Abstract
A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failure: both internal and those provoked by external shocks. Multiple degradation levels are assumed as both internal and external. Degradation levels are observed by random inspections and, if they are major, the unit goes to a repair facility where preventive maintenance is carried out. This repair facility is composed of a single repairperson governed by a multiple vacation policy. This policy is set up according to the operational number of units. Two types of task can be performed by the repairperson, corrective repair and preventive maintenance. The times embedded in the system are phase type distributed and the model is built by using Markovian Arrival Processes with marked arrivals. Multiple performance measures besides the transient and stationary distribution are worked out through matrix-analytic methods. This methodology enables us to express the main results and the global development in a matrix-algorithmic form. To optimize the model, costs and rewards are included. A numerical example shows the versatility of the model.
Highlights
Redundant systems and preventive maintenance are of fundamental importance in ensuring reliability, preventing system failures and reducing costs
Cha et al [3] considered preventive maintenance for items operating in a random environment subjected to a shock Poisson process, Levitin et al [4] evaluated the probability of mission success given an arbitrary redundancy level, and Osaki et al [5] analysed the behaviour of a two-unit standby redundant system
If the repairperson returns and there are less than R operational units he remains at his workplace
Summary
Redundant systems and preventive maintenance are of fundamental importance in ensuring reliability, preventing system failures and reducing costs. Many multi-state reliability systems, over time, are subject to events such as repairable or non-repairable failure, inspections or external shocks. These systems can be modelled using appropriate Markov processes, i.e., PHD and MAP ([17,18]). Ruiz-Castro et al [31] modelled a multi-state complex system subject to multiple events and where preventive maintenance was applied. In this case, the repairperson had various duties and, was entitled to take a vacation.
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