Equations Of Propagation Of Uncertinty On ITS-90 And On Radiation Interpolation Scales

An equation of propagation of uncertainty on the ITS-90 is an important tool for the uncertainty evaluation in temperature measurement. The result presented by the equation is conclusive. In this paper, a study of equations of propagation of uncertainty on interpolation scales is made.Firstly, based on implicit differentiation, a set of the sensitive coefficients of a multivariate non-linear interpolation has been achieved in terms of implicit function for a general case. Those of all interpolation in physical measurement, including temperature measurement, can be deduced from the result. .In particular, the sensitivity coefficients of the interpolation which is linear for their coefficients are still linear combinations of the basis functions comprising the interpolation, only with different constants that can be presented in the determinant form. This solves the question to express the equation of propagation of uncertainty of a complex interpolation comprised of many different basic functions. From the results; this paper gives the equations of propagation of uncertainty on ITS-90 in the range 13.8033K to 933.473K and on radiation interpolation scale. By direct differentiation to the ITS-90 interpolation in the sub-range 0.01℃(273.16K) to 961.78℃(1234.93K), a special sectional function, this paper gives the equation of propagation of uncertainty on ITS-90 in the range, of which the sensitivity coefficients are also linear combinations of basic functions comprising the interpolation only with different constant, and sectional functions. Comparing the curves of the sensitivity coefficients of the equations with those published by Supplementary Information for the International Temperature Scale of 1990, they are consistency.Secondly, the ITS-90 inconsistency, as an uncertainty resource, is considered in the paper. Eighty seven SPRTs in the range 0°C to 660.323°C were investigated. The results show seventy–nine SPRTs with inconsistencies less than 1.0mK in one distribution and the remaining eight SPRTs with inconsistencies much greater than 1.0mK in a separate distribution. The design of the later differs from that of the former to a certain extent. A chi-squared test for the former showed that the inconsistency had a normal distribution N ( 0.061,0.3052). As an uncertainty component, its expanded uncertainty is 1mK, coverage factor is 3. An inconsistency function with respect to temperature above 0℃is obtained and is introduced into the equation of propagation of uncertainty of ITS-90.Thirdly, based on the result of inconsistency, two quadratic deviation functions in the range 0℃to 660.323℃are given, one can be determined from the calibration values at the triple point of water and the freezing points of sin and Aluminum, and another can be determined from the calibration values at the triple point of water and the freezing points of zinc and Aluminum. The two functions are very closing approximate to the ITS-90 deviation function in the range 0℃to 660.323℃. Fifty SPRTs have been used to check the functions and the error are not more than 4.7mK. Using them, we can reduce one of the freezing points of sin and zinc from four fixed points defined by ITS-90 in the range 0℃to 660.323℃and save the cost of calibration. The precision of the deviation functions is sufficient for secondary measurement.