Stochastic Modeling of a System with Maintenance and Replacement of Standby Subject to Inspection
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 5, September 2015, Pages: 339-346
Received: Jul. 2, 2015;
Accepted: Jul. 21, 2015;
Published: Aug. 5, 2015
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R. K. Bhardwaj, Department of Statistics, Punjabi University, Patiala, India
Komaldeep Kaur, Department of Statistics, Punjabi University, Patiala, India
S. C. Malik, Department of Statistics, MD University, Rohtak, India
The present paper develops a probabilistic model of a cold standby system considering the failure of unit in standby mode. Initially the model contains one unit in operation and another identical in cold standby mode. The unit in cold standby mode fails after passage of pre specified time and goes under inspection for feasibility check for maintenance or replacement, whereas the operative unit directly goes under repair at its failure. A single service facility available in the system handles the tasks of repair, inspection, maintenance or replacement. The replacement of unit in standby mode, at its failure, takes some time; that follows certain probability distribution. The theory of semi-Markov processes and regenerative point technique are used to develop and analyze the system model. For illustration, the results are obtained for a particular case.
R. K. Bhardwaj,
S. C. Malik,
Stochastic Modeling of a System with Maintenance and Replacement of Standby Subject to Inspection, American Journal of Theoretical and Applied Statistics.
Vol. 4, No. 5,
2015, pp. 339-346.
R. K. Bhardwaj and Ravinder Singh, "Semi Markov Approach for Asymptotic Performance Analysis of a Standby System with Server Failure." International Journal of Computer Applications vol. 98(3), 2014, pp. 9-14.
S. C. Malik and V. J. Munday, "Stochastic Modelling of a Computer System with Hardware Redundancy." International journal of computer applications vol. 89(7) 2014, pp. 26-30.
Y.F. Lam, “A Maintenance Model for Two-Unit Redundant System,” Microelectronics & Reliability, vol. 37(3), 1997, pp. 497-504.
P. Chanderasekhar, R. Natarajan and V.S.S. Yadavalli, “A Study on Two-Unit Standby System With Erlangian Repair Time,” Asia-Pacific Journal of Operational Research, vol. 21(3), 2004, pp. 271-277.
Jinhua Cao and Yan Hong Wu, “Reliability of Two-Unit Cold Standby System with Replaceable Repair Facility,” Microelectronics & Reliability, vol. 29(2), 1989, pp. 145-150.
R.K. Bhardwaj and Ravinder Singh, “Steady State Behavior of a Cold-Standby System with Server Failure and Arbitrary Repair, Replacement & Treatment,” International Journal of Applied Engineering Research, vol. 9(24), 2014, pp. 26563-26578.
R.K. Bhardwaj and Ravinder Singh, “Semi Markov Approach for Asymptotic Performance Analysis of a Standby System with Server Failure,” International Journal of Computer Applications, vol. 98(3), 2014, pp. 9-14.
S. C. Malik and A.K Dhankar, “Reliability Modeling and Cost-Analysis of a System with Replacement of the Server and Unit Subject to Inspection,” Journal of Statistics and Management Systems, vol. 16 (2-3), 2013, pp. 137-162.
A.K. Dhankar, S.C. Malik, and R.K. Bhardwaj, ”Reliability Modeling and Profit Analysis of a System with Different Failure Modes and Replaceable Server Subject to Inspection,” International journal of Statistics and Analysis (IJSA), vol. 2(3), 2012, pp. 245-255.
M. I. Mahmoud and M. A. W. Mahmoud, "Stochastic Behavior of a 2-Unit Standby Redundant System with Imperfect Switchover and Preventive Maintenance." Microelectronics Reliability vol. 23(1), 1983, pp. 153-156.
M. N. Gopalan and S. S. Waghmare, "Cost-Benefit Analysis of One-Server Two-Unit System with Imperfect Switch." Microelectronics Reliability 25.4 (1985): 643-644.
Who Kee Chung, "Reliability of Imperfect Switching of Cold Stanby Systems with Multiple Non-Critical and Critical Errors." Microelectronics Reliability vol. 35(12), 1995, pp. 1479-1482.
Ying-Lin Hsu, Jau-Chuan Ke, and Tzu-Hsin Liu, "Standby System with General Repair, Reboot Delay, Switching Failure and Unreliable Repair Facility—A Statistical Standpoint." Mathematics and Computers in Simulation vol. 81(11), 2011, pp. 2400-2413.
S. Osaki and T. Nakagawa, “On a Two-Unit Standby Redundant System with Standby Failure,” Operations Research, vol. 19(2), 1971, pp. 510-523.
R. K. Bhardwaj and Komaldeep Kaur, “Reliability and Profit Analysis of a Redundant System with Possible Renewal of Standby Subject to Inspection,” International Journal of Statistics and Reliability Engineering, vol. 1(1), 2014, pp. 36-46.
Limnios, Nikolaos, and Gheorghe Oprisan,“Semi-Markov Processes and Reliability,” Springer Science & Business Media, 2012
W. L. Smith, “Regenerative Stochastic Processes,” Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, vol. 232(1188), 1955, pp. 6-31.
W. L. Smith, “Renewal Theory and its Ramifications,” Journal of the Royal Statistical Society. Series B (Methodological), 1958, pp. 243-302.