The ability of meeting the target production lead times is of fundamental importance in modern manufacturing systems producing perishable products, where the product quality or value deteriorates with the time parts spend in the system, and in manufacturing contexts where strict lead time constraints are imposed due to tight shipping schedules. In these settings, traditional manufacturing system engineering methods and token-based production control policies loose effectiveness as they aim at achieving target production rates while minimizing the inventory, without directly taking into account the effect on the lead time distribution. In this paper a production control policy for unreliable manufacturing systems that aims at maximizing the throughput of parts that respect a given lead time constraint is proposed for the first time. The proposed policy jointly considers the actual level of the buffer and the state of the second machine in the system and stops the part loading at the first machine if there is unacceptable risk of exceeding the lead-time constraint. The effectiveness of this new policy against the traditional Kanban policy is quantified by numerical analysis. The results show that this new policy outperforms the Kanban policy by providing a tighter control on the production lead time. This approach paves the way to the introduction of new lead-time oriented production control policies to maximize the effective throughput in real manufacturing systems.