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The thermal error of machine tools is one of the main factors affecting the machining accuracy of machine tools. Most of the existed literatures do not consider the randomness of the influencing factors of thermal error, there are still difficulties in accurate prediction and compensation of thermal error. Therefore, the new prediction models with higher accuracy and reliability are urgently needed. Through simulating the dynamic process of memory loss of the human brain after receiving external excitation, a new dynamic time-varying memory intelligent algorithm with external excitation is proposed in this paper. Furthermore, a novel random dynamic time-varying memory intelligent algorithm with external excitation is proposed considering the randomness of factors in this paper. Considering the randomness of factors affecting thermal error, the proposed models are used for the prediction of reliability of thermally-deduced positioning accuracy for machine tool ball screw system under external excitation caused by manufacturing process alternations of machine tools. Finally, the effectiveness of the proposed models is verified by the experiment. Because the presented model can consider the randomness of factors affecting thermal error and the impact and hysteresis phenomenon caused by the alternations of multiple processes, it is suitable for the accurate prediction of the dynamic characteristics under the alternation of arbitrary excitation considering the reliability. [Display omitted] • A new time-varying dynamic memory intelligent model with external excitation was proposed. • A novel random time-varying dynamic memory intelligent model with external excitation was proposed. • This model is suitable for the accurate prediction of dynamic characteristics considering reliability. • The experiments verify the effectiveness and feasibility of the proposed models. [ABSTRACT FROM AUTHOR]