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There is currently interest in the digitalisation of metrology because technologies that can measure, analyse, and make critical decisions autonomously are beginning to emerge. The notions of metrological traceability and measurement uncertainty should be supported, following the recommendations in the Guide to the Expression of Uncertainty in Measurement (GUM). However, GUM offers no specific guidance. Here, we report on a Python package that implements algorithmic data processing using ‘uncertain numbers’, which satisfy the general criteria in GUM for an ideal format to express uncertainty. An uncertain number can represent a physical quantity that has not been determined exactly. Using uncertain numbers, measurement models can be expressed clearly and succinctly in terms of the quantities involved. The algorithms and simple data structures we use provide an example of how metrological traceability can be supported in digital systems. In particular, uncertain numbers provide a format to capture and propagate detailed information about quantities that influence a measurement along the various stages of a traceability chain. More detailed information about influence quantities can be exploited to extract more value from results for users at the end of a traceability chain.

This paper considers a future scenario in which digital reporting of measurement results is ubiquitous and digital calibration certificates (DCCs) contain information about the components of uncertainty in a measurement result. The task of linking international measurement comparisons is used as a case study to look at the benefits of digitalization. Comparison linking provides a context in which correlations are important, so the benefit of passing a digital record of contributions to uncertainty along a traceability chain can be examined. The International Committee for Weights and Measures (CIPM) uses a program of international “key comparisons” to establish the extent to which measurements of a particular quantity may be considered equivalent when made in different economies. To obtain good international coverage, the results of the comparisons may be linked together: a number of regional metrology organization (RMO) key comparisons can be linked back to an initial CIPM key comparison. Specific information about systematic effects in participants’ results must be available during linking to allow correct treatment of the correlations. However, the conventional calibration certificate formats used today do not provide this: participants must submit additional data, and the report of an initial comparison must anticipate the requirements for future linking. Special handling of additional data can be laborious and prone to error. An uncertain-number digital reporting format was considered in this case study, which caters to all the information required and would simplify the comparison analysis, reporting, and linking; the format would also enable a more informative presentation of comparison results. The uncertain-number format would be useful more generally, in measurement scenarios where correlations arise, so its incorporation into DCCs should be considered. A full dataset supported by open-source software is available.

A method is described for designing modular instrumentation systems and software frameworks that inherently propagate measurement uncertainty according to current international best-practice. The method uses a mathematical procedure that is equivalent to the 'Law of Propagation of Uncertainty' presented in the "Guide to the Expression of Uncertainty in Measurement [International Organization for Standardization, Geneva, 1995]. System components implement a simple communications interface which allows module details to be fully encapsulated. Advantages include: automated uncertain evaluation, simple conceptual design framework, supports dynamic module changes for plug-and-play operation, simplifies testing and validation.