1. Probabilistic approach to uncertainty

1.1 Introduction

Throughout history, trial and error has provided an initial response to dimensioning under uncertainty, sometimes at the cost of disaster. Then, behavioral modeling led to the development of forecasting tools, which introduced both discrepancies between the model and physics, and data uncertainties. To take this into account, designers capitalized on the experience of manufacturers, transcribed into codes, standards or regulations; the application of formulas containing so-called safety coefficients led to the belief that compliance with them guaranteed reliability. It's true that the resulting reliability is generally satisfactory, but it is neither measured nor quantified.

A first approach consists in setting barriers: foreseeing that a...