:mg:
I don't know how to determine the type-B uncertainty because it has many possibilities such as past experience, calibration certificate.

In type-B uncertainty, the formula is varied by different distribution of measurement values (normal, rectangular, triangular, etc.). How do I know what distribution I should use? Does it assume all measurements rectangular distribution with formula 0.5*limit/sq. root of 3?

Also, I found a very good guide for beginner about calibration. I share it to you all.

Hopefully, someone can answer the thread starter's original question.How do I know what distribution I should use? Does it assume all measurements rectangular distribution with formula 0.5*limit/sq. root of 3?

Dear nick1980:

The following link takes you to a nice presentation by FLUKE on measurement uncertainties.

http://www.npl.co.uk/electromagnetic/dclf/tech-transfer/fluke.pdf

See page 12, which I quote. Type B uncertainties are said to be 1 standard deviation estimates of the likely range of values the value may have (Often considered as systematic uncertainty). See also the following article by Dr. Stephen Phillips of NIST.

http://www.mel.nist.gov/proj/pdf/MeasurementUncertainCA34A.pdf

Charmed :)

Nick,
Welcome to the Cove Forums!

I had asked a similar question in one of the threads here..It may help if you go through it:
http://elsmar.com/Forums/showthread.php?t=5689

I'm sure our calibration experts on board will chip in with more useful replies.

Thanks Charmed!!

From your reference, 1 stand deviation=type-B uncertainty. Can you tell me why?

It's because I found many different formula to calculate type-B uncertainty for normal, rectangular, triangular or uniform distribution.

If type-B is really equal to 1 s.d., that's so great.
It makes the calculation easier a lot. :o

I found a definition of it:

standard uncertainty = one standard deviation.
But in order to minimize the possibility of mistakes at a later stage of the evaluation, it is sometimes necessary to multiply values of type-A estimated standard deviations and type-B standard deviations by suitable sensitivity coefficient to bring them to the same units as the measurand or to take account of other factoes in the funcitonal relationship between input quantities and output quantity.

So what standard uncertainty equals to ? one s.d.? or typeA+typeB uncertainties? (type-A estimated standard deviations = type-A uncertainty??same meaning?)

So what standard uncertainty equals to ? one s.d.? or typeA+typeB uncertainties? (type-A estimated standard deviations = type-A uncertainty??same meaning?)

Please read the article by Stephen Phillips which explains these things nicely, which I gave link to. I will check another source and get back to you.

Charmed :)

Nick,

There are two answers going on here, and I will presume you are in a cal lab, not a test lab.

Standard uncertainty is one standard diviation, or approximately 67%. Expanded uncertainty is two standard diviations, or approximately 95%.

Type B uncertainty distribution model will vary depending on the influence. GENERALLY, the Type B is a normal distribution. GENERALLY, the Type A is rectangular, in that the true value can lie anywhere within the uncertainty range. These are rules of thumb, not hard and fast.

Type B can include the environmental concerns such as temp, RH, vibration, and dust. Recognize that the environmental influences might change. In some cases for example, temp and RH changes have no effect over a wide range. In the test lab world, that is common. Other effects include calibration uncertainty taken from the accredited calibration cert (plug and play number), time, viewing angles, technician proficiency, almost ANYTHING that can affect the measurement to a measurable degree.

Hope this helps.

Hershal

For most of my concern is that it's so trouble and time-consuming to calibrate one equipment with so complicated calculations, esp. type-B uncertainty.

I need to guess all the possibilities of type-B uncertainty. I never know it's correct or not. It's just my assumption.

If possible, I will assume type-B uncertainty as 1 standard deviation to simplify my calbration process.

Any experience can share?

For most of my concern is that it's so trouble and time-consuming to calibrate one equipment with so complicated calculations, esp. type-B uncertainty.

I need to guess all the possibilities of type-B uncertainty. I never know it's correct or not. It's just my assumption.

If possible, I will assume type-B uncertainty as 1 standard deviation to simplify my calbration process.

Any experience can share?

Hi Nick,
I will try to help you in the best way I can.

