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An estimate of a measurand using a nonlinear function of uncorrelated input quantities can be done by either applying the nonlinear function to the means of the input quantities (Method 1) or calculating the mean of a set of values obtained from propagating individual measurement values through the nonlinear function (Method 2). This paper proposes an improvement over the standard Method 2 procedures when the input quantities are assumed to be statistically independent and the nonlinear function has a general sum-of-product form, which covers many common measurement models. This paper shows that the proposed new approach (called Method 2S), if applicable, always produces a mean-squared error smaller than that of the conventional Method 2 procedures. The proposed approach improves the efficiency of Type-A evaluation as well as the Monte Carlo method. It also well complements the mainstream practices in the measurement uncertainty evaluation. [ABSTRACT FROM AUTHOR]

Expanded uncertainty estimation is normally required for mission-critical applications, e.g., those involving health and safety. It helps to get a distribution range of the required confidence level for the uncertainty evaluation of a system. There are a number of available techniques to estimate the expanded uncertainty. However, there is currently no commonly accepted benchmark test distribution set adopted to compare the performances of different techniques when they are used to estimate the expanded uncertainty. Without such a common benchmarking platform, the relative reliability of a particular technique in comparison to other techniques can be untrustworthy. To address the shortcoming, this paper proposes a set of analytically derived benchmark test distributions. It goes on to show the benefits of using them by comparing the performance of existing distribution fitting techniques when applied to the moment-based expanded uncertainty evaluation. The most commonly used moment-based distribution fitting techniques, such as Pearson, Tukey’s gh, Cornish–Fisher expansion, and extended generalized lambda distributions, are employed as test cases in this paper. The test distribution set proposed in this paper provides a common benchmarking platform for metrologists intending to assess the performance of different expanded uncertainty estimation techniques. Results from the performance comparison would help practitioners to make a better choice of a distribution fitting technique that would best suit their respective systems. [ABSTRACT FROM AUTHOR]

The uncertainty propagation law helps to infer the uncertainty of unobservable variables from known or assumed relationship with observable variable. Currently only analytical linear approximation or Monte Carlo simulation methods is widely adopted. The former method is limited to weakly nonlinear systems while the latter does not provide any analytical expression that links the uncertainties of input to uncertainties of output quantities. This paper proposes procedures to evaluate the standard uncertainty of multivariate polynomial using basic algebraic manipulation and tabulated Mellin transform. Case studies are presented whereby the effectiveness and practicality of the proposed method is demonstrated. The proposed method can be readily automated using computer algebra systems, thus negating the need for practitioners to perform the actual complex computation. The work theoretically enriches and extends the validity of the analytic approach in the existing uncertainty evaluation framework, thus enabling the analytic evaluation of uncertainty for many nonlinear cases which was previously an impossible task. [ABSTRACT FROM AUTHOR]