Introduction

This paper describes the present stage of development of a joint research project conducted at EADS/CCR (European Aeronautic Defence and Space Company, Corporate Research Center, Suresnes) and ENSAIT (Ecole Nationale Superieure des Arts et Industries Textiles, Roubaix). The central aim of this project is a reflexion about the determination of uncertainties during mechanical tests.

Since these uncertainties have obvious consequences concerning security and costs for the aeronautic industry as well as for the technical textiles' industry, the focus of the project is onto the effectiveness of the implementation of the protocols. Our research team started working together for a last year project of an ENSAIT student [2].

A first publication of our results has been done in an invited conference at the 2002 UNCERT Symposium in Paris [1]. This conference was given towards the measure labs community, while the present paper is written towards the data mining community and collects new unpublished results in it's second half.

The paper is organized as follows. A short remainder about tensile testing is given in Section II. The main lines of [1] are summarized in Section III, the emphasis being over the following key point: when determining Young's modulus (or more generally, when determining the slope $a$ of a first order effect), one has not to extract one number from data, but four. Beside the slope $a$ itself, one has to detect the best domain of validity of the model, noted $\left[ \alpha , \beta \right]$ in what follows, and a quality factor $q\! f$ describing how relevant is a linear model for what is studied.

Section IV examines which uncertainty can be associated with the obtained slope. This uncertainty is strongly dependent upon assumptions over the collected data, concerning especially the degree of auto-correlation of the "remaining noise". When checking these assumptions, it will be seen that unexpected "long range tendencies" are encountered and are requesting for some explanation.

Thereafter, Section V is devoted to a "reverse paradigm" study, where the data collected for a lot of test pieces are used to characterize not the test pieces themselves, but rather the testing process. It will be shown that many properties can be derived from the fact that, due to discretization, the collected data are not random points in a continuum, but rather integer multiples of some quantum.

The paper ends with a concluding section and a bibliography.

Concerning the statistical versus mechanical notations conflict : the Young's modulus has been noted by an italic $E$ and the expectation by a roman ${\mathrm{E}}\left( \right)$, while $\sigma$ has been reserved for the stress, the standard deviation being noted as $\sqrt{{\mathrm{var}}\left( x \right) }$. Nevertheless, the reduced standard deviation has been shortened as $\sigma _{red}$.