Availability analysis of a consecutive three stages deteriorating standby system considering maintenance and replacement

Year 2018, Volume: 1 Issue: 1, 21 - 26, 27.05.2018

İbrahim Yusuf , Ramatu İdris Gatawa Kabiru Suleiman

https://doi.org/10.33187/jmsm.415195

Abstract

This paper deals with the modelling and evaluation of availability of a system subject to three consecutive stages of deterioration: minor, medium and major deteriorations under minor and major maintenance, and replacement at deterioration and failure respectively. The system has three possible modes: working with full capacity, deterioration and failure mode. In this paper, probabilistic models have been developed to evaluate the relationship between availability and the performance of a standby deteriorating system. Various graphs have been plotted to discover the impact of the deterioration and failure on steady-state availability. The system is analysed using first order linear differential equations.

Keywords

availability, deterioration, maintenance

References

• [1] Bérenguer C.(2008). On the mathematical condition-based maintenance modelling for continuously deteriorating systems, International Journal of Materials and Structural Reliability, 6, 133-151.
• [2] Frangopol, D.M.; Kallen, M.J. and Van Noortwijk, J.M. (2004). Probabilistic models for life-cycle performance of deteriorating structures: Review and future directions. Prog. Struct. Eng. Mater., 6, 197–212.
• [3] Lam,Y and Zhang, Y. L. (2003). A geometric-process maintenance model for a deteriorating system under a random environment, IEEE Trans. Reliability. 52(1), 83-89.
• [4] Liu, D., Xu, G and Mastorakis, N. E. (2011).Reliability analysis of a deteriorating system with delayed vacation of repairman, WSEAS Transactions on Systems, 10(12),
• [5] Nicolai, R.P. Dekker, R. and Van Noortwijk, J.M. (2007). A comparison of models for measurable deterioration: An application to coatings on steel structures. Reliab. Eng. Syst. Saf. , 92, 1635–1650.
• [6] Pandey, M.D.; Yuan, X.X.; van Noortwijk, J.M. The influence of temporal uncertainty ofdeterioration on life-cycle management of structures. Struct. Infrastruct. Eng. 2009, 5, 145–156.
• [7]Rani, T.C and Sukumari, C. (2014). Optimum replacement time for a deteriorating system, International Journal of Scientific Engineering and Research, 2(1), 32-33.
• [8] Tuan K. Huynh, Anne Barros, Christophe Bérenguer. (2013).A Reliability-based Opportunistic Predictive Maintenance Model for k-out-of-n Deteriorating Systems, Chemical Engineering Transactions, 33, 493-498.
• [9] Vinayak, R and Dharmaraja. S (2012). Semi-Markov Modeling Approach for Deteriorating Systems with Preventive Maintenance, International Journal of Performability Engineering Vol. 8, No. 5, pp. 515- 526.
• [10] 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.
• [11] 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.
• [12] Xiao, T.C., Li, Y, -F., Wang, Z., Peng, W and Huang, H, -Z. (2013). Bayesian reliability estimation for deteriorating systems with limited samples Using the Maximum Entropy Approach, Entropy, 15, 5492-5509; doi:10.3390/e15125492.
• [13] Yuan, W., Z. and Xu, G. Q. (2012). Modelling of a deteriorating system with repair satisfying general distribution, Applied Mathematics and Computation 218, 6340–6350
• [14] Yuan, L and Xu, J. (2011).A deteriorating system with its repairman having multiple vacations, Applied Mathematics and Computation. 217(10), 4980-4989.
• [15] Yusuf, I., Suleiman, K., Bala, S.I. and Ali, U.A. (2012). Modelling the reliability and availability characteristics of a system with three stages of deterioration, International Journal of Science and Technology, 1(7) , 329-337.
• [16] Zhang, Y.L. and Wang, G. J. (2007). A deteriorating cold standby repairable system with priority in use, European Journal of Operational Research, Vol.183, 1, pp.278–295.