Network function virtualization (NFV) allows for implementing network functions as softwares running on standard servers, called virtual network functions (VNFs). This raises availability/reliability issues such as hard- and soft-ware failures. Thus, merely mapping primary VNFs is not enough to ensure high availability/reliability. As a result, additional protection schemes are required to improve the availability/reliability of services. With a limited resource allocated for each improvement, selecting the most potential VNFs for improving which can help maximize the reliability improvement with an appropriate cost is desirable. This paper proposes a metric to measure the improvement potential per a unit cost for VNFs. An efficient VNF selection scheme is designed based on the metric. Obtained numerical results show that the proposed selection scheme achieves higher cost efficiency and better system reliability within a limited resource.