# Considerations Relating to Type 1 and Type 3 Non-uniqueness in SPRT Interpolations of the ITS-90

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## Abstract

It is well known that different allowed interpolations using a given standard platinum resistance thermometer (SPRT) in overlapping subranges of the ITS-90 do not lead to identical results. This is termed Type 1 non-uniqueness, or subrange inconsistency (SRI), and it arises because of small incompatibilities in the SPRT characteristic \(W(T_{90})\) with respect to the ITS-90 reference function \(W_{r}(T_{90})\), such that the alternative low-order interpolations, fitted to the deviations \(W(T_{90})\) – \(W_{r}(T_{90})\) at different sets of fixed points, are not in general identical. To some extent SRI may be ‘scale-intrinsic,’ i.e., caused by incompatibilities between the resistance ratios, \(W_{r}(T_{90})\), specified at the fixed points of the ITS-90, and hence the same for all SPRTs. However, it has been found that the SRI varies strongly between different SPRTs, and that variability of \(W(T_{90})\) is much the dominant cause. This raises the question of how SRI is linked to Type 3 non-uniqueness between SPRTs in each separate subrange, which is *entirely* due to differences in SPRT characteristics. This paper explores the connection between them and concludes that they are of similar magnitude and consequently, being different manifestations of the same effects, it is argued that non-uniqueness should be covered by a single component of uncertainty. Following the stated rationale of the ITS-90, it is further suggested that this uncertainty should be estimated only within each subrange, i.e., that shorter subranges should not be deemed subject to potential effects caused by out-of-range data.

## Keywords

ITS-90 Non-uniqueness Standard Platinum Resistance Thermometer Subrange inconsistency## Notes

### Acknowledgements

This work was funded by the UK National Measurement System for Engineering and Flow Metrology.

## References

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