Original scientific paper
https://doi.org/10.17535/crorr.2026.0010
Reliability and performance evaluation of retrial repairable systems with an unreliable repairer using the GSPN model
Kheireddine Boudehane
orcid.org/0000-0003-0677-9089
; Department of Probability and Statistics, Faculty of Mathematics, RIIMA Laboratory, University of Science and Technology Houari Boumediene, Algiers, Algeria
*
Samira Taleb
orcid.org/0000-0003-2385-1062
; Department of Probability and Statistics, Faculty of Mathematics, RIIMA Laboratory, University of Science and Technology Houari Boumediene, Algiers, Algeria
* Corresponding author.
Abstract
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.
Keywords
$K$-out-of-$n:G$ system; reliability; generalized stochastic Petri net; standby redundancy
Hrčak ID:
342139
URI
Publication date:
23.12.2025.
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