In this paper we consider a failure prone production system with deterministic production cycles. The objective is to find the optimal production rate to minimize long-run average cost. We first show that the optimal control policy belongs to a type of switching curve policy which has a special structural property and can be characterized by a single parameter. We then establish a relationship between the surplus process of the system under the optimal control policy and the workload process of a D/G/1 queue, based on which the existing results in queueing theory which can be applied to obtain the steady-state probability distribution of the surplus process under the optimal control policy.