Observations on sub-range inconsistency in the SPRT interpolations of ITS-90

The properties of the sub-range inconsistency (SRI or Type-I non-uniqueness) of the standard platinum resistance thermometer (SPRT) sub-ranges of the International Temperature Scale of 1990 (ITS-90) are investigated. Mathematically, SRI has the form of an interpolation error with zeros at each of the fixed points shared by the two interpolating equations, and a magnitude dependent on the differences in the ratios (W(r) - 1)/(W - 1) for each of the fixed points, where W is the resistance ratio R(T)/R(0.01 degrees C) and Wr is the reference resistance ratio defined by ITS-90. The calibration results for a set of 60 SPRTs were analysed to determine the SRI for the water-zinc and water-aluminium sub-ranges. The maximum SRI occurs near 93.15 degrees C, and has an average value of 0.12 mK and a standard deviation of 0.48 mK. The reciprocal of the ratio (W(r) - 1)/(W - 1), which is proportional to the sensitivity of the SPRT, was found to be 1.0 +/- 0.0004 for all 60 SPRTs, and was within 0.00005 for all fixed points for any one SPRT. This suggests that a single constraint on the value of the ratio might be a more useful and discerning SPRT-quality constraint than the current three ITS-90 constraints.