The Single-Failure Criterion (SFC) is a defined rule for implement convenience with the goal of ensuring high reliability of safety systems coping with design basis accidents. However, from the perspective of the overall plant risk, design failure to meet the SFC does not always mean high risk, as it depends on the frequency of specific accident scenarios, the reliability of certain equipment, and the consequence of the accidents, which cannot be generalized. This paper focuses on the origin and application of the SFC. On one hand, application insights are provided on unclear or ambiguous aspects of the existing SFC, and an analysis process for determining whether system design meets the SFC is provided. On the other hand, to explore ways to improve the application of the SFC using risk insights, three Risk-Informed Single Failure Criterion (RI-SFC) alternatives are discussed, which respectively considers risk-informing SFC application scope in DBA analysis, risk-informing system redundancy requirement based on their safety importance, and generalized reliability criteria combined with functional unreliability target and different level of redundancy and diversity. The paper also outlines the application suggestions of the three RI-SFC improvement alternatives for short-term and long-term, which can serve as supplements and verification means for current deterministic-based reliability design criteria. A specific single failure issue for boundary isolation valves of a passive secondary residual heat removal system (PRS) for a PWR NPP was analyzed with risk-informed method. The results indicate that, in the safety analysis concerning relevant DBAs, it is unnecessary to assume a single failure of main steam isolation valve (MSIV), and redundant design of MSIV is not required. But measures should be taken to enhance the reliability of the rapid closure function for MSIV and the downstream isolation valves.