This letter applies non-orthogonal multiple access to uplink random access systems, where the transmit power from each user equipment (UE) is received at the base station as one of L target (received) powers. More precisely, if a backlogged UE's channel gain is greater than a threshold, it randomly aims at one of the target powers with channel inversion. Then, the BS decodes the received signals with successive interference cancellation. This letter investigates the performance of this system in terms of throughput, access delay, energy efficiency, and bistability.