STOCHASTIC MODELING AND PERFORMANCE ANALYSIS OF A 2(K)-OUT-OF-3(N) SYSTEM WITH INSPECTION SUBJECT TO OPERATIONAL RESTRICTION
Keywords:
Stochastic modeling, performance analysis, operational restriction, arbitrary distribution, re-generative point, semi-Markov process.Abstract
In repairable redundant systems the failed units can either be repaired or replaced by identical standby to reduce the system down time. The failed units are inspected for repair/replacement. In this paper, two stochastic models for 2(k)-out-of-3(n) redundant system of identical units with repair and inspection are examined stochastically. The system is considered in up-state only if 2(k)-out-of-3(n) units are operative in both the models. Normally, the server either attends the system promptly or may take some time, after failure. The system is studied under an operational restriction on the inspection i.e. in case when system has only one unit in operational mode the server has to attend the system for inspection. Semi-Markov processes and Regenerative point technique is adopted to obtain the expressions for measures of system effectiveness such as transition probabilities, mean sojourn times, mean time to system failure, steady state availabilities, busy periods, expected number of visits etc. Cost-analysis is also carried out for the system models.
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References
Barlow, R. E. and Proschan, F. (1965). Mathematical Theory of Reliability,
John Wiley, New York.
Goel, L.R., Sharma, G.C. and Gupta, R. (1985). Cost analysis of two-unit cold
standby system under different weather conditions, Microelectron. Reliab., 25
(4), p. 655-659.
Nakagawa, T. (1989). A replacement policy maximizing MTTF of a system
with several spare units, IEEE Transactions on Reliability, 38(8), p. 1277-
Singh, S.K. (1989). Profit evaluation of a two-unit cold standby system with
random appearance and disappearance time of the service facility,
Microelectron. Reliab., 29, p. 705-709.
Aven, T. (1990). Availability formulae for standby systems of similar units
that are preventively maintained, IEEE Transactions on Reliability, 39(5), p.
-606.
Vanderperre E.J. (1990). Reliability analysis of a warm standby system with
general distributions, Microelectron Reliab., 30(3), p. 487–490.
Goel LR. and Shrivastava P. A. (1992). Warm standby redundant system with
correlated failures and repairs, Microelectron Reliab., 32(6), p. 793–797.
Chung, W.K. (1993). Reliability analysis of a cold standby system with
multiple critical errors, Microelectron. Reliab., 34 (8), p. 1343-1347.
Mokaddis G.S., Labib S.W. and El Said M.K.H. (1994). Two models for two-
dissimilar-unit standby redundant system with three types of repair facilities
and perfect or imperfect switch, Microelectron Reliab., 34(7), p. 1239–1247.
Subramanian R. and Anantharaman, V. (1995). Reliability analysis of a
complex standby redundant system, Reliab. Eng. Syst Saf., 48(1), p. 57–70.
Yadavalli V.S.S., Botha M. and Bekker, A. (2002). Asymptotic confidence
limits for the steady state availability of a two-unit parallel system with
‘preparation time’ for the repair facility, Asia Pac J Oper Res, 19(2), p. 249–
Edmond J. Vanderperre (2004). Reliability analysis of a renewable multiple
cold standby system, Operations Research Letters, 32, p. 288-292.
Chander, S. and Bhardwaj, R.K. (2009). Reliability and economic analysis of
-out-of-3 redundant system with priority to repair, African Journal of
Mathematical and Computer Science Research, 2(11), p. 230-236
