Parametric Reliability Sensitivity Analysis Using Failure Probability Ratio Function

Reducing the failure probability is an important task in the design of engineering structures. In this paper, a reliability sensitivity analysis technique, called failure probability ratio function, is firstly developed for providing the analysts quantitative information on failure probability reduction while one or a set of distribution parameters of model inputs are changed. Then, based on the failure probability ratio function, a global sensitivity analysis technique, called R-index, is proposed for measuring the average contribution of the distribution parameters to the failure probability while they vary in intervals. The proposed failure probability ratio function and R-index can be especially useful for failure probability reduction, reliability-based optimization and reduction of the epistemic uncertainty of parameters. The Monte Carlo simulation (MCS), Importance Sampling (IS) and Truncated Importance Sampling (TIS) procedures, which need only a set of samples for implementing them, are introduced for efficiently computing the proposed sensitivity indices. A numerical example is introduced for illustrating the engineering significance of the proposed sensitivity indices and verifying the efficiency and accuracy of the MCS, IS and TIS procedures. At last, the proposed sensitivity techniques are applied to a planar 10-bar structure for achieving a targeted 80% reduction of the failure probability.