Hi, welcome back to our calibration series. This is the third in the series on measurement
uncertainty and I'm Bob Stern, senior metrologist at Agilent Technologies. You know, measurement
uncertainty is one of those topics that a lot of people easily get confused on and it
really doesn't have to be that hard.
The way I like to show this is with this diagram here. If I have a two sided specification,
meaning there is an upper and a lower, if I get a measured result, the red dot as you
see it there, and it's well outside of the upper specification, everyone knows that's
a fail. And similarly, if I have a measured point that's well inside of the specification,
everyone knows that's a pass. Where the confusion comes about is when you have a measured
point that is either just barely inside or just barely outside the specification and
then the question is, can I believe that measurement?
We never know exactly the true result. So the best you can do is to come up with a statistical
interval over which you can say the measurement is at least between here and here, and that's
really what measurement uncertainty is all about.
So, let's take a look at the formal definition of measurement uncertainty. It is formally
defined as a parameter associated with the result of a measurement that characterizes
the dispersion of the values that could reasonably be attributed to the measurand, that's metrology
speak for the measurement, when you read that, you might be wondering, so what does that
mean? And I have a short hand way that I like to show this, bottom line, what we want to
know is how accurate is the measurement.
It's that simple.
What I would like to do is just quickly draw a distinction between accuracy and measurement
uncertainty.
Let's take a look at how does a metrologist versus an engineer examine the accuracy of
a measurement. So an engineer who is responsible for measurements will develop a system accuracy
by evaluating a measurement and they are going to look closely at the accuracy of any key
specs that matter, they are going to decide if those individual error contributors are
independent and they are going to come up with some way of weighting each of the factors
and combining them into an equation in an appropriate fashion.
All right, so what does a metrologist do? They do almost exactly the same thing, except
they follow all of these different standards that you see here. What we are talking about
in this module is the guide for the expression for uncertainty of measurements.
Engineers and metrologists have essentially the same job, they just talk a different vocabulary.
How do you accomplish and make a error budget using the guide for expression of uncertainty
measurement. So here is the general outline. You analyze the sources of error. You come
up with a measurement equation for each of the performance tests and then you model the
errors and then you combine them per the outlines of the GUM and then finally, as always, you
validate.
If we dive in just a little bit more specifically, these would be the specific steps that you
would take.
We are going to take a power sensor and we are going to take a fairly common measurement,
most power sensors have a linearity specification. The definition of power linearity is really
just the difference in percent between a relative change that of a known change by a reference
power source and the amount that you measure with the power sensor itself.
Now let's move to step two. We start beginning with a model expressing the incident power
on the sensor to the metered value and you see that equation over there on the right
the second one down. Then we use a model expressing the power levels at the various points of
a directional coupler and now the measurand can be expressed as a function of the input
quantities and that's combining these two equations, you see that down below on the
bottom there.
Now let's move to step three. The equation of the top is the general form from the guide
on how you calculate measurement uncertainty and you can see the definitions of all the
variables there. When we put the previous equation that we had into the upper one there,
the actual equation that you would use is showing all along the bottom there and so
that's something that you could substitute values in for each of the coefficients and
then use a computer to calculate that at each point.
What I have got in my hand right now is the test support document that's associated
with our high performance spectrum analyzer series. Earlier on, you saw in one of our
other modules the list of over 40 performance tests that we have for this instrument. What
you can see here is a pretty thick document, and what this does is it documents the measurement
uncertainty associated with each one of those tests. So if we were to thumb through here,
we would find a lot of formulas as part of the measurement uncertainty. And those are
what get coded into our automated calibration software so that when we bring you measurement
uncertainty in a report, this is where they are coming from.
So if you look at one of our reports, it ends up measurement uncertainty, it just looks
like a number. So the reason why I was showing you the actual test support document is to
give you a feeling for the work that goes behind that in generating the number that's
on your report. And you see it here both graphically and as a number.
