A consecutive-k-out-of-n:G system consists of n components which are arranged in a line and the system works if and only if at least k consecutive components work. This paper discusses the optimization problems for a consecutive-k-out-of-n:G system. We first focus on the optimal number of components at the system design phase. Then, we focus on the optimal replacement time at the system operation phase by considering a preventive replacement, which the system is replaced at the planned time or the time of system failure which occurs first. The expected cost rates of two optimization problems are considered as objective functions to be minimized. Finally, we give study cases for the proposed optimization problems and evaluate the feasibility of the policies.