Overview

Complex load-sharing systems are studied to incorporate dependencies among components through a load-sharing rule. Such systems were used to model the strength of fibrous composites. Two representations are obtained for system failure of load sharing systems. One is the Gibbs measure (GM) representation for the component failures that are just due to load transfer (Phase II failures) that are generated by a Markov random field(MRF). The log odds ratios of the individual component strengths are the fundamental building blocks for the related GM representation and define the local structure of such fields. The other is the threshold representation for the breaking strengths of component failures due to increased load (Phase I failure). The mixing distribution for the thresholds of the Phase I breaking strengths is determined by the load-sharing parameters and is based on convolutions of uniforms determined by the breaking patterns and the load-sharing for these patterns. Furthermore, the posterior mixing distribution of these thresholds is particularly simple; the thresholds are independent exponentially tilted convolutions of uniforms when the component strengths are exponential. There can be considerable reduction in the dimension of parameter space since the convolution of uniforms can be approximated by normals.

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9781244044104

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