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Network Function Virtualization (NFV) is a vital player of modern networks providing different types of services such as traffic optimization, content filtering, and load balancing. More precisely, NFV is a provisioning technology aims at reducing the large Capital Expenditure (CapEx) of network providers by moving services from dedicated hardware to commodity servers using Virtualized Network Functions (VNF). A sequence of VNFs/services following a logical goal is referred to as a Service Function Chain (SFC). The movement toward SFC introduces new challenges to those network services which require high reliability. To address this challenge, redundancy schemes are introduced. Existing redundancy schemes using dedicated protection enhance the reliability of services, however, they do not consider the cost of redundant VNFs. In this paper, we propose a novel reliability enhancement method using a shared protection scheme to reduce the cost of redundant VNFs. To this end, we mathematically formulate the problem as a Mixed Integer Linear Programming (MILP). The objective is to determine optimal reliability that could be achieved with minimum cost. Although the corresponding optimization problem can be solved using existing MILP solvers, the computational complexity is not rational for realistic scenarios. Thereafter, we propose a Reliability-aware and minimum-Cost based Genetic (RCG) algorithm to solve this problem with low computational complexity. In order to evaluate the proposed solution, we have compared it with four different solutions. Simulation results show that RCG achieves near-optimal performance at a much lower complexity compared with the optimal solution. [ABSTRACT FROM AUTHOR]