The Time to Failure of Cables Subjected to Random Loads.

The effect on cable reliability of random cyclic loading such as that generated by the wave induced rocking of ocean vessels deploying these cables is examined. A simple model yielding explicit formulas is first explored. In this model, the failure time of a single element under a constant load is assumed to be exponentially distributed, and the random loadings are a two state stationary Markov process. The effect of load on failure time is assumed to follow a power law breakdown rule. In this setting, explicit results concerning the distribution of bundle or cable failure time, and especially the mean failure time, are obtained. Where the fluctuations in load are frequent relative to cable life, such as may occur in long-lived cables, it is shown that randomness in load tends to decrease mean cable life, but it is suggested that the reduction in mean life often can be restored by modestly reducing the base load on the structure or by modestly increasing the number of elements in the cable.