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Abstract: Reliability analysis and reliability-based optimization design require accurate measurement of failure probability under input uncertainties. A unified probabilistic reliability measure approach is proposed to calculate the probability of failure and sensitivity indices considering a mixture of uncertainties under insufficient input data. The input uncertainty variables are classified into statistical variables, sparse variables, and interval variables. The conservativeness level of the failure probability is calculated through uncertainty propagation analysis of distribution parameters of sparse variables and auxiliary parameters of interval variables. The design sensitivity of the conservativeness level of the failure probability at design points is derived using a semi-analysis and sampling-based method. The proposed unified reliability measure method is extended to consider p-box variables, multi-domain variables, and evidence theory variables. Numerical and engineering examples demonstrate the effectiveness of the proposed method, which can obtain an accurate confidence level of reliability index and sensitivity indices with lower function evaluation number.

不完备数据下考虑变量混合不确定性的可靠性度量方法

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