Hazard alerting systems alert operators to potential future undesirable events so that action may be taken to mitigate risk. One way to develop a hazard alerting system based on probabilistic models is by using a threshold-based approach, where the probability of the undesirable event without mitigation is compared against a threshold. Another way to develop such a system is to model the system as a Markov decision process and solve for the hazard alerting strategy that maximizes expected utility. This paper analyzes and compares these two methods. The experiments reveal that an expected utility approach performs better than threshold-based approaches when the dynamic stochasticity is high, where accounting for delays or changes in the alert becomes more important. However, for certain system parameters and operating environments, a threshold-based approach may provide comparable performance.