Title: Imprecise probabilities based on generalised intervals for system reliability assessment

Authors: Yan Wang

Addresses: Woodruff School of Mechanical Engineering, Georgia Institute of Technology, GA 30332, USA

Abstract: Different representations of imprecise probabilities have been proposed, where interval-valued probabilities are used such that uncertainty is distinguished from variability. In this paper, we present a new form of imprecise probabilities for reliability assessment based on generalised intervals. Generalised intervals have group properties under the Kaucher arithmetic, which provides a concise representation and calculus structure as an extension of precise probabilities. With the separation between proper and improper interval probabilities, focal and non-focal events are differentiated based on the associated modalities and logical semantics. Focal events have the semantics of critical, uncontrollable, and specified in probabilistic analysis, whereas the corresponding non-focal events are complementary, controllable, and derived. A logic coherence constraint is proposed in the new form. Because of the algebraic properties of generalised intervals, conditional interval probability can be directly defined based on marginal interval probabilities. A Bayes| rule with generalised intervals allows us to interpret the logic relationship between interval prior and posterior probabilities. The imprecise Dirichlet model is also extended with the logic coherence constraint.

Keywords: interval arithmetic; generalised intervals; imprecise probability; imprecise Dirichlet models; conditioning; updating; system reliability; reliability assessment; uncertainty; variability; logic coherence constraints.

DOI: 10.1504/IJRS.2010.035572

International Journal of Reliability and Safety, 2010 Vol.4 No.4, pp.319 - 342

Available online: 30 Sep 2010 *

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