| E. T. Jaynes' Maximum Entropy Principle is applied to the problem of the reliability of bundles of brittle elastic fibers under a tensile load. If a bundle is inhomogeneous (consisting of fibers of differing cross-sectional areas), and if the ratios of the cross-sectional areas are irrational, then the M.E.P. leads to the result that the log of the survival odds of a fiber is proportional to the cross-sectional area. This result restricts the survival strain distribution of the individual fibers to a class of distributions which generalize the log-logistic distribution. Analysis of individual fiber strength data from Bader and Priest shows that the survival strengths fit an inverse Gaussian distribution, which is not a member of the generalized log-logistic class. There is a one-to-one relationship between the survival strain distribution for the individual fibers and the survival strain distribution for the fibers embedded in an inhomogeneous bundle. Characteristics of a particular member of the generalized log-logistic class, the g*-log-logistic distribution, are discussed, including existence of moments of all orders, parameter estimation, and asymptotic behavior of minima. The distribution is applied to fibers comprising a bundle to obtain the bundle reliability, the hazard function and the Daniels criterion breaking strain. |
