The emergence of new applications (e.g., mobile robots, smart logistics, virtual reality, and augmented reality) in the factory automation scenario has made industrial wireless networks (IWNs) a trend to replace traditional wired networks. One of the urgent challenges is to achieve ultra-reliable and low-latency communications in IWNs. In this article, to cope with massive periodic traffic and lost packets due to volatile channel conditions in IWNs, we, for the first time, combine non-orthogonal multiple access (NOMA) with the automatic on-demand retransmission scheme. To be specific, we formulate an optimization problem to maximize transmission reliability, subject to the constraints of transmit powers and the scheduling policy, and give a detailed analysis of the optimal solution to the formulated problem. To achieve the optimum, we propose an NOMA-based on-demand retransmission (NODR) scheme and derive a closed-form expression for transmission reliability in the case when all the packets experience the same packet error rate. Simulation results demonstrate the effectiveness and efficiency of the NODR scheme over other schemes under different channel conditions.