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

İbrahim Yusuf; Ramatu İdris Gatawa; Kabiru Suleiman

doi:10.33187/jmsm.415195

EN

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

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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

İbrahim Yusuf ^*
Nigeria

Ramatu İdris Gatawa This is me

Kabiru Suleiman This is me

Publication Date

May 27, 2018

Submission Date

April 13, 2018

Acceptance Date

May 15, 2018

Published in Issue

Year 2018 Volume: 1 Number: 1

DOI

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

IZ

https://izlik.org/JA64CT64LB

APA

Yusuf, İ., Gatawa, R. İ., & Suleiman, K. (2018). Availability analysis of a consecutive three stages deteriorating standby system considering maintenance and replacement. Journal of Mathematical Sciences and Modelling, 1(1), 21-26. https://doi.org/10.33187/jmsm.415195

AMA

1.Yusuf İ, Gatawa Rİ, Suleiman K. Availability analysis of a consecutive three stages deteriorating standby system considering maintenance and replacement. Journal of Mathematical Sciences and Modelling. 2018;1(1):21-26. doi:10.33187/jmsm.415195

Chicago

Yusuf, İbrahim, Ramatu İdris Gatawa, and Kabiru Suleiman. 2018. “Availability Analysis of a Consecutive Three Stages Deteriorating Standby System Considering Maintenance and Replacement”. Journal of Mathematical Sciences and Modelling 1 (1): 21-26. https://doi.org/10.33187/jmsm.415195.

EndNote

Yusuf İ, Gatawa Rİ, Suleiman K (May 1, 2018) Availability analysis of a consecutive three stages deteriorating standby system considering maintenance and replacement. Journal of Mathematical Sciences and Modelling 1 1 21–26.

IEEE

[1]İ. Yusuf, R. İ. Gatawa, and K. Suleiman, “Availability analysis of a consecutive three stages deteriorating standby system considering maintenance and replacement”, Journal of Mathematical Sciences and Modelling, vol. 1, no. 1, pp. 21–26, May 2018, doi: 10.33187/jmsm.415195.

ISNAD

Yusuf, İbrahim - Gatawa, Ramatu İdris - Suleiman, Kabiru. “Availability Analysis of a Consecutive Three Stages Deteriorating Standby System Considering Maintenance and Replacement”. Journal of Mathematical Sciences and Modelling 1/1 (May 1, 2018): 21-26. https://doi.org/10.33187/jmsm.415195.

JAMA

1.Yusuf İ, Gatawa Rİ, Suleiman K. Availability analysis of a consecutive three stages deteriorating standby system considering maintenance and replacement. Journal of Mathematical Sciences and Modelling. 2018;1:21–26.

MLA

Yusuf, İbrahim, et al. “Availability Analysis of a Consecutive Three Stages Deteriorating Standby System Considering Maintenance and Replacement”. Journal of Mathematical Sciences and Modelling, vol. 1, no. 1, May 2018, pp. 21-26, doi:10.33187/jmsm.415195.

Vancouver

1.İbrahim Yusuf, Ramatu İdris Gatawa, Kabiru Suleiman. Availability analysis of a consecutive three stages deteriorating standby system considering maintenance and replacement. Journal of Mathematical Sciences and Modelling. 2018 May 1;1(1):21-6. doi:10.33187/jmsm.415195