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G. Iuculano, G. Pellegrini, A. Zanobini
ON THE USE OF MINIMUM CROSS ENTROPY PRINCIPLE AND BAYES’ THEOREM FOR THE UNCERTAINTY EVALUATION IN A MEASUREMENT PROCESS

In this paper the evaluation of measurement uncertainty in a multivariate model is carried out by applying the principle of minimum cross entropy (MINCENT) and Bayes’ theorem.
In particular the MINCENT optimization procedure is used to translate the information contained in the known form of likelihood into a prior distribution for Bayesian inference. The methodology is adapted and tested on a recalibration model. Some basic ideas and general remarks on the Bayesian probability theory and entropy optimization principles are reported too.

Maurice Cox, Alistair Forbes, Peter Harris, João Sousa
ACCOUNTING FOR PHYSICAL KNOWLEDGE IN OBTAINING MEASUREMENT RESULTS AND ASSOCIATED UNCERTAINTIES

This paper considers the determination of measurement results and associated uncertainties when prior physical knowledge of the quantities concerned is available. The scientific concepts that provide a basis for determining realistic solutions to such problems are discussed, and implementations of these concepts are considered. To illustrate the concepts, an example concerning the determination of an analyte concentration in chemical metrology is used. This will be the basis for a discussion concerning the various approaches available to deal with such constraints. Results stating a coverage interval containing infeasible values (values the quantity cannot physically take) should be avoided, and this fact will assist in the comparison of the relative merits of each method.

J. E. Decker, A. G. Steele, R. J. Douglas
HARNESSING SIMULATIONS FOR GUM-COMPLIANT EVALUATION OF UNCERTAINTY IN MEASUREMENT

This paper presents a specific implementation suite and some background for combining uncertainty components, and using them, through the propagation of distributions using Monte Carlo simulation.

Nien Fan Zhang
WEIGHTED MEAN AND ITS UNCERTAINTY ESTIMATION

The weighted mean has been used to estimate the common mean of several populations with unknown and different variances. However, the traditional estimator of the variance of the weighted mean estimator underestimates the variance. Two new variance estimators are proposed with smaller biases and correspondingly formed intervals that have much better coverage probabilities for the mean. Results are extended to the general case with both Type A and Type B uncertainty components being presented.

Fabio. S. Bazilio, Jailton C. Damasceno, Akie K. Ávila, Paulo Roberto Guimarães Couto, Renata M. Horta Borges
EVALUATION OF MEASUREMENT UNCERTAINTY IN ANALYTICAL INORGANIC ASSAYS: A STUDY OF CASE

The uncertainty estimation procedures recommended in ISO-GUM are largely used by several laboratories and institutes. This work compares the ISOGUM approach and the Monte Carlo simulation method for the Cd concentration uncertainty (U) determination, using the A-5 example showed at EURACHEM Guide. The Monte Carlo simulation showed very similar results in comparison to the ISO-GUM approach. It can be concluded that both methods are applicable for the expanded uncertainty determination and provide reliable results.

Eduarda Filipe
UNCERTAINTY CALCULATION IN NESTED STRUCTURES

The experimental design, active statistical tool generally used for the optimization of processes, can also be considered for the evaluation of sample(s) homogeneity. This tool may be applied to Metrology for the analysis of large amount of repeated measurements permitting the "mining" of the results and include this "time-dependent sources of variability" information at the uncertainty calculation.

R. M. H. Borges, I. M. G. Lemos, A. M. S. Antunes, L. A. d’Avila
UNCERTAINTIES SOURCES EVALUATION ASSOCIATED TO SULFUR AND FLASH POINT IN DIESEL FUEL

The international trade, the environmental protection and the science, today, cannot be able to exist without reliable measurements. Nowadays, any results of measurement of a physical or chemical quantity should be accompanied for any quantitative indication of the quality of this data, in order to be able to evaluate its reliability. Thus, an easy concept known and with wide acceptance that could characterize the quality of the result of a measurement is expressed by its uncertainty. In this work, we will present the application of the ISO GUM 95 for estimating uncertainty in the following tests: sulfur and flash point in diesel fuel. This research includes the development of a software based on Delphi version 6.0 to calculate the possible sources of uncertainty associated to the measurement used in both process and an estimation of their value, either by statistical methods (Type A) or by other means (Type B). Later on the individual components are combined to calculate the standard and expanded uncertainty for the whole process. The program developed aimed reducing the time spent in figuring out the main sources of uncertainty, moreover, facilitating the obtainment of the uncertainty result. To visualize the most relevant factor in the uncertainty measurement, the program provides a graphic showing the uncertainty contributions and enables the calculation of final uncertainty combined by the relative method, based on Eurachem/CITAC Guide, allowing the graphic comparison among the different methods in calculating uncertainty in measurement.

Alistair Forbes, Christophe Perruchet
MEASUREMENT SYSTEMS ANALYSIS: CONCEPTS AND COMPUTATIONAL APPROACHES

In this paper, we review measurement systems analysis from the point of view of the Guide to the Expression of Uncertainty in Measurement and ISO 5725: Accuracy (Trueness and Precision) of Measurement Methods and Results. We also consider other computational approaches such as Markov chain Monte Carlo simulations that could be useful for uncertainty evaluation.

L.F. Mouzinho, J.V. FonsecaNeto, B.A. Luciano, R.C.S. Freire, J.F. Carneiro Jr.
PRACTICAL ASPECTS FOR DESIGN OF INDIRECT MEASUREMENT IN DYNAMIC SYSTEMS

In different areas of science and engineering are used different indirect measurement procedures that lead to obtaining the quantity desired. In this paper is described the considerations about indirect measurement system (IMS). Is realized the analysis between direct measurement and indirect measurement, presenting the limitations of the estimator. The IMS are classified under the methodological point of view. Practical considerations for design of IMS in dynamic system are specified, as clock cycle, time of hardware execution and software, size of the memory of data and program, represented for quality; system modelling; error estimations and uncertainty in indirect measurement.

Man-Yong Choi, Jeong-Hak Park, Chin-Ok Lee, Kee-Hwan Jee, Su-Un Kim
NONDESTRUCTIVE EVALUATION BY ANALYSIS FOR DENSITY OF CRACK IN TUNNEL & UNDERGROUND STRUCTURES WITH TUNNEL SCANNER

This study has focused on the method of stateestimation in tunnel and underground structures by analyzing density of cracks. Reliability on this technique is decided by exact measurement and analysis of cracks. The tunnel scanner, one of the nondestructive technologies, is used by high resolution CCD(charge-coupled device) camera because accurate data could not be acquired by the conventional visual inspection method. This method can get reliable image data through detailed shooting on the surface of the target structures and analyze accurate information (width, length, location etc.) of cracks by image processing. The crack density was analyzed by considering section type of structures, length of span and expansion-joint and by using numerical location and distance of cracks like width and length. Cracked area, which is a basis of crack density analysis, was calculated 0.25 m width per crack length. We can specially manage a zone to be concentrically generated through a distribution chart of crack density to be analyzed over all structures. The analyzed data, which were detected by nondestructive tunnel scanner, proffered information for reasonable judgment in evaluating conditions of tunnel and underground structures, and further, they are used as reliable information to determine safety diagnosis, precise safety diagnosis or priority of repair and reinforcement works.

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