The possibilistic reliability theory: Theoretical aspects and applications

The need to treat uncertainties in the design or assessment of structures today induces a lot of concerns in order to ensure the best security levels. This paper presents an original alternative to the probabilistic reliability theory, keeping the same features regarding some theoretical concepts (design paints, reliability indexes) but highlighting easy implementations. The probabilistic or classical reliability theory is built on the principles of probability theory which introduces the probabilistic measure for evaluating confidence levels; the theory introduced in this paper is based on the possibility theory which uses a new confidence measure: the measure of possibility. While the probabilistic approach requires optimization of a multivariate function, the possibilistic approach reduces the study to the optimization of a variable function. Care is taken in explaining how to implement such a technique and for estimating distributions of possibility. Comparisons between the possibilistic and the probabilistic reliability theories are also given. Finally a section is dedicated to a concrete application: the reliability assessment of welded joints damaged by fatigue. This example provides a full application of the possibilistic reliability theory, from uncertainty modeling and possibility distribution estimation to failure possibility determinations. (C) 1997 Elsevier Science Ltd.