Cost-Benefit Analysis of a Redundant System with Server having Refreshment Facility Subject to Inspection
( Vol-4,Issue-6,June 2017 )

M.S. Barak, Dhiraj Yadav, Sudesh K. Barak


Profit Analysis, Cold-standby, regenerative point, steady state and Semi-Markov process, inspection and refreshment.


In this paper two units cold standby system has been discussed with the facility that server inspect the failed unit before repair/replacement of the unit and server may allow to take refreshment whenever needed. The operative unit may fail directly from normal mode and the cold standby unit may be failed owing to remain unused for a longer period of time. There is single server who serves the dual purpose of inspection and repair immediately whenever required. Also, after having refreshment the server may eventually perform the better service efficiently. The time to take refreshment and repair activity follows negative exponential distribution whereas the distributions of unit failure and server failure are taken as arbitrary with different probability density functions. The expressions of various stochastic measures are analyzed in steady state using semi-Markov process and regenerative point technique. The graphs are sketched for arbitrary values of the parameters to delineate the behavior of some important performance measures to check the efficacy of the system model under such situations.

ijaers doi crossref DOI:


Paper Statistics:
  • Total View : 26
  • Downloads : 13
  • Page No: 024-031
Cite this Article:
Show All (MLA | APA | Chicago | Harvard | IEEE | Bibtex)

[1] Osaki, S. and Nakagawa T. [1971]; on a two-unit standby redundant system with standby failure, Operation Research, 19 (2) pp.510-523.
[2] Nakagawa T. and Osaki S.[1975]; stochastic behavior of a two-unit priority standby redundant system with repair, Microelectronics Reliability, 14(3) pp.309-313.
[3] Subramanian R. Venkatakrishan K. S. and Kistner K.P. [1976]; reliability of a repairable system with standby failure, Operation Research, 24(1) pp. 169-176.
[4] Gopalan M.N. and Naidu R.S.[1982]; cost-benefit analysis of a one-server system subject to inspection, Microelectronics Reliability, 22 pp. 699-705.
[5] Gopalan M.N. and Nagarwalla H.E.[1985]; cost-benefit analysis of a one server two unit cold standby system with repair and age replacement, Microelectronics Reliability, 25 pp.977-990.
[6] Singh S.K. and Sriniwas B. [1987]; stochastic analysis of a two unit cold standby system with preparation time for repair, Microelectronics Reliability, 27(1) pp. 55-60.
[7] Singh S.K.[1989]; profit evaluation of a two-unit cold standby system with random appearance and disappearance time of the service facility, Microelectronics Reliability, 29 pp. 705-709.
[8] Dhillon B.S.[1992]; reliability and availability analysis of a System with standby and common cause failures, Microelectronics Reliability, 33(9) pp. 1343-1349.
[9] Lam Y.F.[1997]; a maintenance model for two-unit redundant system, Microelectronics Reliability, 37(3) pp. 497-504.
[10] Kumar, Ramesh [2005]; analysis of reliability models with different types of failure and repair Policies, Ph.D. Thesis, M.D. University Rohtak.
[11] Malik S.C. and Barak M.S.[2007]; probabilistic analysis of a single-server system operating under different weather conditions, Journal of Mathematical Analysis and Approximation Theory, 2(2) pp. 173-182.
[12] Malik S.C.[2009]: reliability modeling and cost-benefit analysis of a system – A case study, Journal of Mathematics and System Sciences, 5(2) pp. 26-38.
[13] Bhardwaj R.K. and Singh R. [2014]; semi-Markov approach for asymptotic performance analysis of a standby system with server failure, International journal of computer Applications, 98(3) pp.9-14.
[14] Malik,S.C., Bhardwaj R.K. and Komaldeep Kaur [2015]; performance analysis of a stochastic system with standby failure and maintenance, International journal of computer Applications, 125(1) pp. 6-11.
[15] Barak M.S. and Dhiraj [2016]; stochastic analysis of a cold standby system with server failure. International Journal of Mathematics and Statistics Invention(IJMSI) ( ISSN 2321-4767) 4, Issue 6 ||August 2016|| pp. 18-22.