The USAF Airworthiness Bulletin Risk Identification and Acceptance for Airworthiness Determination defines airworthiness in terms of the probability of aircraft loss per flight hour1 with one important component being the aircraft structure. The probability-of-failure of an aircraft component is challenging to compute due to its small size, typically 10-7 or less. As a result, simplified fracture mechanics models are usually used with a small number of random variables. However, these simplifications may lead to an inaccurate probability-of-failure estimate. To address this issue, an adaptive multiple importance sample method was developed that can compute very low probabilities with significant efficiency. This allows one to consider more realistic fracture mechanics models and a larger number of random variables than has been previously possible. The method is adaptive in that it will adjust to the varying relative importance of the random variables for different applications. Convergence is ensured such that the coefficient of variation is below a user-defined threshold. Results to date show efficiency gains of 5 or 6 orders of magnitude over standard Monte Carlo sampling for typical problems of interest. The methodology will be outlined and demonstrated using aircraft example problems.