Component assignment problem is a common challenge of reliability optimization, which is a non-deterministic polynomial hard problem widely used in the linear consecutive k-out-of-n systems. In consideration of the advantages of quantum computing and importance measure, this article proposed a novel algorithm, which is Birnbaum importance-based quantum genetic algorithm, to improve the efficiency and accuracy for solving component assignment problem. First, the model of reliability optimization for linear consecutive k-out-of-n systems is established. Second, the detailed procedure of Birnbaum importance-based quantum genetic algorithm is introduced to solve the component assignment problem. Moreover, the effectiveness and the convergence of the quantum genetic algorithm, Birnbaum importance-based genetic local search, and Birnbaum importance-based quantum genetic algorithm is discussed through two comparative experiments. Finally, the case of production monitor systems is introduced to illustrate the effectiveness of Birnbaum importance-based quantum genetic algorithm comparing with the Birnbaum importance-based two-stage approach.