  In this paper, we study the distribution function of the time of explosion of
a stochastic differential equation modeling the length of the dominant crack
due to fatigue. The main novelty is that initial condition is regarded as an
anticipating random variable and the stochastic integral is in the forward
sense. Under suitable conditions, we use the substitution formula from Russo
and Vallois to find the local solution of this equation. Then, we find the law
of blow up time by proving some results on barrier crossing probabilities of
Brownian bridge.
