Complex multi-state systems modelled through marked Markovian arrival processes

Complex multi-state warm standby systems subject to different types of failures and preventive maintenance are modelled by considering discrete marked Markovian arrival processes. The system is composed of K units, one online and the rest in warm standby and by an indefinite number of repairpersons, R. The online unit passes through several performance states, which are partitioned into two types: minor and major. This unit can fail due to wear or to external shock. In both cases of failures, the failure can be repairable or non-repairable. Warm standby units can only undergo repairable failures due to wear. Derived systems are modelled from the basic one according to the type of the failure; repairable or non-repairable, and preventive maintenance. When a unit undergoes a repairable failure, it goes to the repair facility for corrective repair, and if it is non-repairable, it is replaced by a new, identical one. Preventive maintenance is carried out in response to random inspections. When an inspection takes place, the online unit is observed and if the performance state is major, the unit is sent to the repair facility for preventive maintenance. Preventive maintenance and corrective repair times follow different distributions according to the type of failure. The systems are modelled in transient regime, relevant performance measures are obtained, and rewards and costs are calculated. All results are expressed in algorithmic form and implemented computationally with Matlab. A numerical example shows the versatility of the model presented.