the combination of the uncertainties of all the measurement standards employed in the test."

I am in the process of promoting the use of uncertainty analysis techniques within our organization; however, we currently rely on the "4 to 1" rule for calibration of process instrumentation.

The catch is that for some loops we perform "component" calibrations. Typically, these calibrations employ two M&TE to characterize a sensor and a third M&TE to simulate an input to a transmitter or display. The tolerance being tested results from the combination of both of the independent calibrations. An example would be a thermocouple calibration and calibration of a temperature transmitter to a computer system.

My problem comes in applying the Z-540 statements to the loop calibration. Each calibration uses an M&TE transfer standard that has a tolerance 4 times better than the characteristic being calibrated. However Z-540 uses the terms "collective uncertainty" and "combination of uncertainties". How does one combine or collect uncertainties for independent characteristics in order to come up with an overall TAR for a loop? In my example, I would need to combine the uncertainties of my temperature standard (deg C), my meter (uV) and my voltage source (uV). I have been told that although each component calibration uses equipment that meets 4:1, my loop TAR would not necessarily meet 4:1.
Any direction or comments would be greatly appreciated.

#### Jerry Eldred

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I don't have all my documents in front of me. But as my recollection serves me, there is a common method for calculating TAR (or TUR - Test Uncertainty Ratio) called RSS (Root Sum Square).

In this method. You square the tolerance for each standard used, add the squares together, then derive the square root of that sum.

For example if you use three standards. One has a tolerance of +/-1%, the second has a tolerance of +/-.1%, and the third standard has a tolerance of +/-1.5%. You square each of those (I get 1, 0.01, and 2.25). The sum of the squares is 3.26. The square root of that is 1.805% (which would be the RSS uncertainty).

There are varying opinions on this, but RSS is accepted by many in the metrology field.

Depending on what depth you want, there are also the aspects of confidence level. That is, in your calibration recall system, you set calibration intervals based on a percent confidence the units will remain in tolerance (95% is quite common). All items included in the RSS should be maintained at calibration intervals established based on the same confidence level. If you happen to have a copy of Fluke Corporation's book, "Calibration: Philosophy In Practice", 2nd Edition, it has a description on page 22-4 and 22-5 of this method of combining uncertainties. NCSL also has (I believe) a recommended practice on this, which I can not locate at the moment.

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#### Ryan Wilde

John wrote:

How does one combine or collect uncertainties for independent characteristics in order to come up with an overall TAR for a loop? In my example, I would need to combine the uncertainties of my temperature standard (deg C), my meter (uV) and my voltage source (uV)

It seems that you have two pieces already in µV. I would bet that the uncertainty of your temp standard can be converted. Say your standard is ±1°C, and your UUT nominally measures 1 µV/°C. Your uncertainty of your standard in like terms would be ± 1 µV.

I have been told that although each component calibration uses equipment that meets 4:1, my loop TAR would not necessarily meet 4:1

This is true. Say your component tolerance is ±10µV, Your meter is ±2µV, your voltage source is ±2µV, and your converted temperature standard uncertainty is ±2µV.

Your combined uncertainty of standards would be SQR(2^2 + 2^2 + 2^2), or 3.464µV. In this case, you do not meet TUR.

One big problem with my overly simplified analogy is the lack of use of distribution. If these are straight manufacturer's specifications, then I actually have a rectangular distribution (which means it is within this range, but there is an equal possibility that the actual error is anywhere within the range). Rectangular distribution is the total tolerance divided by the square root of 3. In the case of ±2µV, it would be 2/SQR(3), or 1.155 in a normal distribution. Using this pattern, your combined uncertainty of standards would be SQR(1.155^2 + 1.155^2 + 1.155^2), or approximately 2. This is a single standard distribution, so it is not quite adequate. The accepted use in metrology these days is two standard distributions (k=2). So now we have to multiply our standard distribution by 2 (the k), which is 4 (I know, that's a duh). So our uncertainty of standards would be ±4µV, which again is inadequate, but even worse.

Hope this helps!

Ryan

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#### John McIntosh

Thank you!

Although I have used "dithering" to come up with sensitivity coefficients for my uncertainty analyses, I did not know I could use a characteristic conversion to convert my standard's uncertainty to the same units as my meter and voltage source. In this case I can take advantage of the NIST monagraph tables for thermocouples or DIN tables for RTDs to determine the conversion for my temperature standard over the range of interest.

Fortunately my standards are calibrated at an on-site calibration laboratory and their uncertainties are reported with k=2.
Thanks again. John

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#### assuranceman

John mentions a Z-540 Handbook. Could you tell me where the handbook comes from? This is the second time I have seen a reference to an interpretative handbook.

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#### Ryan Wilde

Hal,

I highly suggest the Z540-1 Handbook also, as it demistifies the standard some.

Ryan

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#### John McIntosh

ANSI/NCSL Standard

Hal,
The American National Standard For Calibration - Calibration Laboratories and Measuring and Test Equipment - General Requirements Handbook (ANSI/NCSL Z540-1-1994 Handbook)is available from NCSL for \$40 (book) \$45 (cd rom)at their website http://www.ncslinternational.org - Link was: /publications/pubs-list.cfm (and other quality related literature websites). Another standard with some interpretation added is the American National Standard for Calibration Systems (ANSI/ASQC M1-1996).
John

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