Non-orthogonal multiple access (NOMA) is a promising air-interface technology for its ability to support massive wireless mobile terminals. In this paper, the outage performance for uplink NOMA systems employing the dynamic ordered successive interference cancellation receiver is analyzed under the independent but not identically distributed (i.ni.d.) fading environment. We theoretically reveal the general approach to derive the closed-form outage probability expression for an arbitrary number of serving users. Under the i.ni.d. fading environment, the probability for each possible decoding order is derived respectively based on the observation of the time-varying received power strength for each user. Furthermore, encountering the challenge of solving the multidimensional integration, a recursive method is proposed to deal with the conditional outage probabilities under a certain decoding order as a joint probability problem with the linear constraints of the decoding order and the required data rate. Finally, we derive the closed form outage probability expressions. The simulations are performed to validate the accuracy of the theoretical results and reveal the superiority of the dynamic mode over the fixed one.