Performance Analysis of a Repairable K-out-of-M + W + C:G System with Mixed Standbys Using Generalized Stochastic Petri Nets

We investigate a retrial [Formula: see text]-out-of-[Formula: see text]:[Formula: see text] system that includes both cold and warm standbys and [Formula: see text] reliable repairers through generalized stochastic Petri nets (GSPNs). The system comprises [Formula: see text] active units, [Formula: see text] warm units in standby, and [Formula: see text] cold units in standby. The failures of both primary and warm standby components are modeled as a Poisson process. Failed components immediately undergo repair if a repairer is available; otherwise, they join an FCFS orbit. The tangible marking process of the GSPN model can serve to generate a Markov chain with continuous-time (CTMC). After solving the statistical equilibrium equations in matrix form, various performance measures are obtained. From the reliability viewpoint, using the Laplace transform method, the expression for the reliability function and the mean-time to failure (MTTF) are derived. The influence of the system parameters on performance measures, [Formula: see text], reliability function, and MTTF is clarified with numerical examples.