Abstract: The identity between the probability of occurrence of a crack which is larger than a given crack size a0 at t=t* and the probability of fatigue life which is less than t*at a=a0 is proved in this paper. The functional relation between the distribution of fatigue, life and the. distribution of crack sizes is established by probabilistic approach. In virtue of this relation the probability of crack exceedence and the probability density function of crack sizes at a given life, can be derived from those of fatigue life at a prescribed crack size. A P-a-t surface is also presented in this paper.