In this paper, we study a layered random access scheme based on non-orthogonal multiple access (NOMA) to improve the throughput of multichannel ALOHA. At a receiver, successive interference cancellation (SIC) is carried out across layers to remove the signals that are already decoded. A closed- form expression for the total throughput is derived under certain assumptions. It is shown that the transmission rates of layers can be optimized to maximize the total throughput and the proposed scheme can improve the throughput with multiple layers. Furthermore, it is shown that the optimal rates can be recursively found using multiple individual one-dimensional optimizations. We also modify the proposed layered random access scheme with contention resolution repetition diversity for reliable transmissions with a delay constraint. It is shown to be possible to have a low outage probability if the number of copies can be optimized, which is desirable for high reliability low latency communications.