Abstract: The likelihood ratio (LR) method was chosen as the basic derivative/gradient estimation method for reliability sensitivity analysis. The implementation of the LR method in crude component-based Monte Carlo (MC) and especially in the setting of classical reliability was first derived. To speed up the simulation, a biasing technique was then developed, which defines an unbiased importance sampling estimator based on system structure functions, and identifies the optimal set of biasing parameters via minimizing the variance of this estimator. One important advantage of this estimator is that, the task of minimizing its variance can be achieved by optimizing at the component level, thus avoiding the difficulty of high dimensional optimizations. A simple example with analytical solution available was studied to test the effectiveness of the LR method for reliability sensitivity analysis, and also the effectiveness of the proposed biasing technique for reducing the variance of LR derivative estimators. The results show that, the proposed biased MC method produced accurate estimates for all the quantities, and achieved at least six orders of magnitude of variance reduction for all of them, compared to crude MC．