In normal non-orthogonal multiple access (NOMA) network, perfect successive interference cancellation (SIC) and perfect hardware impairments are usually admitted at transceivers. However, imperfections of SIC and hardware exist in mathematical analysis of practical system, and such imperfections provide guideline to deploy NOMA in practical circumstances effectively. To overcome these disadvantages, this paper considers relaying NOMA as existence of hardware noise and interference of imperfect SIC operation and hence degraded performance under related factors can be addressed. We examine the system performance of the proposed system and develop a closed-form formulation of outage probabilities for each user. In high signal to noise ratio regime, we consider the corresponding asymptotic outage probability to provide meaningful insights in our proposed schemes. We also exhibit comparison study with other works related performance evaluation and with Decode and Forward based NOMA as useful benchmark. To further examine system performance of the proposed scheme, we derive formula and verify results in term of the throughput performance. Finally, numerical examples are performed to validate the effectiveness of the proposed scheme as practical challenges are raised, and compare these performance considerations with that in other system models with respect to outage behavior as varying related parameters.