Response surface method (RSM) is widely used in structural reliability analysis with implicit performance function (PF) which requires formidable computational effort. The ill conditioned coefficient matrix of normal equation in classical RSM prevents it from being used in high order conditions. The stochastic response surface method (SRSM), deriving from classical RSM, offers one alternative to solve this problem. Yet the regression method of conventional SRSM is based on normal least square method which ignores the different significance of each sample point through which the response surface function (RSF) is formed. To yield RSF close to the limit state which leads to better estimation of probability of failure, this paper introduces the weighted regression into SRSM and several examples with hypothetic explicit PF are given to test the performance of SRSM. In addition, we use this method in the fatigue reliability analysis of crankshaft with implicit PF. All these examples demonstrate the advantages of the proposed method.

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