Aiming at overcoming the problem that the mechanism function of the unlocking trigger device is difficult to obtain and the corresponding reliability analysis cannot be performed, a motion reliability analysis method based on the CPSO-BR-BP neural network proxy model is proposed. Firstly, the particle swarm algorithm is optimized through the chaotic sequence, and the back-propagation (BP) neural network is optimized using Chaos Particle Swarm Optimization (CPSO) and Bayesian Regularization (BR) algorithm. The CPSO-BR-BP neural network proxy model is established, and the reliability of shape memory alloys (SMA) wire unlocking based on the structural function is calculated. Moreover, according to the structural function of the separation process, the motion reliability based on the proxy model and the improved membership function is calculated. Finally, a series reliability model is established based on the unlocking process and the separation process to calculate the reliability of the whole machine. The reliability of the unlocking trigger device is analyzed by the proposed method. Results show that the proposed method is computationally efficient with the calculated reliability of 0.9987.