Asymptotic behavior of repairable device systems under warranty and beyond warranty periods
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In this paper, we present a new mathematical model generalizing the model of a single unit repairable device system, with preventive maintenance under warranty period, and the model of a repairable multi-state device system. To study the time dependance solution of the resulting system, we present in this paper a new analytic approach. So, by using the \(C_0\)-semigroup theory of linear operators and some spectral properties, we proof that the dynamic solution of the system converges to steady state solution when the time go to infinity.
KeywordsRepairable system \(C_0\)-semigroup Well-posedness Positivity Irreducibility Spectral theory Stability
Mathematics Subject Classification47D06 34G10 49K40
- 1.Ramniwas, R., Kaydan, M.S., Kumar, J.: Stochastic modeling of single-unit repairable system with preventive maintenace under warranty. Int. J. Comput. Appl. 75(13), 36–41 (2013)Google Scholar