How to Evaluate Measurement of Uncertainity After Calibration?

Google: mean or absolute deviation.

someone has statistics in their background, GA

There are 4 values in the calibration report from the outside lab.(Following is an example)

1) Specification valus: 25.000 mm

2) Measured value: 25.000 mm

3) Deviation: 0.000 mm

4) Acceptable deviation: 40 um

5) Uncertainty: 8.26 + 9*L (what dose this L stand for?)

Is There a formula for evaluating this uncertainty in order to decide whether this equipment is good enouph for usage)

I think everyone has missed the point that the uncertainty value specified following a calibration is the uncertainty of the calibration itself.

This figure depends on how well the instruments, gauges etc. used for the calibration, and the methods employed, can determine the accuracy of the calibration. It also depends to some extent on the inherent uncertainty of the instrument.

For example, when calibrating a radiation dosemeter, the uncertainty figure would depend on the measurement (integration) time, the doserate, how accurately the applied doserate is known, and what interpretation the technician performing the calibration places on the readings (particularly important for instruments with an "analogue" display (old-fashioned meter type), etc.

I do not know what "L" stands for in this context. If this were an instrument for measuring length, my best guess would be that "L" represents the length of the item being measured.

How all this has any bearing on your "general rule", I cannot conceive.

You never mentioned "what is the instrument" for which you are talking about.

Now, the picture is more clear, though not fully clear. The instrument under calibration is Vernier calliper. The specification value is 25 mm. As I understand this means, the gauge block used for testing the calliper under test is 25 mm thick.

Now this gauge block will have certain uncertainty, as the dimension 25 mm of the gauge itself can not be absolutely 25 mm. It may be 24.99967 mm for example. This dimension itself will again depend upon the temperature of the gauge block (ambient temperature). If we are going to correct (and has to) for the temperature, the temperature measurement itself will have certain uncertainty. Etc. Etc.

I understand from the figures you have given (or I interpret these) as: deviation accepted is 40 micron.

You say that actual deviation observed is 0.000 mm. This may be true only for single reading. If you take many more observations.... not less than 10, the average deviation may not be 0.000 mm. Or may be average deviation of these many readings will be 0.000 mm, with max and min readings quite away from ideal 25 mm.

You have to calculate uncertainty (standard deviation of population) of these all (many more readings). These will be called type A uncertainty. This figure you have overlap with BMC of the gauge block, by root mean square, to get the uncertainty of the all observations.

Deviation is deviation from ideal reading. Uncertainty is figure showing how much you are getting these repeatedly. More the uncertainty figure, less confidence we have in the figure. But if uncertainty is very small figure, and still the deviation is a large figure, we can compensate the actual reading by this large/small deviation, to get the true measurement.

To know more about these concept please read ISO 5168

Now regarding calibration of vernier: Vernier can not be calibrated. It can only be tested to find out the deviations for the already engraved markings. The test certificate figures can be used to correct the measured figures by deviations observed for diffferent dimensions.

Calibration is a process, where we can adjust the displays or indicated figures to match with the master figures. As vernier markings can not be adjusted, it can not be calibrated.

What I mean, I am sure you have understood clearly:

If say vernier when used to measure the gauge block of 25 mm thick, always shows as 24.94, the deviation is -0.6. This means that the surface of the vernier contact face has worn out to that extent or there is some problem with slider of the vernier. Here you can not mark a new line for 25 mm, but whenever you are measuring something around 25 mm, you add 0.06 mm to your indicated value.

Thus, though conventionally it is called calibration, actually it is testing to find the deviations at various mesurement points.

I agree with JohnDG. The uncertainty (of the calibration) has nothing whatsoever to do with the equipment being usable. The uncertainty can be just barely better that the specifications. If the unit is in specs, then it is usable. The problem with the above scenario is that the unit may fail, and need to be adjusted. With better uncertainty, the risk of false failures and false passes will be reduced. A four to one ratio is considered to be a good calibration. A better question to ask is: "Can I get a better calibration (lower uncertainty) from another lab?" If so, "Is it worth the extra cost?"

Thank you all for your valuable comments. The instrument was a vernier calliper.

Let me ask like that: Which figure on the calibration report of an outside calibration lab should be considered for judging the usability of a measurement equipment?

Yes, You will have to do a MSA analysis on the instrument to certify whether it is usable or not.

If R&R is under 10, then it is 100% usable. If R&R between 10 and 30 then it is conditionally acceptable

Else , not acceptable.

Hope this helps