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We propose a method for assigning a probability distribution to an input quantity. The distribution is used in a Monte Carlo method described in Supplement 1 to the Guide to the Expression of Uncertainty in Measurement for uncertainty evaluation. The proposed method provides an alternative to other methods, such as the principle of maximum entropy and Bayesian procedure that were used in Supplement 1 for the same purpose. The method is based on an exact or approximate pivotal quantity and is easily applied. We use several examples from commonly known models to illustrate the implementation of the proposed approach.

This paper presents an approach for making inferences about the intercept and slope of a linear regression model when both variables are subject to measurement errors. The approach is based on the principle of fiducial inference. A procedure is presented for computing uncertainty regions for the intercept and slope that can be used to assess agreement between two instruments. Computer codes for performing these calculations, written using open-source software, are listed.

This paper presents an approach for making inference on the parameters µ and σ of a Gaussian distribution in the presence of resolution errors. The approach is based on the principle of fiducial inference and requires a Monte Carlo method for computing uncertainty intervals. A small simulation study is carried out to evaluate the performance of the proposed procedure and compare it with some of the existing procedures. The results indicate that the fiducial procedure is comparable to the best of the competing procedures for inference on µ. However, unlike some of the competing procedures, the same Monte Carlo calculations also provide inference for σ and many other related quantities of interest. (Some figures in this article are in colour only in the electronic version)

This paper presents a method for constructing uncertainty regions for a vector measurand in the presence of both type-A and type-B errors. The method is based on the principle of fiducial inference and generally requires a Monte Carlo approach for computing uncertainty regions. A small simulation study is carried out to evaluate the performance of the proposed method. Computer programs written using public-domain software for computing uncertainty regions are listed. An example, involving complex S-parameter measurements, is used to illustrate the proposed method.

The Guide to the Expression of Uncertainty in Measurement (GUM) recommends the use of a first-order Taylor series expansion for propagating errors and uncertainties. The GUM also requires the use of a second-order Taylor series approximation for calculating uncertainties when the first-order approximation alone is not adequate. When only first-order Taylor expansions are used as a basis for propagating uncertainties, the first-order approximation to the standard deviation coincides with the first-order approximation to the root mean square error of an estimate. However, this is generally not true when using higher-order approximations. In this paper, we derive the second-order approximation of the standard deviation and the root mean square error of an estimate. We compare them with the correction terms given in the GUM and demonstrate their use via examples. We also provide a computer program that uses symbolic derivatives to calculate the second-order approximations of the uncertainty in measurement results.