In real-world industrial environments, unplanned events and unforeseen incidents can happen at any time. Scheduling under uncertainty allows these unexpected disruptions to be taken into account. This work presents the study of the flexible job shop scheduling problems (FJSP) under machine breakdowns. The objective is to solve the problem such that the lowest makespan is obtained and also robust and stable schedules are guaranteed. A two-stage particle swarm optimization (2S-PSO) is proposed to solve the problem assuming that there is only one breakdown. Various benchmark data taken from the literature, varying from Partial FJSP to Total FJSP, are tested. Computational results prove that the developed algorithm is effective and efficient enough compared to literature approaches providing better robustness and stability. Statistical analyses are given to confirm this performance.