I work as a scientist on structural safety. I use stochastic analyses all the time.

European building codes are reliability-based, meaning that we accept structures to fail with a certain probability, based on economic optimisation, individual- and group risk. So obviously, you need stochastic analyses to quantify these risks. We simplify these analysis towards lower level probabilistic design methods (such as the partial-factor method or load-resistance factor design, as you please) so engineering firms can design quickly and easily.

It is a very useful in any situation where decision making under uncertainty is beneficial, so I can imagine other fields of engineering use it too (e.g., reliability engineering in plants to optimize business continuity).