This study addresses the stochastic parallel assembly line balancing problem with equipment costs and presents a hyper-heuristic approach based on simulated annealing for solving it. A cost-based objective function is employed to represent the incompletion, equipment, and station installation costs. The hyper-heuristic approach is utilized to search on sequencing heuristics search space, rather than a problem-specific solution space. This study focuses on the consideration of equipment costs while balancing a stochastic parallel assembly line. The performance of the solution approach is also tested on the single-model stochastic assembly line balancing problems and stochastic parallel assembly line balancing problems due to the generalizability of hyper-heuristics. The results of the benchmark problems show that in most cases the proposed algorithm provides better solutions than the best-known solutions in literature. An extensive computational study performed to determine the parameter levels derived from the problem and the solution method. The effect of the equipment costs for stochastic parallel assembly lines is also analyzed in detail.