An Order Statistics Perspective for System Reliability

ABSTRACT Structural reliability integrates the design variables over the safety region characterized by a positive limit state function when the reliability of the entire system is of concern. Calculating the structure function can be challenging for high‐dimensional systems or intricate system architectures. In order to enhance the efficiency of time‐dependent system reliability assessment, we emulate the integral formulation in structural reliability. To elaborate further, we treat each individual unit's lifetime variable as a design variable and subsequently perform calculations involving multiple integrals. Given the ordered nature of unit failure times, we leverage the order statistics distribution to simplify the multiple integrals into a double integral, and then multiply this result by the survival signature to obtain reliability. A two‐terminal nine‐unit network system configuration is illustrated to assess the performance and effectiveness of the proposed method.