Reliability sensitivity by method of moments

Abstract

Based on the available methods of moments for structural system reliability assessment and point estimate methods for the first few moments of performance functions, an effective method is proposed to analyze reliability sensitivity of a structural system. The proposed method for analyzing reliability sensitivity includes two steps. Firstly, the reliability sensitivity, usually measured by partial differential of the failure probability P f with respect to distribution parameter θ of the basic random variable is derived according to the moment based reliability assessment. The derived expression of ∂ P f / ∂ θ is related to the derivative of the performance function moment α with respect to θ . Secondly, by using the integral formulation between α and the probability density function (PDF) of the basic random variable, ∂ α / ∂ θ could be derived as an expectation of a transformed performance function, and the expectation could be approximated by the point estimate methods. Through the two steps above, the reliability sensitivity can be obtained easily. The obvious advantages of the proposed method include independence of the explicit expression of the performance function, no limitations on the types of PDF of the basic random variables, wide applicability for multiple failure modes and high efficiency for low and medium dimensional problem, which are illustrated by the given examples. However, the efficiency of this method decreases as the dimension of the basic random variables increase, therefore, it is not suitable for the high dimensional problems.