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This paper proposes a new stochastic composite iterative learning control for batch processes with actuator faults that happen with a certain kind of probability. The main contribution lies in the fact that stochastic control theory is used to analyze the stability issues and consider controller designs of batch processes with actuator faults that happen under various kinds of probability, which paves the way for reliable control theory. Firstly, the batch process is represented as a system with stochastic uncertainty for iterative learning control design; and with the state and output error, it is further treated into a two dimensions (2D) Rosser system with stochastic errors. Using such transformation, the iterative learning control design is transformed into the updating control law design. Secondly, 2D Lyapunov stochastic theory is used to design the controller with actuator faults under various kinds of probability, together with the stability results of the control system in terms of LMI conditions. Finally, the proposed method is tested on the injection molding process to demonstrate the effectiveness.