Shuang Li
Department of Statistics
University of South Carolina
A Gibbs Measure/Markov Random Field Representation for Complex
Load-Sharing Systems
Complex load-sharing systems are proposed to incorporate dependencies
between components through a load-sharing rule. Such systems were used to
model the strength of fibrous composites where component failures occur in
cycles having two phases. As the load on the system increases, the first
phase is a single component failure (Phase I), which then causes a cascade
of component failures (Phase II) due to the load transfer as these Phase II
failures occur. Under monotone load sharing the failures have a simple
Markovian structure. Given the history of failures, the current state of the
system only depends on the latest Phase I failure and the corresponding
Phase II failures have a Gibbs measure/Markov random field representation
when the component strengths are independent.
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