Let's take a look at how measurement uncertainty is referred to formally and the various calibration
standards. There is an international series of calibration standards which is ISO Guide
25 and also the European 45001. Similarly, there was a MIL-STD-45662, which was often
times used in aerospace defense work in the Americas. MIL standards were all repealed
in 1994 and that's when the NCSL organization came out with ANSI Z540-1, which replaced
it at that time. The ISO guide for expression of uncertainty measurement came out in 1995
and pretty much thereafter all the following standards that I'm going to show you refer
to that, ANSI Z540.2 that is simply the American version or the America's version which changes
some of the English for North American readers. 45001 and Guide 25 merged together and became
17025 in 1999 and that continues today after the renewal in 2005. Another standard which
came along in 2007 is Z540.3 and that one makes explicit references to the GUM. And
finally, ILAC-G8 which is very important to many customers on how do you comply with specifications,
makes specific references to the GUM as does ILAC P14 which is a policy document that came
out in 2010 for when you use the accreditation symbol you must have the GUM measurement uncertainty
included in the report.
So again, we'll go back to our chart where we have the two-sided specification and let's
say we have two measurement results that are actually the same result and they are from
two different calibration labs. Now I'm going to put in the ISO GUM measurement uncertainty
associated with each of those measurements. So in laboratory A, in the yellow, you see
a fairly small interval. In laboratory B, you see a fairly larger interval. Now you
might have noticed on the slides that were slipping by before that we had highlighted
in yellow that measurement uncertainty is essentially a statistical standard deviation.
And that's important because those of you who know statistics know that if you for reasonable
distributions for which most instruments fall, if you take two of those and in the metrology
parlance, they say K equals 2, you get the 95 percent expanded uncertainty interval.
That's a really important term because what it says is, we don't really know the true
measurement of either A or B, but what we do know is that there is a 95 percent coverage
interval where the true result could be, between the yellow marks or between the two red marks.
Those are pretty different.
If you were to look at the intervals outside of the specification either above the upper
or below the lower those represent where your true measurement could be and obviously if
that's the case, then you measured the instrument to pass when in fact, it didn't. So hopefully,
you can see having a smaller 95 percent expanded interval is a really important thing because
that takes the doubt of where the true measurement really could be and keeps it to the minimum.
The actual instrument accuracy that you can depend on is not just looking at the data
sheet. What you can depend on is only as good as the measurement uncertainty from your last
calibration. So, I hope that you can see that this is not just some esoteric concept. This
is really important.
In fact, at Agilent, we think it's so important, that we actually rearranged all of our calibration
services and the naming of those so that people could easily see that we have an Agilent calibration
service. We have the same service, but also with reported uncertainties and we have another
one with guard banding that I'll get into in a second.
Here I want to call your attention to the fact that the ISO GUM was first published
in 1995. At Agilent, we have been using that in new product introductions ever since about
1996 and that's why we are in a position to offer calibration service as you see circled
in red here for more than 700 instruments.
Now the exact table that you just saw there varies just a little bit worldwide and you
should be able to click on which region you are in here on the left hand side and see
the exact particular table for your region.
Now you might have noticed there that I went over a little quickly the Agilent Cal plus
uncertainties plus guard banding. I can show you diagrammatically what that means. Supposed
you have a measurement as received which is inside the specification, but a portion of
your uncertainty interval goes outside of that specification. Well, the little area
there in red represents the risk that the instrument may in fact be out of specification.
Some of our customers tell us that they cannot afford risk, so what we then do with guard
banding is we take that same expanded measurement uncertainty and then we establish on the yellow
dotted line a tighter acceptance limit and then we readjust and what we end up with after
adjusting is a measurement result like this.
So, this represents the lowest risk calibration, risk in terms of the result that's reported
maybe incorrect and this is, in fact, if you need the highest insurance that your instrument
meets the specification, for example, like new from the factory, then this is the calibration
service that would be best for you. We provide choices because not everyone needs this, but
for those who do, this is why we have it and now you can understand what it is and if it's
right for you.
This concludes the module on measurement uncertainty, we are going to reconvene with traceability
and I hope to see you there. Thank you.