A Stochastic Analysis to Calculate the Mean Time to System Failure (MTSF) of A Two Identical Unit Parallel System

Authors

  • Bestun Merza Abdulkareem Department of Statistics and Informatics, College of Administration and Economics, Salahaddin University-Erbil

DOI:

https://doi.org/10.21271/zjhs.28.2.17

Keywords:

Parallel system with repairs, Mean time to failure (MTTF), transition probability matrix.

Abstract

In this research two identical parallel electric generators with repair a failed one have been analyzed stochastically by two methods, first by method based on certain probability assumptions and second through three state Markov chain, classified as one recurrent ( absorbing ) state and two transient states. For the purpose of this study the data about the failure and repair time intervals of electric generators of the months november and december 2022 are obtained from the electricians of several places in Erbil city, whereas  they supplied electricity to their lanes whenever the national electric power is interrupted. This research  aimed  to define the mean time to system failure by the two previous methods.

References

- BHAT, U. NARAYAN & MILLER, GREGORY K. (2002). Elements of Applied Stochastic Processes, 3rd Edition, John Wiley & Sons, Inc.

- Beichelt, F.E & Paul Fatti (2002) Stochastic processes and their applications. USA, CRC press.

- B. Çekyay and S. Özekici. Mean time to failure and availability of semi- markov missions with maximal repair. European Journal of Operational Research, 207(3):1442-1454, 2010.

- Dhillon, B. S. (2006). Maintainability, Maintenance, and Reliability for Engineers. Taylor & Francis Group, LLC.

- Goswami A. & Rao B.V. (2006). A course in applied processes, Hindustan Book Agency, New Delhi 110016, India.

- KIRKWOOD, JAMES R. (2015). Markov Processes; Taylor & Francis Group.

- Kumar, P., Bharti, A. and Gupta, A. (2012), "Reliability analysis of a two non identical unit system with repair and replacement having correlated failures and repairs", Journal of Informatics & Mathematical Sciences, Vol. 4 No. 3, pp. 339-350.

- Kishor S. Trivedi and Andrea Bobbio. Continuous-Time Markov Chain: Reliability Models, page 357-422. Cambridge University Press, 2017. doi:10.1017/9781316163047.014.

- Lawler. Gregory F. (2006), Introduction to Stochastic processes, 2nd edition, Taylor & Francis Group.

- Madhu,j (1998) Reliability Analysis of a two unit system with common cause shock Failures, Indian J. Pure appl. Math. 29(12), 1281 - 1289.

- MEDHI, J. (2004). Stochastic Processes; 2nd Edition; New Age International (P) limited; publishers.

- MCAO Keizer, SDP Flapper, and RH. Teunter. Condition-based mainte- nance policies for systems with multiple dependent components: a review. European Journal of Operational Research, 2017.

- Mohamed, S. and Sherbeny, E.L. (2013),"Stochastic analysis of a two non identical unit parallel system with different types of failures subject to preventive maintenance and repairs", Mathematical Problems in Engineering, Vol. 2013, Article ID 192545, p. 10. Pham, H.(2007), System Software Reliability, Springer-Verlag,London.

- Ram, M. and Manglik, M. (2014),"Stochastic behaviour of a Markov model under multi-state failures",International Journal of System Assurance: Engineering and Management, Vol. 5 No. 4, pp. 686-699. 26

- Ram, M., Singh, S.B. and Singh, V.V. (2013), "Stochastic analysis of a standby system with waiting repair strategy", IEEE Transactions on Systems, Man and Cybernetics, Vol. 43 No. 3, pp. 698-707.

- RANDAL, DOUC; ERIC, MOULINES; PIERRE, PRIOUET & PHILIPPE, SOULIER (2018). Markov chain; Springer Nature Switzerland AG.

- Yang, G. (2007), life cycle reliability engineering, John Wiley & sons , Inc.

Published

2024-04-15

How to Cite

Abdulkareem, B. M. (2024). A Stochastic Analysis to Calculate the Mean Time to System Failure (MTSF) of A Two Identical Unit Parallel System. Zanco Journal of Human Sciences, 28(2), 301–310. https://doi.org/10.21271/zjhs.28.2.17

Issue

Section

Articles