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In this paper, the reliability performance of a non-orthogonal multiple access (NOMA) system is addressed. We characterize the reliability performance of the users in a downlink power domain NOMA system with arbitrary ordered pulse-amplitude modulation and quadrature amplitude modulation. In particular, the exact symbol error rate (SER) expressions are derived. Furthermore, by taking the power allocation between users into account, a reliability optimization problem is formulated, which minimizes the SER of the user with a good channel quality while guaranteeing the reliability requirement for the user with a relatively poor channel. Based on the characterized SER model, a suboptimal power allocation approach for this problem is provided with a performance extremely close to the optimal solution. Through simulations, we validate the provided SER characterization and confirm the effectiveness of the proposed suboptimal power allocation policy.