A discrete MMAP for analysing the behaviour of a multi-state complex dynamic system subject to multiple events.

A complex multi-state system subject to different types of failures, repairable and/or nonrepairable, external shocks and preventive maintenance is modelled by considering a discrete Markovian arrival process with marked arrivals (D-MMAP). The internal performance of the system is composed of several degradation states partitioned into minor and major damage states according to the risk of failure. Random external events can produce failures throughout the system. If an external shock occurs, there may be an aggravation of the internal degradation, cumulative external damage or extreme external failure. The internal performance and the cumulative external damage are observed by random inspection. If major degradation is observed, the unit goes to the repair facility for preventive maintenance. If a repairable failure occurs then the system goes to corrective repair with different time distributions depending on the failure state. Time distributions for corrective repair and preventive maintenance depend on the failure state. Rewards and costs depending on the state at which the device failed or was inspected are introduced. The system is modelled and several measures of interest are built into transient and stationary regimes. A preventive maintenance policy is shown to determine the effectiveness of preventive maintenance and the optimum state of internal and cumulative external damage at which preventive maintenance should be taken into account. A numerical example is presented, revealing the efficacy of the model. Correlations between the numbers of different events over time and in non-overlapping intervals are calculated. The results are expressed in algorithmic-matrix form and are implemented computationally with Matlab.Junta de Andalucía, Spain, under the grant FQM307Ministerio de Economía y Competitividad, España, MTM2017-88708-PEuropean Regional Development Fund (ERDF

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

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.Junta de Andalucía (Spain) FQM-307Ministerio de Economía y Competitividad (España) MTM2017-88708-