# Calculating overall gas metering system accuracy

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#### xtranox

Could anybody please share the best method to calculate the overall accuracy of a gas metering system comprising a turbine meter, pressure & temperature transmitter, a GC and a flow computer?

From a literature that I found, one of the ways is to find out the accuracy for each individual instrument and the overall accuracy is equal to square root of the sum of squares of errors, e.g.:

a = sqrt (err1^2+err2^2+err3^2+...)
where a is the overall accuracy.

I believe this formula does not take account of the weighting of a certain error towards the overall error but instead it assumes that all errors have equal contribution for the total error.

Can we apply the same principle in this application or is there a better way of calculating this? Thank you.

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#### syurish

>a = sqrt (err1^2+err2^2+err3^2+...)
>where a is the overall accuracy.
>
>I believe this formula does not take
>account of the weighting of a certain
>error towards the overall error but
>instead it assumes that all errors have
>equal contribution for the total error.

This formula gives the best results if:

1) errN are mean-square errors in this formula;
2) The number of components (err1; err2 ... errN) is more than five (N >= 5);
3) All error components are distributed according to the normal (Gaussian) distribution law;
5) The correlation factors should be taken into account.

>Can we apply the same principle in this
>application or is there a better way of
>calculating this? Thank you.

In the opposite case, for example, if N < 5 and if all components have different distribution laws it is necessary to use the calculation methods, which take into account the distribution laws for each of components. For example, such method is based on Lyapunov's characteristic functions.

Here is some references that should be useful:

[1]. Kirianaki N.V., Shpak N.O., Yurish S.Y., Khoma V.V., Dzoba Y.S. Novel Technique for Computer-based Estimation of Measurement Errors, in Proceedings of the 10th International Symposium on Development in Digital Measuring Instrumentation September 17-18, 1998, Naples Italy, pp.196-200.
[2]. Yurish S.Y., Kirianaki N.V., Shpak N.O., Improved Analytical Approach to Evaluation of ADCâ€™s Error in Proceedings of the 4th IMEKO Workshop on ADC Modelling and Testing, 9-10 September 1999, Bordeaux, France, pp. 51-54.
[3].Kirianaki N.V., Shpak N.O., Yurish S.Y., Khoma V.V., Dzoba Y.S., New Method of Summation for Measurement Errors Based on Piece-Wise Linear Approximation of Probability Distribution, Journal of Electrical Engineering, No. 51, 2000, pp.94-99.
[4]. Sergey Y. Yurish, Ferran Reverter, Ramon Pallas-Areny, Measurement error analysis and uncertainty reduction for period-and time interval-to-digital converters based on microcontrollers, Measurement Science and Technology, Vol.16, No.8, 2005, pp.1660-1666.

Good luck.

X

Regards,
xtranox

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#### W.L. Mostia

I wrote a series of articles on accuracy in CONTROL magazine about ten years ago and you are welcome to copies of the articles, just provide me an e-mail address. My articles cover both instrument and system accuracy and covers what is commonly used in the process industries for accuracy calculations.

You might also find the following helpful.

http://www.arbiter.com/ftp/datasheets/1133a_what_is_accuracy.pdf

http://www.kostic.niu.edu/Uncertainty-Analysis-of-Measurement-Results.pdf

Books:

Measurement Uncertainty: Methods and Applications By Ronald H. Dieck, ISA

In regards to your questions, I think that you need to give an example of the errors and the weighing you are talking about. The typical RSS equation (sqrt(sum of +/- errors squared)) does weigh larger errors more than smaller errors, assumes that there are no biases, that the errors have the same error distribution, that the +/- errors are equally probable, and that the uncertainty of the errors are equal. Like all calculations that are estimates, the assumptions are extremely important in assuring the accuracy (uncertainty) of the estimate. Except for unusual cases, the RSS method should be adequate for estimating errors of instruments and systems used in the process industries.

William (Bill) L. Mostia, Jr. PE
Sr. Consultant
SIS-Tech Solutions
[email protected]

This is provided on a Caveat Emptor basis.

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#### xtranox

Great info! Thanks for the help and yes I am interested in getting a copy of your articles. I will drop you an email in due time.

Regards,
Xtranox