Many problems in stochastic modeling come down to study the crossing time of a certain stochastic process through a given boundary, lower or upper. Typical fields of application are in risk theory, epidemic modeling, queueing, reliability and sequential analysis. The purpose of this talk is to present a method to determine boundary crossing probabilities linked to stochastic point processes having the order statistic property. A very well-known boundary crossing result is revisited, a detailed proof is given. the same arguments may be used to derive results in trickier situations. We further discuss the practical implications of this classical.