A multi-state warm standby system with preventive maintenance, loss of units and an indeterminate multiple number of repairpersons

Abstract A Markovian Arrival Process with Marked arrivals is used to model a discrete-time complex warm standby multi-state system in a well-structured way. The online unit is subject to internal failure, repairable or non-repairable, and/or external shocks. These shocks can produce total failure, modification of the internal performance or cumulative damage. To avoid serious damage and considerable financial loss, random inspection is performed. Internal degradation and cumulative external damage are partitioned into minor and major states. Both are inspected and if a major state is observed the unit is sent to the repair facility for preventive maintenance. Each warm standby unit may undergo a repairable failure at any time. Thus, three different time distributions are applicable to the repairpersons: corrective repair for the online unit and the warm standby units, and preventive maintenance. The repair facility is composed of multiple and variable repairpersons. When a non-repairable failure occurs, the system continues working with one less unit and the number of repairpersons may be modified. The system continues working with fewer units as long as this is possible. Measures of interest in the reliability field are calculated. Costs and rewards are included in the model. A numerical example shows how the optimum system may be achieved, according to the number of repairpersons and the preventive maintenance performed. The model is built in an algorithmic form, which facilitates its computational implementation.