  We propose an approach to approximate the boundary crossing probabilities for
general one-dimensional diffusion processes, and derive the convergence rate
for this approximation scheme. There results are based on the explicit
expression of the Laplace transforms of the first passage densities for
diffusions with piecewise linear drifts. The proposed method is applied to a
reliability problem where the standard degradation model based on Wiener
process is extended to diffusion processes with piecewise linear drifts.
