Optimizing a Multi-State Cold-Standby System with Multiple Vacations in the Repair and Loss of Units

A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failure: both internal and those provoked by external shocks. Multiple degradation levels are assumed as external. Degradation observed random inspections and, if they major, the goes a repair facility where carried out. This composed single repairperson governed vacation policy. policy set up according operational number units. Two task be performed repairperson, corrective maintenance. times embedded in phase type distributed model built using Markovian Arrival Processes marked arrivals. performance measures besides transient stationary distribution worked out through matrix-analytic methods. methodology enables us express main results global development matrix-algorithmic form. To optimize model, costs rewards included. numerical example shows versatility model.