Probabilistic design approach. Uncertainty quantification and Monte-Carlo method

The designer's art is to propose a technical solution that satisfies functional requirements and guarantees safety for goods, people and the environment. Functional requirements must ensure that the systems in question operate correctly, and among these is reliability, i.e. the ability of a device to perform a required function under given conditions, for a given period of time. The designer's role is to optimize sizing by justifying sufficient reliability in terms of risk, i.e. the consequences of an undesirable event: absolute reliability cannot exist, and there is always a possibility of failure. Today, it can be said that the precautionary principle only consists in demonstrating that all current knowledge has been applied to ensure that the gain obtained by the success of the device is sufficient to accept the cost of the possible failure due to its malfunction.

These few lines set out the framework of the approach: it proposes an approach to the theoretical reliability of mechanical systems, but it should be noted that it is likely to have applications in many other fields. By theoretical reliability, we mean everything that can be simulated by modeling to predict possible behaviors. It complements practical reliability, which is assimilated to the quality approach: theoretical reliability is conditioned by practical reliability, by quality assurance. Designing a mechanical system and calculating its parameters is a search for a dimensioning whose reliability must be justified.

This dossier is divided into two articles. The first [BM 5 003] deals with the modeling of uncertainty through the necessary notions of probability and statistics. It aims to convince readers of the need for a probabilistic approach to mechanical design, and is illustrated by the Monte-Carlo method. The second [BM 5 004] deals with resistance approximation methods – stress, the basic scheme of which is generalized, and reliability index methods. It shows how to use the results of mechano-fiabilistic analyses as an aid to reliable design. A simple example is used to illustrate the concepts. Finally, it opens up a number of perspectives.