Browsing by Author "Lira, I."

Now showing 1 - 16 of 16
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    Analysis and comparison of Bayesian methods for type A uncertainty evaluation with prior knowledge
    (2022) Lira, I.
    If a number of observations about a certain quantity may be assumed independent, drawn from a Gaussian distribution, Supplement 1 to the GUM recommends that the standard uncertainty associated with the quantity be obtained by a formula that is applied to more than three observations. Various articles have recently appeared proposing Bayesian methods to surmount this limitation. Some of these methods, which require prior knowledge about the quantity, are reviewed in this article.
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    Analysis of key comparison data and laboratory biases
    (2008) Chunovkina, A. G.; Elster, C.; Lira, I.; Woeger, W.
    The analysis of key comparison data is at the focus of metrology-related research and many papers have been published on this issue in recent years. Typically, the approaches make use of quoted combined uncertainties. We propose an approach which is based on more detailed uncertainty information. We assume that each of the participating laboratories has knowledge about the precision of its measurements and, in addition, provides a probability density function ( PDF) which encodes its assessment on the size of its bias. Only the case of a single stable travelling standard is considered.
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    Analysis of plastic strain localization by a combination of the speckle interferometry with the bulge test
    (ELSEVIER SCI LTD, 2007) Montay, G.; Francois, M.; Tourneix, M.; Guelorget, B.; Vial Edwards, C.; Lira, I.
    The process of localization of strains, diffuse and localized necking, up to fracture in equi-biaxial loading was analyzed through the images obtained by electronic speckle pattern interferometry (ESPI). The problem of localization is important in the sheet metal forming processes. The ESPI technique is used to have a better resolution on the measured strains (10(-5)) than other technique such as the image correlation (10(-2), 10(-3)). The bulge test is currently used to determine the mechanical properties of materials by measuring the deformation that occurs in response to the application of a controlled pressure. This test is used to determine the mechanical properties of sheet metals submitted to an equi-biaxial loading path, the strains at failure are used as data to determine forming limit diagrams (FLDs).
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    Assigning a probability density function for the value of a quantity based on discrete data: the resolution problem
    (2012) Lira, I.
    It often happens that knowledge about a particular quantity has to be reached by processing a series of resolution-limited indications. It is a well-established fact that if the variability of the data is large compared with the resolution interval, the effect of discretization can be ignored. Otherwise, it needs to be taken into account since it can then be an important source of uncertainty, sometimes more significant than randomness itself. The objective of this paper is to derive a probability density function (pdf) for the value of a quantity based on discretized data. This pdf allows the standard uncertainty associated with the best estimate of the quantity to be computed and, perhaps more importantly, it can be used as an input to evaluate a measurement model in which the quantity is involved. Bayesian concepts are used towards this goal. Although reaching an appropriate pdf has been attempted before, limited success has been attained, as the pdfs that have been obtained exhibit some undesirable characteristics. Herein a new approach is proposed. Unlike previous efforts, this time the quantity of interest is modelled as a sum of two other quantities, one that can only assume discrete values and the other that takes values within the resolution interval centred on zero. The resulting pdf exhibits a satisfactory behaviour, but further work would be required to provide firmer theoretical grounds for the employed prior.
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    Assignment of a non-informative prior when using a calibration function
    (2012) Lira, I.; Grientschnig, D.
    The evaluation of measurement uncertainty associated with the use of calibration functions was addressed in a talk at the 19th IMEKO World Congress 2009 in Lisbon (Proceedings, pp 2346-51). Therein, an example involving a cubic function was analysed by a Bayesian approach and by the Monte Carlo method described in Supplement 1 to the 'Guide to the Expression of Uncertainty in Measurement'. Results were found to be discrepant. In this paper we examine a simplified version of the example and show that the reported discrepancy is caused by the choice of the prior in the Bayesian analysis, which does not conform to formal rules for encoding the absence of prior knowledge. Two options for assigning a non-informative prior free from this shortcoming are considered; they are shown to be equivalent.
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    Equivalence of alternative Bayesian procedures for evaluating measurement uncertainty
    (IOP PUBLISHING LTD, 2010) Lira, I.; Grientschnig, D.
    Current recommendations for evaluating uncertainty of measurement are based on the Bayesian interpretation of probability distributions as encoding the state of knowledge about the quantities to which those distributions refer. Given a measurement model that relates an output quantity to one or more input quantities, the distribution of the former is obtained by propagating those of the latter according to the axioms of probability calculus and also, if measurement data are available, by applying Bayes' theorem.
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    Evaluating systematic differences between laboratories in interlaboratory comparisons
    (2009) Chunovkina, A. G.; Elster, C.; Lira, I.; Woeger, W.
    A Bayesian analysis of the data from interlaboratory comparisons involving a single stable traveling standard is presented. The approach is based on the assumption that each participating laboratory provides an estimate of the value of the measurand with zero estimated bias. In addition, it is assumed that each of the reported uncertainties is given in the form of two separate components, one associated with random effects and the other associated with systematic effects. It is finally assumed that all information is consistent. Using Gaussian probability density functions, simple formulas for the joint estimate of the value of the measurand and for the a posteriori estimates of the biases and of their differences are derived. Formulas for the uncertainties of all these estimates are also given.
