The susceptibility of masonry walls to out-of-plane failure under seismic loading presents a significant engineering concern. In adherence to contemporary limit state design philosophy and as mandated by performance- based design guidelines, it is crucial to accurately estimate statistics parameters such as the mean and variance of out-of-plane resistance. To achieve this, two deterministic models are often considered within the Monte Carlo simulation framework: design-code models, known for their computational efficiency but potential for significant model error, and mechanics-based finite element models, noted for their accuracy but computational intensity. Relying solely on either model for statistics estimation presents challenges due to their respective inherent limitations. This study introduces an improved strategy that synergizes the strengths of both models, resulting in enhanced statistics estimators for the out-of-plane resistance of masonry walls. The proposed methodology involves the use of the control variate method by integrating numerous design-code model evaluations to boost computational efficiency while incorporating a limited number of finite element model evaluations to ensure accuracy. The constructions of the proposed estimators follow rigorous optimization procedures to minimize associated errors and variances. Theoretical derivations are provided for essential elements in the estimator constructions, such as model evaluation numbers for finite element and design-code models and control variate coefficients. Moreover, the accuracy of the proposed estimators is compared with that of the crude Monte Carlo estimator. A key benefit of the proposed estimators is their unbiased nature, and their accuracy is not compromised by the discrepancies between the finite element model and the design-code model. To demonstrate the practicality of these estimators, two case studies are illustrated: one focusing on unreinforced masonry walls and the other on reinforced masonry walls. The results indicate that design-code model-based estimators exhibit large bias, and compared to the estimators that solely rely on the finite element model, the proposed estimators achieve higher accuracy given the same computational budget.
