In this work, we investigate the relationship between the reliability and security of a typical two-user downlink non-orthogonal multiple access (NOMA) communication system. The level of successive interference cancellation on NOMA user is considered. Firstly, the impact of various key parameters on transmit signal-to-noise ratio (SNR) of the NOMA users with the reliability outage probability (ROP) constraint is discussed. Taking the minimum of transmit SNR for ROP into account, the secrecy outage performance of the downlink NOMA systems is studied and the analytical expressions of the secrecy outage probability of the NOMA system are derived under two cases of eavesdropping capability. Furthermore, the sum effective secrecy throughput of the NOMA system under two scenarios with considering ROP constraint is derived. Monte Carlo simulations are provided to verify the accuracy of our analysis.