This study discusses the application of sequential decision making under uncertainty and mixed observability in a mixed-initiative robotic target search application. In such a robotic mission, two agents, a ground robot and a human operator, must collaborate to reach a common goal using, each in turn, their recognized skills. The originality of the work relies in considering that the human operator is not a providential agent when the robot fails. Using the data from previous experiments, a Mixed Observability Markov Decision Process (MOMDP) model was designed, which allows to consider aleatory failure events and the partial observable human operator's state while planning for a long-term horizon. Results show that the collaborative system was in general able to successfully complete or terminate the mission, even when many simultaneous sensors, devices and operators failures happened. So, the mixed-initiative framework highlighted in this study shows the relevancy of taking into account the cognitive state of the operator, which permits to compute a policy for the sequential decision problem which prevents to re-planning when unexpected (but known) events occurs.