ABSTRACT
Many complex industrial systems have such high safety requirements that no failure is observed during their lifetime. Nevertheless, companies have to periodically justify their resistance to several extreme scenarios. In this context, the behaviour of certain critical components is modelled and simulated using complex numerical codes. The system’s reliability properties are then obtained by propagating uncertainties from the input variables to the output quantity of interest. In this structural reliability context, a key input parameter of a steel component physical model is the distribution of non-evolutive conception flaw sizes. This distribution can be estimated from a mixture of measures from destructive lab experiments, seen as a perfect sample of the target distribution, and measures from periodic in-service inspections, plagued by noise and limited numerical precision. Moreover, during these inspections, any given flaw may be detected or not, with a probability depending on its size. This crucial characteristic of the measurement process is modeled as an increasing function of the flaw size, known as the Probability Of Detection (POD). POD function are often modeled assuming a parametric form, such as a log-normal or logistic CDF. However, we show that in certain cases such models are invalidated by the data at hand, and propose instead a much more flexible way of estimating the POD function, which does not assume any predefined shape.