One of the basic things in the GUM is that the square of all uncertainties should be added together at the 1 std dev. level. (You should not add an uncertainty on 1 std.dev with another that is expressed in e.g. 2.std.dev).

In order to do this you need to know the distribution and the coverage factor.
E.g. resolution is rectangular and the accuracy from a manufacturer might be normal distributed (or worst case=rectangular).

To get the 1-std.dev uncertainty (def. = standard uncertainty)for the resolution you divide the resolution with 2 (as the uncertainty is half the resolution) and the you divide it with the sqt.rot of 3 (due to the distribution).
To get the 1-std.dev uncertainty for the accuracy you need to know what coverage factor they used (2 =appr. 95% and 3 = appr. 99%).
The accuracy value from the manufacturer has to be divided with the coverage factor to get the 1 .std.dev. uncertainty.

In order to add all squared uncertainties you will also have to use the correct sensitivity coefficient.

In the end when you follow the GUM-method, you multiply the total uncertainty with the coverage factor 2 to get the expanded total uncertainty.

Did this give you any better understanding ? Even if it is not a in deept explanation.

Please also check the EA-10 documents on this link http://www.european-accreditation.org/documents.html where several examples are availiable.

Good luck, Martin :confused:

Correction
Coverage factor 1 = appr. 68%
Coverage factor 2.58 = 99%
Coverage factor 3 = 99,7%

//Martin

There seems to be some confusion on type-A versus type-B, and standard deviations, standard uncertainties and coverage factors.

A very short tutorial: The basics of the GUM method is to regard any measurand (a quantity you wish to measure and all the influence factors affecting its value) as random variables, i.e. not fixed values, but something that can assume a range of values, each with some probability. Hence, you can describe a measurand by a probability density function (pdf). The GUM method then states: 1) The value of the measurand is an estimate of the mean of the pdf. 2) The standard uncertainty of the value is the square root of an estimate of the variance of the pdf.

How do I find the pdf? The GUM describes two methods: Type-A) The pdf or the parameters of the pdf are estimated using statistical methods, or Type-B) the pdf is selected by other methods.

How do I do a Type-A? The simplest Type-A estimation is to do repeated observations (say, readings of some meter). The best estimate of the mean is the artihmetic average, the square root of the best estimate of the variance is the standard deviation. Hence, in this case the value = the average, the standard uncertainty = the standard deviation.

How do I do Type-B? Well, the method is, that you have to choose an appropriate pdf. The simplest is the so-called rectangular or uniform distribution: There is equal probability that the measurand takes any value in the interval 'a' to 'b'. Doing the math on the mean and variance of this distribution gives you: the mean = (b-a)/2, the standard uncertainty = square root of variance = (b-a)/sqrt(12). If the interval is -a to +a, or 0 +/- a, the result is: mean = 0, standard uncertainty = a/sqrt(3).

So, if you can state: "I'm pretty sure this measurand, say, an influence factor on the quantity you wish to determine, say, the temperature is somewhere in the interval 22 C to 24 C. I have no reason to beleive that any temperature in this interval is more likely than another." Hence, you assign a rectangular distribution for the interval 23 C +/- 1 C, thus the mean = 23 C, the standard deviation = 1/sqrt(3) = 0,58 C. If the influence on the quantity you wish to determine has, say, a temperature coefficient of 1 % per C, the combined effect is thus a contribution to the combined standard uncertainty of 1 %/C * 0,58 C = 0,58 %. As some earlier poster noted, you must then add all these contributions in quadrature (i.e. sum the squares and take the square root) to get the final standard uncertainty.

Your uncertainty budget should document the assumptions you have made, e.g. the distribution you chose and its parameters. For a general measurement setup, you may only need to do this once; re-use of assumptions is fine.

The expanded uncertainty is then the standard uncertainty multiplied by a factor k determined by how large a coverage probability you want, i.e. the probability that the 'true value' is in the interval: value +/- k * standard uncertainty ... provided that your assumptions hold, that is.

[There are several assumptions in the last statement, I know (model function is a simple sum, no second-order contributions, etc.]

As Martin suggested, take a look at http://www.european-accreditation.org/documents.html; I recommend EA-4/02, which gives a resonably condensed full story and several examples.

Hans.