Time-dependent analysis for a Two-Unit System with Connecting and Disconnecting Effect

Year 2015, Volume: 28 Issue: 1, 27 - 35, 23.02.2015

Alim Mijit

Abstract

By studying the spectrum of the underlying operator corresponding to the two-unit system with connecting and disconnecting effect, we prove that the time-dependent solution of the system conversges stronly to its steady-state solution as time tends to infinity.

Keywords

two-unt system , connecting and disconnicting effect , eigenvalue , resolvent set.

Connecting and Disconnecting Effect

Abstract

References

• Dhillon, B. S., Singh, C., “Engineering Reliability, New Techniques and Applications”. John Wiley, New York, (1981).
• Gaver, D. P., “Time to failure and availability of parallel redundant systems with repair”, IEEE Trans. Rel. R12: 30–38, (1963) .
• Goel, C. K., Narmada, S. and Jacob, M. , “Analysis of a two-unit system with connecting and disconnecting effect”, Microelectron. Reliab. 37: 1271–1274, (1997).
• Goel, L. R., Gupta, P., Singh, S. K., “A two unit parallel redundant system with three modes and bivariate exponential life times”, Microelectron. Reliab. 24: 25–28, (1984).
• Gupta, P. P. and Agarwal, S. C., “Cost analysis of 3-state 2-unit repairable system”, Microelectron. Reliab. 24: 55–59,(1984).
• Gupur, G., Li, X., Zhu, G., “Functional Analysis Method in Queueing Theory”, Research Information Ltd., Hertfordshire, (2001).
• Mijit, A., Gupur, G., “Semigroup approach of a two-unit system with connecting and disconnecting effect”. Int. J. Appl. Math. Stat. 41: 23–30, (2013).
• Mijit, A., Gupur, G., Asymptotic behavior of the time-dependent solution of the M/M/1 queueing model with optional second service, Int. J. Pure Appl. Math. 69: 289–328, ( 2011).