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By P. Ciarlini, E Filipe, A B Forbes, F Pavese, C Perruchet, B R L Siebert

This quantity collects the refereed contributions according to the shows made on the 7th Workshop on complex Mathematical and Computational instruments in Metrology, a discussion board for metrologists, mathematicians and software program engineers that would motivate a more advantageous synthesis of talents, services and assets. the amount includes articles by means of international popular metrologists and mathematicians occupied with size technological know-how and, including the six prior volumes during this sequence, constitutes an authoritative resource of the mathematical, statistical and software program instruments beneficial in smooth metrology.

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Runger, J. Quality Technology 31 3, 309 (1999). 3. G. E. P. Box and D. R. Cox, J. Royal Statist. Soc. B 26, 211 (1964). 4. L. K. Chan, K. P. Hapuarachchi and B. D. Macpherson, IEEE Transactions on Reliability 37 1, 117 (1988). 5. L. K. Chan and J. K. Heng, Naval Research Logistics50, 555 (2003). 6. Y. S. Chang and D. S. Bai, Qual. Reliab. Engng. Int. 17, 397 (2001). 7. M. G. Cox and E. P. Iguzquiza, Advanced Mathematical and Computational Tools in Metrology, 5, 106 (2001). 8. O. Figueiredo, Proc.

The best estimate y of the value of Y is given by solving the generalized least squares problem 9 minF(r]) = eT(Ux)~1e, e = x - An, (4) where Ux is taken as Ux or Ux , and Y is regarded as the vector of artefact properties, or the vector of artefact properties and NMI systematic effects, according, respectively, to whether model (1) or (2) is used. , A A is invertible, the solution to formulation (4) and the associated uncertainty matrix are y = UyA^U^x, Uy = {ATU~lA)-\ (5) Numerically, a recognized solution algorithm 9 employing matrix factorization methods to avoid explicit matrix inversion would be used.

R. Dapoigny, N. Mellal, E. Benoit, L. Foulloy, Service Integration in Distributed Control Systems: an approach based on fusion of mereologies, IEEE Conf. on Cybernetics and Intelligent Systems (CIS'04), 1282-1287 (2004). Advanced Mathematical and Computational Tools in Metrology VII Edited by P. Ciarlini, E. Filipe, A. B. Forbes, F. Pavese, C. Perruchet & B. Siebert © 2006 World Scientific Publishing Co. (pp. 23-34) DATA EVALUATION OF K E Y COMPARISONS INVOLVING SEVERAL ARTEFACTS M. G. C O X , P.

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