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    Monte Carlo evaluation of the uncertainty associated with the construction and use of a fitted curve
    (ELSEVIER SCI LTD, 2011) Lira, I.
    A Monte Carlo procedure is presented for computing the joint state-of-knowledge probability distribution to be assigned to the coefficients of a curve fitted to a set of points in a two-dimensional coordinate system. Experimental data about this set may be available, but other relevant information may also be taken into account. The procedure is fully in line with the approach in Supplement 1 to the Guide to the Expression of Uncertainty in Measurement. It consists of propagating the joint probability distribution of the input quantities through the mathematical model of the measurement by which the coefficients are defined. The model is usually obtained by least-squares adjustment, which is here interpreted differently than in the conventional formulation. However, applying other fitting criteria is also possible. Examples illustrate the application of the procedure. (C) 2011 Elsevier Ltd. All rights reserved.
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    On the long-run success rate of coverage intervals
    (2008) Lira, I.
    When constructing a coverage interval from the probability density function that describes the state of knowledge about a measurand, it seems reasonable to expect that the long-run success rate of that interval will be about equal to the stipulated coverage probability. Through a specific example, the validity of this criterion is examined.
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    On the meaning of coverage probabilities
    (2009) Lira, I.
    It has been argued that the probability associated with a coverage interval calculated following the procedure proposed in Supplement 1 to the GUM should be about equal to the proportion of independent intervals reckoned over time that contain the measurand (Willink 2006 Metrologia 43 L39-42, Hall 2008 Metrologia 45 L5-8, Possolo et al 2009 Metrologia 46 L1-7). The opposite point of view maintains that a coverage probability can only be interpreted as the degree of belief in the quoted interval containing the unknown value of the measurand (Lira 2008 Metrologia 45 L21-3). In this paper, two simple examples are presented to reinforce the latter interpretation.
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    Strain and strain rate measurement during the bulge test by electronic speckle pattern interferometry
    (ELSEVIER SCIENCE SA, 2007) Montay, G.; Francois, M.; Tourneix, M.; Guelorget, B.; Vial Edwards, C.; Lira, I.
    This paper presents a new experimental method to measure the strain increment and the strain rate during the bulge of a copper sheet. The electronic speckle pattern interferometry (ESPI) is combined with the bulge test to measure the field of strain increment. The strain rate is used to detect heterogeneity in the strain distribution.
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    The generalized maximum entropy trapezoidal probability density function
    (2008) Lira, I.
    Quantities that lie within inexactly prescribed intervals arise frequently. A formula for the maximum entropy probability density function (PDF) that describes the state of knowledge of such a quantity is given in Supplement 1 to the Guide to the Expression of Uncertainty in Measurement. However, this formula applies only to the case for which the limits of the interval are known to lie within subintervals of equal lengths centred on the best estimates of the limits. In this paper, a PDF is derived for a quantity that is not so restricted.
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    The probability distribution of a quantity known to be contained within an interval having uncertain limits
    (2010) Lira, I.
    A probability distribution is derived that applies to a quantity known to be contained within an interval whose limits are estimated but not exactly known. A Monte Carlo procedure for numerically computing the distribution is described. Analytic expressions for the expectation and variance are given.
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    The probability distribution of a quantity with given mean and variance
    (2009) Lira, I.
    Supplement 1 to the Guide to the Expression of Uncertainty in Measurement states that if a best estimate and associated standard uncertainty are the only information available regarding a certain quantity, then, according to the principle of maximum entropy, a Gaussian probability distribution with support on the real line should be assigned to that quantity. This recommendation holds true if one does not know the range of the possible values of the quantity. However, usually such a range will also be known. It is shown that in this case a Gaussian distribution supported on (-infinity,infinity) can be used, but only if the standard uncertainty is sufficiently small. Otherwise, the parameters of the distribution have to be computed numerically.
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    Uncertainty of residual stresses measurement by layer removal
    (PERGAMON-ELSEVIER SCIENCE LTD, 2006) Bendek, E.; Lira, I.; Francois, M.; Vial, C.
    A model to evaluate the uncertainty in the measurement of the through-thickness residual stress distribution in plates by the layer removal technique is presented. Thin layers were chemically etched from a stripe on rectangular specimens cut from a low carbon cold-rolled steel sheet. Phase shifting laser interferometry was used to measure the ensuing curvature. Polynomials were least-squares adjusted to the curvatures as a function of the etched depth. The polynomials were inserted into an integro-differential equation relating the curvature to the residual stresses, which were assumed to be a function of depth only. A comparison with X-ray diffraction measurement of the surface residual stresses showed good agreement. The uncertainty was found to increase steeply at the surfaces and to depend mainly on the assumed value for the modulus of elasticity, on the curvature fit, and on the depth of etching. (C) 2006 Elsevier Ltd. All rights reserved.