This paper presents a comprehensive analysis of time and action operational costs on an objective function developed by Bechar et al. (A. Bechar, J. Meyer and Y. Edan, “An objective function to evaluate performance of human–robot collaboration in target recognition tasks,” IEEE Trans. Syst. Man Cybern. Part C39(6), 611–620 (2009)) for collaborative target recognition systems. Different task types, system reaction types, and environments were evaluated. Results reveal two types of task and system reactions – one focused on minimizing false alarms, and the second on detecting a target when one is presented. In addition, the analysis reveals a new property of the objective function based on a specific ratio between the weight differences that generalizes the model's objective function and facilitates its analysis. Results indicate that human decision time strongly influences system performance.