Supplement 1 to the ‘Guide to the expression of uncertainty of measurement’ describes a Monte Carlo method as a general numerical approach to uncertainty evaluation. Application of the approach typically delivers a large number of values of the output quantity of interest from which summary information such as an estimate of the quantity, its associated standard uncertainty, and a coverage interval for the quantity can be obtained and reported. This paper considers the use of a Monte Carlo method for uncertainty evaluation in calibration, using two examples to demonstrate how so-called ‘digital calibration certificates’ can allow the complete set of results of a Monte Carlo calculation to be reported.

Fitting a polynomial function to data, accounting for uncertainty information associated with that data, is a problem that is commonly encountered in metrology and for which algorithms and software are widely available. For reasons of numerical stability, Chebyshev polynomials are often employed rather than monomials. The problem of fitting a polynomial function that is constrained to pass through the origin, again taking uncertainty information into account, which arises in a number of metrology areas, has not been addressed to the same extent. This paper describes algorithms to determine the best fit polynomial function passing through the origin to data, accounting for uncertainty, and using Chebyshev polynomials. Software that implements the algorithms, and is available free to download, is also described.