Negative Log‐Gamma distribution for data uncertainty modelling in reliability analysis of complex systems ‐ Methodology and robustness

Abstract

In the paper, the problem of uncertain data in reliability analysis of complex systems is examined. The analysis is addressed to system reliability assessment with imprecise knowledge of component reliabilities, an item becoming more and more important for systems affected by considerable technological change. Starting from component uncertain data, a new method for the whole system reliability uncertainty description, based upon a Bayesian approach and not depending on the reliability model of each component, is proposed. The reliability value of each component is considered as a random variable described by a Negative Log‐Gamma distribution. The proposed methodology makes it possible to compute the features of system reliability uncertainty (i.e. reliability distribution, confidence intervals, etc.) as functions of component uncertain data, thus characterizing the propagation of uncertainty from the components to the system. Numerical applications, related to a test system, are presented to show the validity of the method and its “robustness”, i.e. it is shown that it yields satisfactory results also when component reliabilities are not Negative Log‐Gamma but Beta distributed.