A Method to Construct a System Performance Function for Structural Reliability Analysis

System performance functions constructed using traditional methods are generally non-differentiable, which requires the use of finite difference methods or virtual stochastic processes when implementing the probability density evolution method (PDEM). This approach not only compromises computational accuracy but also diminishes efficiency due to the implementation of additional computational procedures. To address this issue, this study introduces a new method to construct system performance functions using sign functions. These functions allow for derivative operations on parameters, making them more suitable for integration with PDEMs, as well as for calculations using integration methods and Monte Carlo simulations (MCSs). Furthermore, the study establishes analytical expressions for the performance functions of systems in series, parallel, and mixed configurations. Case studies on system reliability using the constructed functions demonstrate that the proposed method enhances both accuracy and efficiency in PDEM applications.