2 research outputs found
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 Andaluc铆a, Spain, under the grant FQM307Ministerio de Econom铆a y Competitividad, Espa帽a, MTM2017-88708-PEuropean Regional Development Fund (ERDF