Wireless technologies are nowadays being considered for implementation in industrial automation. However due to strict reliability and timeliness requirements of time-critical applications, there are many open research challenges for the merger of wireless technologies with the industrial systems. Although many medium access and control (MAC) protocols are proposed in recent years, a coherent effort on both the physical (PHY) and MAC layers is needed. In this paper, we propose a protocol termed as multiple equi-priority MAC (MEP-MAC) which combines the functions of MAC and PHY layers: the MAC layer ensures a deterministic behavior of the system by assigning priorities to the nodes, while non-orthogonal multiple access (NOMA) at PHY layer enables multiple nodes of equal priorities to simultaneously gain the channel access and transmit data to the gateway. We adapt a discrete-time Markov chain (DTMC) model to handle multiple nodes of equal priorities and perform the analytical analysis of the proposed protocol. The results show that the proposed protocol can provide up to 70% and 40% improvement in terms of system throughput and latency respectively as compared to a system that does not leverage NOMA at PHY layer.