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Repeatability vs. Instrument Specifications

B

brianpbg

#1
I use specifications for a measuring instruments as a Type-B standard uncertainties in uncertainty calculations per GUM.

Some external standards (such as ISO 17025 via A2LA) seem to require specific values for repeatability as Type-A standard uncertainties.

I feel that the repeatability of the measuring instruments is already captured in their specifications. If I determined their repeatability and included it in my calculation I feel I would be double-counting their repeatability. I'd rather not have to increase my uncertainties to explicitely accomodate repeatability, but that seems to be the mandate.

Am I missing something?

Thanks,

Brian
 
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D

dv8shane

#2
Re: Repeatabily vs. Instrument Specifications

I use specifications for a measuring instruments as a Type-B standard uncertainties in uncertainty calculations per GUM.

Some external standards (such as ISO 17025 via A2LA) seem to require specific values for repeatability as Type-A standard uncertainties.

I feel that the repeatability of the measuring instruments is already captured in their specifications. If I determined their repeatability and included it in my calculation I feel I would be double-counting their repeatability. I'd rather not have to increase my uncertainties to explicitely accomodate repeatability, but that seems to be the mandate.

Am I missing something?

Thanks,

Brian
Yes you are missing the point that repeatability and reproducibility are both contributors to over all uncertainty. You take the same measurement 20 times the odds are there will be variation this has nothing to do with specification. Uncertainty includes everything in the measurement system including the ability of the UUT to reproduce the same result consistently
 
N

NumberCruncher

#3
I use specifications for a measuring instruments as a Type-B standard uncertainties in uncertainty calculations per GUM.

Some external standards (such as ISO 17025 via A2LA) seem to require specific values for repeatability as Type-A standard uncertainties.

I feel that the repeatability of the measuring instruments is already captured in their specifications. If I determined their repeatability and included it in my calculation I feel I would be double-counting their repeatability. I'd rather not have to increase my uncertainties to explicitely accomodate repeatability, but that seems to be the mandate.

Am I missing something?

Thanks,

Brian

Hi Brian

It's well known that the dwarfs made Thor's hammer Mjollnir, which was a little short in the handle. What is less well known is the dwarfs also made a micrometer for Thor (played by Arnold Schwarzenegger). This micrometer was of equal quality to the hammer and always returned to zero after use (although it was not much use for killing giants, which is why you don't hear much about it).


But the micrometer also had a systematic error. The screw thread pitch was slightly out, so that it always measured 10 microns too big. (The dwarfs were very far sighted by the way, which is why they used metric units over 1000 years before they were invented). The dwarfs were also scared of Thor, so whilst they didn't know exactly what the systematic error was, they included an uncertainty statement which said that the uncertainty in the measurement was +/- 10 microns.

When Thor received the micrometer from Loki (played by Danny DeVito), Thor was suspicious of its accuracy. But since Thor was not too good at statistics, he got Loki to carry out a repeatability study. Loki measured five gauge blocks, twenty times each and estimated the type A uncertainty as +/- 1 micron. When Loki told Thor of the error, Thor was very pleased. "I am making precision pistons for my father's toy train set. They must be correct to the nearest micron or they will not fit. This is perfect!"

However, Loki was deceitful. He had deliberately ignored the 10 micron uncertainty statement given by the dwarfs. "It doesn't matter." he said, "Every measurement will have the same instrument error, so I don't need to include the dwarf's uncertainty statement in my calculations".

After Thor had made the pistons, he gave them to his father Odin (played by Samuel L Jackson) who was initially delighted. "At last I will be able to complete my model of 'The Mallard' ".

But when Odin tried to fit the pistons into the piston rings, they were too loose! Steam would escape from the seals and the train would not work. He demanded to know what had happened, so he ordered his first wife, Frigg, (played by Jessica Alba) to investigate what had happened.

Frigg compiled a report which concluded with the following statement. "Loki failed to take into account the manufacturer's uncertainty in his calculation. He correctly calculated the error due to repeatability, but failed to understand that systematic error is not corrected by repeated measurements"

This, by the way, is the real reason why Loki was bound and left in a cave until the day of Ragnarok. The death of Balder was just an excuse, Odin was actually angry about his toy train.

NC
 
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B

brianpbg

#4
Re: Repeatabily vs. Instrument Specifications

Yes you are missing the point that repeatability and reproducibility are both contributors to over all uncertainty. You take the same measurement 20 times the odds are there will be variation this has nothing to do with specification. Uncertainty includes everything in the measurement system including the ability of the UUT to reproduce the same result consistently
I'm not sure where on the same page.

I tried to be clear that I felt the instrument specification already included repeatability. Since I'd included the instrument specification as a Type-B uncertainty, repeatability would be captured in that term. If it's already captured, there's no reason to count it again.

Now, I notice that you say repeatability has nothing to do with specification. I don't understand what you mean, so that may be where the disconnect lies.

Brian
 
B

brianpbg

#5
Hi Brian

It's well known that the dwarfs made Thor's hammer Mjollnir, which was a little short in the handle. What is less well known is the dwarfs also made a micrometer for Thor (played by Arnold Schwarzenegger). This micrometer was of equal quality to the hammer and always returned to zero after use (although it was not much use for killing giants, which is why you don't hear much about it).


