Probabilistic estimates for multivariate analyses

Abstract

The ways in which engineering systems fail (i.e., their occurence and frequency) demonstrate considerable differences between hypothetical models assumed for design and actual performance. All materials contain imperfections. All systems are subject to complex interrelationships, material defects, structural deficiencies, human errors, ambient fluctuations, and, hence, to varying degrees of randomness (uncertainties). Various methods have been offered to accomodate uncertainty. The most common, by far, is to assign single-valued point estimates that reflect central tendencies or implied levels of conservatism. Analyses are then reduced to deterministic treatments. More direct probabilistic methods employ Monte Carlo simulations or truncated Taylor series. However, analyses rapidly become exceedingly difficult, if not impossible, for these methods for all but a very few uncorrelated random variables. These matters and others have been ameliorated by Rosenblueth's point estimate method. 1 Many problems are encountered that require numerous correlated random variables. For such systems all of the above methods become untractable. This paper presents a simple procedure that accomodates the analyses of such systems.