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 JAMP  Vol.4 No.8 , August 2016
Existence and Uniqueness of the Dynamic Solution of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman
Abstract: We investigate a series-parallel repairable system consisting of three-unit with multiple vacations of a repairman. By using C0-semigroup theory of linear operators in the functional analysis, we prove that the system is well-posed and has a unique positive dynamic solution.
Cite this paper: Haji, A. , Keyim, T. and Yunus, B. (2016) Existence and Uniqueness of the Dynamic Solution of a Series-Parallel Repairable System Consisting of Three-Unit with Multiple Vacations of a Repairman. Journal of Applied Mathematics and Physics, 4, 1585-1591. doi: 10.4236/jamp.2016.48168.
References

[1]   Li, W., Alfa, A.S. and Zhao, Y.Q. (l998) Stochastic Analysis of a Repairable System with Three Units and Two Repair Facilities. Microeletronics and Reliability, 38, 585-595.

[2]   Kovalenko, A.I. (2001) Analysis of the Reliability of a Three-Component System with Renewal. Journal of Mathematical Science, 103, 273-277.

[3]   Hu, L.M., Tian, R.L., Wu, J.B. and Cao, J. (2007) Reliability Analysis of Series-Parallel Repairable System Consisting of Three Units with Vacation. Journal of Y. Uni., 103, 299-303.

[4]   Engel, K.-J. and Nagel, R. (2000) One-Parameter Semigroups for Linear Evolution Equations. Graduate Texts in Mathematics, 194, Spring-er-Verlag.

[5]   Casarino, V., Engel, K.-J., Nagel, R. and Nickel, G. (2003) A Semigroup Approach to Boundary Feedback Systems. Integr. Equ. Oper. Theory, 47, 289-306. http://dx.doi.org/10.1007/s00020-002-1163-2

[6]   Greiner, G. (1987) Perturbing the Boundary Conditions of a Generator. Houston J. Math., 13, 213-229.

[7]   Haji, A. and Radl, A. (2007) A Semigroup Approach to Queueing Systems. Semigroup Forum, 75, 610-624. http://dx.doi.org/10.1007/s00233-007-0726-6

[8]   Nagel, R. (1986) One-Parameter Semigroups of Positive Operators. Spring-er-Verlag.

 
 
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