All large transport aircraft are required to be equipped with a collision avoidance system that instructs pilots how to maneuver to avoid collision with other aircraft. Uncertainty in the compliance of pilots to advisories makes designing collision avoidance logic challenging. Prior work has investigated formulating the problem as a Markov decision process and solving for the optimal collision avoidance strategy using dynamic programming. The logic was optimized to a pilot response model in which the pilot responds deterministically to all alerts. Deviation from this model during flight can degrade safety. This paper extends the methodology to include probabilistic pilot response models that capture the variability in pilot behavior in order to enhance robustness.