The Reliability of Series-parallel Load-sharing Systems that Contain Flaws |
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An,i approximation ax+b bundle failure probability bundle size increases bundle strength bundle survives calculations chain-of-bundles model composite compute consecutive failures consecutive fibers Consider a bundle distribution for bundle equal load sharing F K.x failed fiber failure criterion fiber adjacent fiber bundles fiber carries fiber fails fiber strength distribution Figure flaw probability flaws adjacent four fibers G₁(x G₂(x graph Harlow and Phoenix implies individual fiber ineffective length limit distribution load sharing rule local load sharing Markov chain median strength mixed flaw model model as bundle nine fibers nonfailed fiber nP{A number of fibers number of flaws occurs probability distribution pure flaw model r-minimal failure sequence shape parameter single fiber Smith sub-bundle survival configurations Survival probabilities surviving fibers three fibers three flaws unflawed fiber unit strength fiber values weakest link Weibull distribution Weibull probability paper