For discrete decision-making problem with potential system faults, one-way strategy (i.e., fault diagnosis for decision or decision for fault diagnosis) has been generally adopted. However, considering the interdependency between decisions and fault diagnosis, joint operation between them can be a better solution. From this point of view, a joint decision and fault estimation (JDFE) strategy is presented in this paper. In the strategy, we introduce fault hypothesis probability as a latent variable and the Bayes risk concept for decision making. Also, we propose a sophisticated fault hypothesis probability update law that takes mission performance into account, and prove the convergence of the update law in terms of a quadratic Lyapunov function. Finally, the proposed JDFE algorithm is applied to the formation control of interconnected UAVs. Numerical simulations demonstrate that the JDFE is a robust optimal decider and fault estimator with satisfactory performance.