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Metrology, the science of measurement, involves the determination from experiment of estimates of the values of physical quantities, along with the associated uncertainties. In this endeavour, a mathematical model of the measurement system is required in order to extract information from the experimental data. Modelling involves model building : developing(More)
Algorithms exist for least-squares tensor-product splineapproximation to data (a) on a rectangular mesh, (b) on a family of parallel lines and (c) that is generally scattered. In contrast,direct algorithms for tensor-product splineinterpolation are available only for data type (a). The structure of the data in cases (a) and (b) is such that the(More)
When analysing a sample statistically, the quality of the resulting parameters (measures of location, dispersion, etc.) depends on the reliability or credibility of the data and on the analysis undertaken. The data provided by interlaboratory comparisons, and especially key comparisons, is of sufficient importance that approaches are required which are as(More)
This guide provides best practice on the evaluation of uncertainties within metrology, and on the support to this topic given by statistical modelling. It is motivated by two principle considerations. One is that although the primary guide on uncertainty evaluation, the Guide to the Expression of Uncertainty in Measurement (GUM), published by ISO, can be(More)
This paper addresses a fundamental problem in mathematics and numerical analysis, that of determining a polynomial interpolant to specified data. The data is taken as consisting of a set of points (abscissae), at each of which is specified a function value. Additionally, at each point, any number of leading derivative values of the function may be given.(More)
Many mathematical and statistical problems that arise in metrology can be posed in such a way that they possess a unique correct solution. However, algorithms in standards or software libraries, such as METROS, may only provide an approximate solution or the solution to a nearby problem. An approximate or nearby problem is often introduced so as to give a(More)