Title: Imprecise reliability assessment when the type of the probability distribution of the random variables is unknown

Authors: Efstratios Nikolaidis, Zissimos P. Mourelatos

Addresses: Mechanical Industrial and Manufacturing Engineering Department, The University of Toledo, 4035 Nitschke Hall, MS 312, Toledo, OH 43606, USA. ' Department of Mechanical Engineering, Oakland University, 133 Dodge Hall of Engineering, Rochester, MI 48309-4478, USA

Abstract: In reliability design, often, there is scarce data for constructing probabilistic models. It is particularly challenging to model uncertainty in variables when the type of their probability distributions is unknown. Moreover, it is expensive to estimate the upper and lower bounds of the reliability of a system involving such variables. A method for modelling uncertainty by using Polynomial Chaos Expansion is presented. The method requires specifying bounds for statistical summaries such as the first four moments and credible intervals. A constrained optimisation problem, in which decision variables are the coefficients of the Polynomial Chaos Expansion approximation, is formulated and solved in order to estimate the minimum and maximum values of a system|s reliability. This problem is solved efficiently by employing probabilistic re-analysis to approximate the system reliability as a function of the moments of the random variables.

Keywords: imprecise probability; importance sampling; PRRA; probabilistic re-analysis; reliability assessment; unknown probability distribution; random variables; reliability design; uncertainty modelling; polynomial chaos expansion.

DOI: 10.1504/IJRS.2011.039300

International Journal of Reliability and Safety, 2011 Vol.5 No.2, pp.140 - 157

Published online: 31 Mar 2011 *

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