Reliability and performance evaluation of retrial repairable systems with an unreliable repairer using the GSPN model

Generalized Stochastic Petri Nets (GSPNs) are widely used in reliability analysis to model and optimize the dependability of complex systems, enabling assessments of availability, failure probabilities, and repair processes through stochastic timing. This study investigates a repairable redundant retrial system incorporating warm and cold standbys and an unreliable repairer through a Generalized Stochastic Petri Nets. The repairer experiences both active (during repair) and passive (idle) breakdowns. Component and repairer lifetimes are exponentially distributed. A component that fails undergoes immediate repair if the repairer is available; otherwise, it enters a retrial FCFS orbit. A Continuous Time Markov Chain (CTMC) derived from the GSPN model yields steady state probabilities and availability. System reliability and time to first failure are then determined via Laplace transforms. Numerical examples demonstrate the system reliability performance.