Modelling consequences from failure and material properties by distribution mixtures

摘要

The main result of this paper is the finding that the maximum variance of any distribution mixture is attained from sampling one or at most two individual distributions composing the mixture. An upper bound for the variance of the properties from sampling inhomogeneous microstructure is derived which does not depend on the probabilities with which the individual microstructural zones are sampled. A powerful analogy exists between the distribution of the mechanical properties from sampling inhomogeneous microstructure and the distribution of consequences given failure. The consequences from failure are modelled by a distribution mixture composed of the individual distributions of the consequences from failure characterising mutually exclusive failure modes. Similarly, an efficient algorithm is developed which determines the upper bound of the variance of the consequences from failure irrespective of the probabilities of triggering the separate failure modes. The concept 'potential losses from failure' is introduced. It is demonstrated that the potential losses from failure is a distribution mixture and its expected value equals the risk of failure. An expression for the variance of the potential losses from failure is also derived. Using the model of the consequences from failure as a distribution mixture, a method is developed for setting reliability requirements based on minimum failure-free operating periods (MFFOP). The MFFOP reliability requirements limit the risk of premature failure below a maximum acceptable level.