Tensile failure load and fiber diameter as stochastic variables in the determination of fiber strength statistics

The combined effect of treating failure load and fiber diameter as stochastic variables, on reliability is examined. The approach assumes specific distributions for diameter and failure load to determine the reliability of the system, through a joint probability distribution function defined over a two-dimensional region of feasibility. It is shown that neglecting diameter variations results in a lower probability of failure making the prediction for the system potentially unsafe. This effect is significant for high Weibull modulus materials.