A non-probabilistic concept of reliability

Uncertainty can be modelled either probabilistically or non-probabilistically. The former option leads to the concept of reliability as the probability of no-failure. In this paper non-probabilistic convex models of uncertainty are used to formulate reliability in terms of acceptable system performance given uncertain operating environment or uncertain geometrical imperfections. It is shown that probabilistic reliability can be very sensitive to small inaccuracy in the probabilistic model. Consequently, the non-probabilistic concept of reliability is useful when insufficient information is available for verifying a probabilistic model. In addition, a theorem is presented showing that analogous convex and probabilistic models of input uncertainty can lead to very different predictions of the range of output variation.