Time-dependent failure probability function(TDFPF) of parameters is one of the key problems of structural time-dependent reliability-based optimization. The accuracy and efficiency of TDFPF estimation determine the effect of time-dependent reliability-based optimization of structures. In this work

a weighted importance sampling (WIS) approach was proposed for theTDFPF estimation based on the concept of the composite limit states. The proposed method extends importance sampling to obtain the estimation of the TDFPF with only one reliability analysis

avoiding repeated reliability analyses. To verify the accuracy and efficiency of the proposed method

numerical examples and industrial robot reducer examples are given and solved by the proposed method. The results indicated that the proposed method has wide applicability

high efficiency in obtaining the satisfactory estimation of the TDFPF.