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 displays 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 beneficial synthesis of abilities, functions and assets. the amount includes articles through global popular metrologists and mathematicians keen on dimension technological know-how and, including the six prior volumes during this sequence, constitutes an authoritative resource of the mathematical, statistical and software program instruments precious in sleek metrology.

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**Additional info for Advanced Mathematical and Computational Tools in Metrology VII: 7 **

**Sample text**

2 we introduce some background about the control statistics to be herewith considered, and present a simulation study on their robustness and efficiency. In Sec. 3 we provide information about Box-Cox transformations, and advance with a procedure for monitoring non-normal data, based on a Box-Cox transformation of the original data, followed by the use of the previous "robust" statistics. Finally, in Sec. 4 we present some overall comments about monitoring non-normal processes and conclusions. 2.

Siebert © 2006 World Scientific Publishing Co. (pp. 35-46) BOX-COX T R A N S F O R M A T I O N S A N D R O B U S T CONTROL CHARTS I N SPC FERNANDA OTILIA FIGUEIREDO Faculdade de Economia da Universidade do Porto and CEAUL Rua Dr Roberto Frias, 4200-464 Porto PORTUGAL MARIA IVETTE GOMES CEA UL and DEIO, Universidade de Lisboa Bloco C2, Campo Grande, 1700 Lisboa PORTUGAL In this paper we consider some asymetric models to describe the d a t a process. We assess that, in general, it is possible to find an adequate Box-Cox transformation which enables us to deal with the transformed data as approximately normal.

4. 1. Obtaining the best estimates Viewing key comparison data evaluation as an appropriately defined least squares problem can be fully justified 16 . 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.