We show that the failure time τf in the fiber bundle model, taken as a prototype of heterogeneous materials, depends crucially on the strength of the disorder δ and the stress release range R in the model. In the mean-field limit, the distribution of τf is log-normal. In this limit, the average failure time shows the variation τf∼Lα(δ), where L is the system size. The exponent α has a constant value above a critical disorder δc (=1/6), while it is an increasing function of δ in the region δ<δc. On the other hand, in the limit where the local stress concentration plays a crucial role, we observe the scaling τf∼Lα(δ)φ(R/L1-α(δ)), where R is the stress release range. We find that the crossover length scale Rc, between the above two limiting cases, scales as Rc∼L1-α(δ).