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

In this study, three discrete-time multi-state complex systems subject to multiple events are modeled, in a well structured form, as Markovian arrival processes with marked arrivals. The systems, ranked by the number of events affecting the online unit, have multiple and variable repairpersons, and the online unit are partitioned into performance stages. The first system is subject only to internal failures. The second, additionally, considers external shocks, which can produce any of three consequences; extreme failure, degradation of the internal performance of the online unit or cumulative damage. Failure may be repairable or non-repairable. The repair facility is composed of an indeterminate number of repairpersons. When a non-repairable failure occurs, the number of repairpersons may be modified. Finally, the third system includes preventive maintenance in combination with random inspections. Various measures are incorporated, in an algorithmic and computational form, in transient and stationary regimes. Costs and rewards are included in the model to optimize the system from different standpoints. The results of this study are implemented computationally with Matlab, and a numerical example shows the versatility of the modeling.