A Rapid Method for Calculating the Damage Probability of Aircraft Subjected to Multiple-Munition Impacts Considering Conditional Dependencies

Aircraft vulnerability assessment is essential for survivability analysis. In multi-munition impact scenarios, successive fragment impacts may cause cumulative damage and evolving target vulnerability, while conventional conditional independence assumptions can introduce errors in damage probability estimation. Although shot-line-based Monte Carlo simulations can provide highly accurate statistical estimates, their high computational cost limits their application in time-critical scenarios. To address this issue, this study proposes an improved simplified method for multi-munition damage probability evaluation considering conditional dependencies. A shot-line-based Monte Carlo method is established as a reference approach to analyze errors introduced by conventional simplified methods. Based on this analysis, a correction formulation is developed within the framework of component average damage probability method to account for vulnerability evolution while maintaining computational efficiency. Numerical results from multi-munition scenarios show that the proposed method achieves a median relative error of 0.2%, with all relative errors within ±10% compared with Monte Carlo results. Meanwhile, online evaluation of 100 test cases is completed within less than 0.1 s, compared with approximately 12 h required by the Monte Carlo method. The proposed method provides a fast and accurate approach for damage probability assessment under multi-munition impact conditions.