INDIVIDUAL COMPONENT FAILURE'S ROLE IN AN IMPERFECT ONE-OUT-OF-THREE COLD AND WARM STANDBY SYSTEM

Résumé

This study investigates the reliability and failure behavior of a non-repairable one-out-of-three standby system incorporating both cold and warm redundancy under imperfect switching conditions. Motivated by real-world challenges in hospital emergency power systems, the model includes three critical components: the primary power grid, a cold standby generator, and a warm standby UPS, along with a fillable switching mechanism. A continuous-time Markov chain (CTMC) framework is constructed to evaluate system dynamics, where each component is subject to exponentially distributed failures. System performance is quantified via key reliability metrics, including the reliability function , the failure probability , hazard rate , mean time to failure (MTTF), and steady-state probabilities. Numerical solutions are derived through matrix exponential computations and linear system solvers in MATLAB (R2023b). Results indicate that reliability degrades exponentially with time, the hazard rate stabilises around a constant value, and the system has an expected operational lifespan of approximately 43.19 hours. The steady-state analysis reveals that certain operational states dominate prior to system failure, providing valuable insights for redundancy planning and component prioritisation in critical systems.