Trying to understand measurement uncertainty - Page 1
Forum section: electronics / general

author: Dexter_Bunco
author_rank: Contributor
timestamp: June 29, 2019, 04:12:00 pm
content: For fear of revealing my own ignorance, I struggle to conceptualize measurement uncertainty. I can do the math, no problem. What I lack is the understanding of why it works this way. This is becoming problematic as I develop automated procedures which calculate uncertainties for techs behind the scenes. So far, I have been using previously written code as a crutch but this is becoming problematic as I find more and more unique situations were I actually do need to understand this on a conceptual level. So let me toss you some code that Fluke gave me as an example.This is an example of a 5A/100mV shunt as the UUT, using a 5522A as the current source and an 8508A as the DMMFluke calculates the 5522A accuracy as follows:@SourceAcc = ((REFACC() / CONF("Fluke 5522A") ) / @Val_5522) * 100orSource Accuracy = Reference accuracy (let's assume 5A DC which is 0.05% + 0.0005) / The confidence level (the K factor) / The source's output value (so, 5) * 100In numbersSource Accuracy = ((0.003 / 2.58) / 5) * 100 = 0.02325581Then they do the same for the 8508A (lets assume 100mV):@MeterAcc = ((REFACC() / CONF("Fluke 8508A") ) / @Actual) * 100Meter Accuracy = ((720E-9 / 2.58) / 0.1) * 100 = 2.790697E-4Then these are RSS'd togetherL = RSS2(@SourceAcc, @MeterAcc) * 2 = 4.65149E-2The purpose of the *2 is because Fluke expresses their uncertainties with K = 2Lastly, this is expressed as a percentage of nominal. So, in this example, the shunt is a 20mOhm Shunt so the system accuracy is then 4.65E-2% of 20mOhm. So ~9.3µΩSo, here are some questions I have:1) Why would you divide the reference accuracy by the sigma value?2) Why would you further divide this dividend by the real value?3) What is the actual significance of having a 2 sigma confidence. Is this just something the industry just decided and we are running with?4) Math me hard in teh murdle maf haf blargle gurgle....Know any good books to read on this subject when I'm feeling masochistic?

author: FransW
author_rank: Frequent Contributor
timestamp: June 29, 2019, 08:58:18 pm
content: To 1; wiki:https://en.wikipedia.org/wiki/Coefficient_of_variationThe coefficient of variation (CV) is defined as the ratio of the standard deviation sigma to the mean cv=sigma/mu : It shows the extent of variability in relation to the mean of the population.To 3; Wiki:https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_ruleIn statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively.

author: dl1640
author_rank: Regular Contributor
timestamp: June 30, 2019, 09:56:04 am
content: https://www.bipm.org/en/publications/guides/gum.htmlI think the GUM has some practical examples.

author: Magnificent Bastard
author_rank: Regular Contributor
timestamp: June 30, 2019, 05:16:48 pm
content: Fluke specs their instruments at 99%, hence the "k-factor" of 2.58 in your equations. It is important to reduce the uncertainty of the sources to a "k-factor" of 1, before doing the RSS calculation (just the square root of the sum of the squares of ALL of the known or presumed error sources-- not just the instruments). Then, when you have that answer, you then multiply by the "k-factor" that you want to base your uncertainty on-- it is usually 2 or 3, but Fluke uses the 2.58 to get very close to 99%-- (I think Fluke has a whitepaper on why they do that). You also need to factor in other sources of uncertainty, including technician error (measure by 3 different techs, three times in one day, and for voltage references repeat that cycle for 3 days). There are some effects that come into play when you are running large currents through a shunt-- the Thompson effect, the Johnston effect, and the Peltier effect. These can add up to a couple of ppm to the uncertainty. (IIRC, Ohms-Labs has a whitepaper on measuring shunts.)Shunts should also be measured at 10%, 20%, 30%, ... , 100% power, and should be checked (at 10% power) in an alcohol or oil bath at 0C, 25C and 50C--- this will help to establish the power coefficient and the temperature coefficients (alpha, beta).I would also obtain a "golden shunt" that is calibrated at a lab that has at least 4 times better uncertainty than your lab-- (Ohms-Labs?)--- then compare the UUT with the shunt with the known value (and uncertainty), using the "substitution method". Have that shunt calibrated on a regular basis. This will help you to monitor your process so that an instrument or a technician error does not "spoil the soup", and can help lower the uncertainty of your measurements.

author: thermistor-guy
author_rank: Frequent Contributor
timestamp: June 30, 2019, 11:17:42 pm
content: Quote from: Dexter_Bunco on June 29, 2019, 04:12:00 pmYeah, prettty much:https://physics.nist.gov/cuu/Uncertainty/coverage.htmlSome research papers written by metrologists, for metrologists, use k=1. If you were doing a critical experiment in physics, to test a new controversial theory, you might use k=3 or more. Industrial calibration labs typically use k=2 for their cal. certificates they give to customers.

author: Dexter_Bunco
author_rank: Contributor
timestamp: July 01, 2019, 12:36:59 pm
content: FransW, dl1640 & thermistor-guy - Thank you for the links and details. I'll dive into them this evening.Magnificent Bastard - Appreciate the explanation! I not actually calibrating shunts, though. This was just a hypothetical that Fluke presented when I was at their headquarters a few weeks ago. They use this same method of uncertainty calculation for most things so it's important that I learn to conceptualize it. Your methodology might be a tad intense for a 1% shunt used for engineering development purposes.