American Journal of Applied Mathematics and Statistics. 2014, 2(1), 29-33
DOI: 10.12691/AJAMS-2-1-5
Evaluation of Mean Time to System Failure of a Repairable 3-out-of-4 System with Online Preventive Maintenance
U.A. Ali1, Saminu I. Bala2, 3 and Ibrahim Yusuf2,
1Department of Mathematics, Usmanu Danfodio University, Sokoto, Nigeria
2Department of Mathematical Sciences, Bayero University, Kano, Nigeria
3Department of Mathematics, Federal University, Dutse, Nigeria
Pub. Date: January 07, 2014
Cite this paper
U.A. Ali, Saminu I. Bala and Ibrahim Yusuf. Evaluation of Mean Time to System Failure of a Repairable 3-out-of-4 System with Online Preventive Maintenance.
American Journal of Applied Mathematics and Statistics. 2014; 2(1):29-33. doi: 10.12691/AJAMS-2-1-5
Abstract
Most of the literature assumed that systems undergo preventive maintenance. Little literature is found on whether the preventive maintenance is online or offline. It is known that most of the engineering systems undergo both online and offline preventive maintenance. In this paper, we studied the mean time to system failure of a repairable redundant 3-out-of-4 system with online preventive maintenance involving four types of failures. We develop the explicit expressions for mean time to system failure for the system using Chapman-Kolmogorov equations. Various cases are analyzed graphically to investigate the impact of system parameters on mean time to system failure. Results have shown that system with online preventive maintenance is better in terms of mean time to system failure of system than system without preventive maintenance.
Keywords
Mean time to system failure, online preventive maintenance
Copyright
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References
[1] | Bhardwj, R.K. and Chander, S. (2007). Reliability and cost benefit analysis of 2-out-of-3 redundant system with general distribution of repair and waiting time. DIAS- Technology review- An Int. J. of business and IT. 4(1), 28-35. |
|
[2] | Chander, S. and Bhardwaj, R.K. (2009). Reliability and economic analysis of 2-out-of-3 redundant system with priority to repair. African J. of Maths and comp. sci, 2(11), 230-236. |
|
[3] | Bhardwj,R.K., and S.C. Malik. (2010). MTSF and Cost effectiveness of 2-out-of-3 cold standby system with probability of repair and inspection. Int. J. of Eng. Sci. and Tech. 2(1), 5882-5889. |
|
[4] | Wang, k. Hsieh, C. and Liou, C (2006). Cost benefit analysis of series systems with cold standby components and a repairable service station. Journal of quality technology and quantitative management, 3(1), 77-92. |
|
[5] | El-Said, K.M., (2008). Cost analysis of a system with preventive maintenance by using Kolmogorov’s forward equations method. American Journal of Applied Sciences 5(4), 405-410. |
|
[6] | Haggag, M.Y., (2009). Cost analysis of a system involving common cause failures and preventive maintenance, Journal of Mathematics and Statistics 5(4), 305-310. |
|
[7] | Haggag, M.Y., (2009). Cost analysis of k-out-of-n repairable system with dependent failure and standby support using Kolmogorov’s forward equations method .Journal of Mathematics and Statistics 5(4), 401-407. |
|
[8] | Wang, K.H and Kuo, C.C. (2000). Cost and probabilistic analysis of series systems with mixed standby components. Applied Mathematical Modelling, 24, 957-967. |
|
[9] | Wang, K..C., Liou, Y.C, and Pearn W. L. (2005). Cost benefit analysis of series systems with warm standby components and general repair time. Mathematical Methods of operation Research, 61, 329-343. |
|
[10] | Yusuf, I. Availability and profit analysis of 3-out-of-4 repairable system with preventive maintenance, International Journal of Applied Mathematics Research, 1(4), 2012, 510-519. |
|