The computation of upper probabilities of failure involves solving a global optimization problem over a family of probability distributions under epistemic uncertainty. Each optimization step requires the estimation of a failure probability by Monte Carlo simulation, leading to high computational cost due to repeated evaluations of an expensive failure indicator. Since successive parameter values arising in the optimization process are typically close, previously generated samples can be reused via importance sampling. This work proposes a partitioning-based importance sampling and reweighting strategy for efficient failure probability estimation. The sample space is dynamically partitioned according to importance sampling ratios, and only newly generated samples with sufficiently small ratios are admitted at each step. This mechanism stabilizes importance weights, reduces estimator variance, and significantly lowers computational cost by limiting the number of new indicator evaluations. The effectiveness of the approach is demonstrated by a numerical example.