Discrete-time Markovian arrival processes to model multi-state complex systems with loss of units and an indeterminate variable number of repairpersons.

•Multi-state complex systems are modeled in an algorithmic and computational form.•Internal failures and external shocks with multiple consequences are assumed.•Multiple and variable number of repairpersons are assumed in the repair facility.•When a non-repairable failure occurs, internal and/or external, the unit is removed.•The performance-profitable is analyzed through marked Markovian arrival processes.