Uncertainty Analysis Formula

Hutch,

You can conduct a gauge R&R (repeatability and reproducibility) study (sometimes called a Measurement System Analysis) on the gauge to determine the precision of its measurements. A quick estimate can be obtained by measuring the same set of "parts" multiple times (usually by 2 or 3 opeartors) and then doing a little statistical analysis of the variance in results. Because of the nature of things measured by pressure gauges, you'll have to treat it as an MSA for a destructive test.

For the a pressure gauge, I'd set up the study as follows.

1) Get a pressurizable vessel, and plumb a source of pressurized air into the vessel. Put a regulator on the intake side to hold the vessel at constant pressure.

2) ASSUME (key point) that any variations in pressure that are measured are attribultable to the gauge rather than to the pressure regulator (better use a pretty high quality regulator).

3) Plumb a 'T' out of the vessel with the pressure gauge on it. You'll want a valve between the 'T' and the vessel, and a 'bleed off' valve for the 'T.'

4) Set the regulator to an arbitrary pressure in the range you want to use the gauge to measure.

5) Take multiple pressure readings by a) closing off the 'bleed off' valve on the 'T' b) opening the valve between the vessel and the 'T' c) recording the pressure reading d) closing the valve between the vessel and the 'T' e) bleeding off the pressure in the 'T' f) go back to a)

6) Set the regulator to a different pressure in or near the range of interest and repeat step 5. Do this for 5 to 10 different settings on the regulator.

7) Run the analysis of the data.

If you need a hand with the analysis, find a good stats person, a Six Sigma Black Belt, a Quality guru, or similarly disturbed person to help out. As a Six Sigma Black Belt, I can vouch that such folks are a little disturbed but very helpful.

What you do is a comparative calibration with a reference which was calibrated against an other reference of lower uncertainty. You should thus have at you disposal the uncertainty of your reference.

The use of air is only to be accepted it you analyse a low pressure gauge, if not it is better to use a fluid which will not interfere with the medium with which the gage will work0 You could also use a dad weight calibrating system but it is much more expensive.

What you need is a pressure source which allows a reading on both gages and which maintains pressure constant for a time long enough for the 2 readings. If you use a pressure regulator it must have a good dynamic behaviour and be stable in time (not all are) in the pressure range where you make the calibration.

What you get is a series of readings (pairs of values). The first step is to consider your reference gauge as "perfect" and determine the differences between the reference gauge and the to be calibrated one.

Those differences are to be considered as the "errors" of the gauge and are us for the uncertainty definition. It is important as stressed already to measure at different pressure levels but also several times at each level. The minimal number of readings per level should not be less 5 (better 10...15). Obtained data are processed to obtain as well the dispersion as function of the pressure as the non linearity of calibrated gauge with respect to the reference.

But you should not forget that the reference is in fact NOT perfect so that for the final uncertainty of the gauge results AND reference uncertainty MUST be added (not algebraically or arithmetically but in a probabilistic manner).

For each measurements group you should compute the mean value and the standard deviation. The first gives the relative non linearity of you gauge and the second the dispersion of its behaviour.

It is not so complicated and in every book about statistics or measurements you can get ALL necessary input and be sure even if you make the computations you will stay normal and not be disturbed by them. For all computations you can use EXCEL which has all above mentioned functions.

Unit under test tolerance divided by standard tolerance equals TAR (total accuracy ratio). To determine TUR (Total uncertainty ratio) is considerably more complicated as the previous two posters answered. Many times TAR is acceptable to define the turn down ratio. Depends if you are trying to meet some ISO spec or simply trying to determine if the calibration is satisfactory for your use.

Guest:

Yes, I am trying to meet ISO spec. (ISO17025). Thanks.