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Brief overview of methods for measurement uncertainty analysis: GUM uncertainty framework, Monte Carlo method, characteristic function approach | IEEE Conference Publication | IEEE Xplore

Brief overview of methods for measurement uncertainty analysis: GUM uncertainty framework, Monte Carlo method, characteristic function approach


Abstract:

The basic working tool in measurement uncertainty analysis, as advocated in recent discussions related to the possible revision of the Guide to the expression of uncertai...Show More

Abstract:

The basic working tool in measurement uncertainty analysis, as advocated in recent discussions related to the possible revision of the Guide to the expression of uncertainty in measurement (GUM), and in particular by its Supplements, is the state-of-knowledge distribution about the quantity derived based on the currently available information. The GUM uncertainty framework (GUF) provides a method for assessing uncertainty based on the law of propagation of uncertainty and the characterization of the output quantity by a Gaussian distribution or a scaled and shifted t-distribution. Supplement 1 is concerned with the propagation of probability distributions through a measurement model as a basis for the evaluation of measurement uncertainty, and its implementation by a Monte Carlo method (MCM). Supplement 2 describes a generalization of MCM to obtain a discrete representation of the joint probability distribution for the output quantities of a multivariate model. An alternative tool to form the state-of-knowledge probability distribution of the (scalar) output quantity in linear measurement model, based on the numerical inversion of its characteristic function, which is defined as a Fourier transform of its PDF. Here we present brief overview and some remarks on applicability of these approaches for uncertainty analysis, with emphasized focus on the Characteristic function approach (CFA).
Date of Conference: 29-31 May 2017
Date Added to IEEE Xplore: 20 July 2017
ISBN Information:
Conference Location: Smolenice, Slovakia

1. Introduction

Here we consider mathematical model of a measurement (the measurement model) of a single scalar quantity, say , which can be expressed by a functional relationship \begin{equation*} \text{Y}=f(X), \tag{1} \end{equation*} where is a scalar output quantity of interest (associated with the true value of the measurand) and represents the input quantities . Each is regarded as a random variable (RV) with possible values and is a RV with possible values . The joint probability density function (PDF) for is denoted here by and cumulative distribution function (CDF) is denoted by , where is a vector variable describing the possible values of the vector quantity PDF for is denoted by and the CDF by . Marginal distribution functions (PDFs/CDFs) for are denoted by and , respectively. Frequently, it is adequate to assume that the functional relationship is linear in , i.e.\begin{equation*} \text{Y}=c_{1}X_{1}+\cdots+c_{n}X_{n}, \tag{2} \end{equation*} for some known constants (the sensitivity coefficients), and moreover, that the input quantities are mutually independent RVs with known distributions.

References

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