Time-Dependent Reliability Analysis Based on Quantile Function and Fourth-Order Moment Saddle-Point Approximation Under Small Sample Conditions

Time-dependent reliability analysis (TRA) is essential for the life-cycle risk assessment of engineering systems. However, existing TRA methods often require extensive statistical data or computationally expensive surrogate models, which limit their applicability under sparse sampling conditions. This paper presents a novel TRA framework that integrates probability-weighted moments (PWMs), a maximum entropy-based quantile function, and a fourth-order moment saddle-point approximation (FMSPA). The PWM method provides asymptotically unbiased moment estimates for small samples, while the maximum entropy-based quantile function directly computes the first four central moments of random variables. Subsequently, the FMSPA method is extended for use in TRA to efficiently evaluate the cumulative failure probability at each time point. The effectiveness of the proposed method is demonstrated through three engineering examples. The results indicate that the method delivers accurate and efficient TRA under sparse sampling conditions.