An MMAP to model a complex warm standby system with a repair facility vacation policy
Conference
64th ISI World Statistics Congress - Ottawa, Canada
Format: CPS Abstract
Keywords: markov, mmap, multi-state, reliability
Abstract
One of the main problems in the fiel of reliability is to model complex multi-state systems in an algorthmic way that allows the computational implementation of the process and the interpretation of the results obtained. The Markovian Arrival Processes with marked arrivals (MMAP) is a counting process wich is dense in the set of the counting processes class and enables this fact. In this work, a complex multi-state warm standby system subject to multiple events is modeled through an MMAP. Units are exposed to repairable and non repairable failures, wear and shocks failures are also introduced with multiple consequences. Preventive maintenance is introduced. Three different tasks are posible in the repair facility; online unit repair, repair of any warm standby unit and preventive maintenance. A vacation policy is included in the model and it is developed. Multiple reliability measures of interest are worked out. As has been commented, the study has been carried out in a matrix algorithm form that facilitates the computational implementation. A numerical example shows the versatility of the model and an optimization problem is performed. The development and the results have been implemented computationally with Matlab.