This paper encloses an in-depth investigation of a novel cost-efficient reliability-guaranteed deployment scheme for service function chains (SFCs) to tackle the drawbacks of the existing studies for the virtual network function (VNF) redundancy allocation. We model the VNF redundancy allocation as a cost minimization problem using the integer linear programming (ILP). For the VNF redundancy allocation, we first examine various reliability importance measures in the system reliability theory for the VNF environments. We then propose a novel cost-aware criticality-based priority index (CCI) to evaluate the priority level of VNFs in the SFC level and the network level for the VNF redundancy allocation. Based on CCI, we design a cost-efficient VNF redundancy allocation algorithm, namely, CCI-RA. Through our comprehensive simulation and analysis results, we show that the proposed scheme achieves a significant improvement in terms of the cost efficiency, scalability, and the percentage of the admitted services compared to the existing approaches. INDEX TERMS Service function chaining, SFC deployment scheme, cost efficiency, on-demand requirement.