Abstract

The paper stochastically investigates a two unit cold-standby system with a server subject to failure and getting delayed treatment thereafter. Semi-Markov process is used to develop the system model. The model is analyzed at different regeneration points using regenerative-point technique. The steady-state expressions are derived for various system performance measures such as mean time to failure, availability, busy period of server, expected number of treatments, profit etc. Finally, numerical examples are given to discuss the effect of various parameters on system performance measures.

References

• Nakagawa T, Osaki S. 1975. Stochastic behavior of a two-unit priority standby redundant system with repair. Microelectron Reliab. 14(3), 309–13.
• Bieth, B., Hong, L., and Sarkar, J. A. 2010. Standby system with two repair persons under arbitrary life-and repair times. Mathematical and Computer Modelling 51(5), 756-767.
• Mahmoud, M.A.W. and Moshref, M.E. 2010. On a two-unit cold standby system considering hardware, human error failures and preventive maintenance, Mathematical and Computer Modelling 51 (5–6), 736–745.
• Bhardwaj, R. K., and Malik, S. C. 2011. Asymptotic performance analysis of 2oo3 cold standby system with constrained repair and arbitrary distributed inspection time. International Journal of Applied Engineering Research 6 (08), 1493-1502.
• Bhardwaj R. K. and Kaur, Komaldeep. 2014. Reliability and Profit Analysis of a Redundant System with Possible Renewal of Standby Subject to Inspection, International Journal of Statistics and Reliability Engineering, 1 (1), 36-46.
• Avi-Itzhak, B & Naor, P. 1963. Some queuing problems with the service station subject to breakdown, Operations Research 11 (3), 303-320.
• Mitrany, I.L. Avi-Itzhak, B. 1968. A many-server queue with service interruptions, Operations Research 16, 628–638.
• Neuts, M. and Lucantoni, D. 1979. Markovian queue with N-servers subject to breakdowns and repairs, Management Science 25 (9), 849–861.
• Federgruen, A. and Green, L. 1986. Queueing systems with service interruptions, Operations Research 34 (5), 752–768.
• Lee, D. 1997. Analysis of a single server queue with semi-Markovian service interruption, Queueing Systems 27 (1–2), 153–178.
• Yang, X., & Alfa, A. S., 2009. A class of multi-server queuing system with server failures, Computers & Industrial Engineering, 56(1), 33-43.
• Dhankar, A.K., Bhardwaj, R.K., Malik, S.C., 2012. Reliability Modeling and Profit Analysis of a System with Different Failure Modes and Replaceable Server Subject To Inspection, Int. J. of Statistics and Analysis 2(3), 245-255.
• Malik, S. C., Dhankar, A.K.. 2013. Reliability Modeling and Cost-Analysis of a System with Replacement of the server and Unit subject to Inspection”, Journal of Statistics and Management Systems, 16 (2-3), 137-162.
• Bhardwaj, R.K., Singh, Ravinder, 2014. Semi Markov Approach for Asymptotic Performance Analysis of a Standby System with Server Failure, International Journal of Computer Applications 98 (3), 9-14.
• Bhardwaj, R.K., Singh, Ravinder, 2014. Steady State Behavior of a Cold-Standby System with Server Failure and Arbitrary Repair, Replacement & Treatment”, International Journal of Applied Engineering Research 9 (24), 26563-26578.
• Bhardwaj, R.K., Singh, Ravinder, 2015. Semi-Markov Model of a Standby System with General Distribution of Arrival and Failure Times of Server. American Journal of Applied Mathematics and Statistics, 3 (3), 105-110.
• Bhardwaj, R.K., Singh, Ravinder, 2015. An Inspection-Repair-Replacement Model of a Stochastic Standby System with Server Failure”, Mathematics in Engineering, Science and Aerospace 6 (2), 191-203.
• Ross SM. 1996. Stochastic processes. Wiley.
• Smith, W. L. 1955. Regenerative stochastic processes. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 232 (1188), 6-31.
• Johnson, R. 2015. Miller and Freund’s probability and Statistics for Engineers, PHI.
• Ross, S. M. 2010. Introduction to probability models. Academic press.