Finding uncertainty values for a measurement made using DAQ

[smenon]

Hi,
I am trying to make an uncertainty estimate of a measuremet that i am doing using DAQ and SCXI. I have checked the site and it gives a good account of the calculation for uncertainty. But i have a NI reference manual that gives me a different formula for the same. I just want to ensure that the right formula is as follows:
Uncertainty = ±((Input Voltage * % of Reading)/100 + Offset + Noise & Quantization + Drift)
This formula is for the DAQ card.
Another thing is whether the same formula is to be used for the SCXI devices as well.And finally if i get the uncertainty for the DAQ and SCXI individually then do i sum it up to get the total uncertainty value for the measurement?

[AVR]

Actually, the equation is not correct. The correct determination of measurement uncertainty is one of the most overlooked aspects of data analysis. For a detailed reference I suggest the ASME PTC 19.1-1998. It is the supplement to the American Society of Mechanical Engineers Performance Test Codes. The standard is labled "Test Uncertainty". Also consider another "benchmark reference", the book "Experimentation and Uncertainty Analysis for Engineers" by Coleman and Steele (1989 Wiley&Sons).

While the equation you reference may provide a "first-order estimate", it fails to consider the most basic fact that the uncertainty you want is actually classified as a systematic uncertainty (as opposed to a random uncertainty). Systematic uncertainties are expressed in terms of confidence level (3-sigma, 6-sigma) and can be loosely expressed as follows:

U(95) = 2 * square root of [(B/2)^2 + Sxbar^2]

where
U(95) is the systematic uncertainty to a 95% confidence level
Sxbar is the standard deviation divided by the square root of the number of samples
B is the square root of the sum of the systematic errors times the sensitivities of each measurement. For example:

B = sqrt [ (theta1*b1)^2 + ... + (thetan*bn)^2]

where b1, b2,..., bn are the uncertainties of your individual components (offset, drift, quantization) and, for your example, all of the thetas are = 1.

(I omitted the noise error term as it is classified as a "random" uncertainty - and the effects actually are introduced in the Sxbar term.)

Now, the theta term allows the equation to be appplied to a process where the variables are related. An example of this would be the uncertainty of a compressor efficiency that is based upon the measurements of flow, pressure, and temperature. For that process, the theta values are dependant upon the fact that the pressure and temperature are related according to phyisical laws. The theta values could vary by as much as an order of magnitude - giving much higher "weight" to the error of one sensor versus the other. There would also be "cross terms" such as :

theta1*b1*theta2*b2 - and on, and on, and on ...

Sorry about the length of my response (I AM a rocket scientist you know); however, I wanted to let you know that your question (and my answer) is only the tip of a broad topic that is quite often ignored.

[ole]

There is also GUM, "Guide to the Expression of Uncertainty in Measurement", International Organization for Standardization, Geneva Switzerland, ordered directly from ISO. And "Expression of the Uncertainty of Measurement in Calibration", European co-operation for Accreditation, which can be found on the Internet. Computer programs for calculation of uncertainty and more information can be found on the net. Search for GUM

[JustinBritten]

Another good calculation of accuracy is the online accuracy calculator. You can select your DAQ card and, if applicable, your SCXI module to determine the accuracy of your system.

Accuracy Calculator
http://www.ni.com/advisor/accuracy/

As found on the following page, the formula you quoted above is correct.

Accuracy and Uncertainty
http://www.ni.com/support/calibrat/accuracy.htm

The Absolute System Accuracy RTI (Relative to the Input) is defined as +/- SQRT[(Module Absolute Accuracy RTI)^2 + DAQ Device Absolute Accuracy RTI)^2]