: pp. 65-72
Industrial Research Institute of Automation and Measurements, Warszawa Pl
Central Metrology Office, Warszawa Pl

In  this paper  three examples of processing uncertainties of a  indirect multi-variable measurement system are considered. It was proposed to extend the vector method of estimating measurement uncertainties, given in Supplement 2 to GUM, on  the  statistical  description  of  the  accuracy  of  whole  ranges  of  indirect multivariable measurement  system.  Formula  for  the covariance matrix of relative uncertainties of the vector measurand is given. The covariance matrixes of uncertainties of few DC electrical measurement circuits are presented, i.e.: for indirect measurement of three resistances with using them in three variants of  balanced  Wheatstone  bridge  or  without  disconnection  this  circuit  but  with  apply  unconventional  current  supplies;  the measurement  of  three  internal  resistances  of  the  star  circuit  from  its  terminals  and  estimation  of  uncertainty  of  powers  of  two currents  if two other currents are measured and their uncertainties are known. Formulas for absolute and relative uncertainties and their correlation coefficients are given. The general conclusion  is that  in  the description accuracy of multivariable measurement systems  the relative uncertainties are sometimes preferable than  the absolute ones, and uncertainties of  their main measurement functions have been also considered.

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[2] M. Dorozhovets,  Processing  the measurement  results. Lviv, Ukraine: Publ. House of Lviv Pol. Nat. Univ., 2007.

[3]  Warsza, Z.  L., Puchalski,  J.:  Estimation  of  vector uncertainties  of multivariable  indirect  instrumental  measurement systems  on  the  star  circuit  example. Congress  IMEKO 2018 CD Proceedings PO-062

[4]  L.  Finkelstein,  “Fundamental  concepts  of measurement”, ACTA IMEKO, vol. 3, no. 1, p. 10–15 May 2014.