Estimation of stress‐strength reliability based on tail‐modelling

In probabilistic design it is common to use parametric statistical models to calculate the probability of failure (Pf) obtained from stress‐strength interference theory. In this respect, it is well known that Pf is sensitive to the shape of the upper and lower tails of the stress and strength distributions respectively and also to their interference. If the true shapes of these tails could be discovered, it would be possible to improve the existing techniques. However, in practice there is seldom sufficient real data available to establish these tails with statistical significance. Moreover, often one or both variables are expensive to sample. Thus a separate tail estimation may not always be possible. Motivated to define a theoretical safety factor, the author presents a method here which provides a general solution to the problem by considering the tail estimation for a sample of increased sized. This is obtained by a reformulation of the problem in terms of excesses over a threshold, and by breaking the analysis into two parts; estimation of the number of exceedances and modelling the excesses. The analysis is carried out by non‐parametric estimation of the former and parametric modelling of the latter based on data from the critical region.