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On Asymptotic Behavior of the Time-Dependent Solution of a Reliability Model

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Abstract:

On the basis of our previous work we study asymptotic behavior of the time-dependent solution of a reliability model of two identical units and a repairman and prove the following result: If the repair rate μ(x) is Lipschitz continuous and there exist two positive constants μ and μ such that 0 < μ ≤μ(x)≤ μ < ∞, then its time-dependent solution exponentially converges to its steady-state solution.

Info:

Periodical:
International Frontier Science Letters (Volume 2)
Pages:
1-11
DOI:
10.18052/www.scipress.com/IFSL.2.1
Citation:
G. Gupur "On Asymptotic Behavior of the Time-Dependent Solution of a Reliability Model", International Frontier Science Letters, Vol. 2, pp. 1-11, 2014
Online since:
Oct 2014
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References:

J. H. Cao and K. Cheng. Introduction to Reliability Mathematics. Higher Education Press, Beijing, (2006).

K. J. Engel and R. Nagel. One-Parameter Semigroups for Linear Evolution Equations. Springer, New York, (2000).

G. Gupur. Functional Analysis Methods for Reliability Models. Springer, Basel, (2011).

G. Gupur. Mathematical Methods in Reliability Theory. Xinjiang University Press, Urumqi, (2012).

R. Nagel. One-Parameter Semigroups of Positive Operators. Springer, Berlin, (1986).

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