Exact Reliability Evaluation of a Bridge Structure Using the Power Bilal Distribution

ABSTRACT

This paper studies the exact reliability evaluation of the classical five‐component bridge network when the component lifetimes follow the Power Bilal distribution. The Power Bilal model extends the classical Bilal distribution by adding a shape parameter, which increases modeling flexibility while preserving a simple and analytically tractable survival function. Under the assumption of independent and identically distributed components, an explicit expression for the bridge‐system reliability is derived. A closed‐form expression for the mean time to failure is also obtained in terms of the lower incomplete beta function. In addition, two single‐component reinforcement strategies are investigated. It is shown analytically that, for the same improvement level, reinforcing an outer branch component always gives a larger reliability gain than reinforcing the middle component. A real data application based on waiting times of bank customers is included to assess the empirical suitability of the Power Bilal model and to compare it with standard lifetime distributions. The numerical and empirical results show that the Power Bilal distribution provides a flexible and analytically convenient framework for bridge‐network reliability analysis and for guiding targeted reliability‐improvement decisions.