But the micrometer also had a systematic error. The screw thread pitch was slightly out, so that it always measured 10 microns too big. (The dwarfs were very far sighted by the way, which is why they used metric units over 1000 years before they were invented). The dwarfs were also scared of Thor, so whilst they didn't know exactly what the systematic error was, they included an uncertainty statement which said that the uncertainty in the measurement was +/- 10 microns.

When Thor received the micrometer from Loki (played by Danny DeVito), Thor was suspicious of its accuracy. But since Thor was not too good at statistics, he got Loki to carry out a repeatability study. Loki measured five gauge blocks, twenty times each and estimated the type A uncertainty as +/- 1 micron. When Loki told Thor of the error, Thor was very pleased. "I am making precision pistons for my father's toy train set. They must be correct to the nearest micron or they will not fit. This is perfect!"

However, Loki was deceitful. He had deliberately ignored the 10 micron uncertainty statement given by the dwarfs. "It doesn't matter." he said, "Every measurement will have the same instrument error, so I don't need to include the dwarf's uncertainty statement in my calculations".

After Thor had made the pistons, he gave them to his father Odin (played by Samuel L Jackson) who was initially delighted. "At last I will be able to complete my model of 'The Mallard' ".

But when Odin tried to fit the pistons into the piston rings, they were too loose! Steam would escape from the seals and the train would not work. He demanded to know what had happened, so he ordered his first wife, Frigg, (played by Jessica Alba) to investigate what had happened.

Frigg compiled a report which concluded with the following statement. "Loki failed to take into account the manufacturer's uncertainty in his calculation. He correctly calculated the error due to repeatability, but failed to understand that systematic error is not corrected by repeated measurements"

This, by the way, is the real reason why Loki was bound and left in a cave until the day of Ragnarok. The death of Balder was just an excuse, Odin was actually angry about his toy train.

NC
Yes, I've had people say things that imply a perspective that uncertainty is completely defined by Type-A terms. Of course, if that were the case things would be amazingly simple! No GUM, do discussion here. Just run the experiment a bunch of times, get the standard deviation and the uncertainty analysis is complete!

A little twist to this is that the GUM procedure implies determining all the sources of repeatability separately, then folding them in to the measurement equation as Type-A uncertainties. This precludes the sort of simple repeatability test implied by A2LA because that test can't separate out and quantify the various sources of repetability.

Brian .
 
D

dv8shane

#6
Re: Repeatabily vs. Instrument Specifications

I'm not sure where on the same page.


Now, I notice that you say repeatability has nothing to do with specification. I don't understand what you mean, so that may be where the disconnect lies.

Brian
Try this, the accuracy specification says the value should be within X tolerance relative to the calibration standard nominal. Now the actual value you measure can still vary within the specification, and remember you are only reporting one number with ± Y uncertainty. For simple items like a Fluke meter it is a small contributor. Now picture a spectrum analyzer calibration. Multiple instruments with connector/connection repeatability issues repeatability of all the instruments involved, all combined in one measurement system. Say the power meter drifts a couple digits right after you take the measurement, and record the result. Instead of rewriting the number what you do is account for the fact the number is going to change, you do not keep changing what you record
 
N

NumberCruncher

#7
I use specifications for a measuring instruments as a Type-B standard uncertainties in uncertainty calculations per GUM.

Some external standards (such as ISO 17025 via A2LA) seem to require specific values for repeatability as Type-A standard uncertainties.

I feel that the repeatability of the measuring instruments is already captured in their specifications. If I determined their repeatability and included it in my calculation I feel I would be double-counting their repeatability. I'd rather not have to increase my uncertainties to explicitely accomodate repeatability, but that seems to be the mandate.

Am I missing something?

Thanks,

Brian
Hi Brian

In answer to your question about double counting of uncertainty please refer to the following.

JCGM 100:2008
GUM 1995 with minor corrections


"4.3.10 It is important not to “double-count” uncertainty components. If a component of uncertainty arising from a particular effect is obtained from a Type B evaluation, it should be included as an independent component of uncertainty in the calculation of the combined standard uncertainty of the measurement result only to the extent that the effect does not contribute to the observed variability of the observations. This is because the uncertainty due to that portion of the effect that contributes to the observed variability is already included in the component of uncertainty obtained from the statistical analysis of the observations."

You haven't mentioned what you are measuring. For concreteness I will take the simple example of weighing.

You have several sources of error, mechanical repeatability, buoyancy due to air pressure, and I expect more that I haven't thought of. Most of these uncertainties can be combined into a type A uncertainty by repeated weighing of standard lab weights.

However, the lab weights constitute a type B uncertainty. Suppose the the weighs are only verified to +/-1 mg (yes, very poor, but bear with me).

Now, each of your weighs constitutes a systematic error in your measurements. The 1g weight is actually 1.001g (you don't know this). All you know is that when you measure the 1g weight, you get an average of 1.000g. Unfortunately, the actual reading you should be getting is 1.001g. You can't possibly know this. All you know is that, from the certificate, the weight could be anywhere between 0.999g and 1.001g.

All you can do is include the quoted uncertainty from the certificate as a type B estimate in the final uncertainty budget.

I agree with you. Calculating the repeatability from actual measurements, then including the manufacturer's quoted uncertainty would be a case of double counting.

You will need to decide for yourself where the systematic errors arise.

NC
 
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