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

Gupur, Geni

doi:10.18052/www.scipress.com/IFSL.2.1

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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:

https://doi.org/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:

October 2014

Authors:

Geni Gupur

Keywords:

Eigenvalue, Resolvents, The System Consisting of Two Identical Units and a Repairman

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Distribution:

Open Access

This work is licensed under a
Creative Commons Attribution 4.0 International License

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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Cited By:

[1] E. Kasim, G. Gupur, "Dynamic analysis of a complex system under preemptive repeat repair discipline", Boundary Value Problems, Vol. 2020, 2020

DOI: https://doi.org/10.1186/s13661-020-01366-9