Achieving efficient estimation of reliability sensitivity of a multi-mode system without requiring knowledge of design point

Aim. Discussing at the beginning of the paper Ref.1 by Melchers et al, Ref.2 by Wu and Ref.3 by Wu et al, we propose a reliability sensitivity analysis method that is highly efficient and independent of design point and capable of handling multi-mode system. In the full paper, we explain our method in some detail. In the abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is: calculating reliability sensitivity with importance sampling function. In this topic, we present the solutions for reliability sensitivity analysis using importance function, thus greatly raising the efficiency of the reliability sensitivity calculation. The second topic is: the adaptive importance sampling function based on the estimation of kernel density function. Its two subtopics are: establishing the kernel density function (subtopic 2.1) and the procedure for adaptive importance sampling (subtopic 2.2). In subtopic 2.1, we first utilize the Markov chain to quickly simulate samples in a failure region, then use the kernel density evaluation method to obtain the density function of the samples and finally take it as the importance sampling density function, namely eq.(8) in the full paper, to analyze the reliability sensitivity of a structure. We also put forward the reliability sensitivity estimation values and the formulas for calculating the variances and variation coefficients of the estimations. Finally, we provide two application examples to calculate respectively the reliability sensitivities and their variation coefficients using the Monte Carlo simulation (MCS), the importance sampling (IS) and the kernel density importance sampling (KDIS). The calculation results of the application examples, given in Tables 2 through 5 in the full paper, show preliminarily that our KDIS has high sampling efficiency, is independent of design point, and can handle multi-mode systems and is more accurate than the MCS.