Title: Stochastic modelling and analysis of a repairable 2-out-of-4 system

Authors: Ibrahim Yusuf; K. Suleiman; Yusuf Bashir; U.A. Ali

Addresses: Department of Mathematical Sciences, Faculty of Science, Bayero University, P.M.B. 3011, Kano, Nigeria ' Department of Mathematics, Federal University, P.M.B. 7156, Dutse, Jigawa State, Nigeria ' Department of Mathematics, Federal University, P.M.B. 7156, Dutse, Jigawa State, Nigeria ' Department of Mathematics, Faculty of Science, Usmanu Danfodio University, P.M.B. 2346, Sokoto, Nigeria

Abstract: In this study, stochastic modelling and analysis of a repairable 2-out-of-4 system is presented. The system under study is exposed to four types of failures and is attended by four repairmen. The failure and repair time are assumed exponentially distributed. Explicit expressions for mean time to system failure (MTSF), the steady-state availability, and busy period of repairman and profit function of the system are analysed stochastically using Kolmogorov's forward equation method. Numerical results giving some particular values to the costs and other parameters have also been obtained. Graphical studies on MTSF, steady-state availability and profit has been shown with respect to both failure and repair rates.

Keywords: mean-time-to-system-failure; MTSF; system availability; 2-out-4 systems; stochastic modelling; repairable systems; repair rates; failure rates.

DOI: 10.1504/IJMOR.2014.057850

International Journal of Mathematics in Operational Research, 2014 Vol.6 No.1, pp.29 - 40

Received: 27 Jul 2012
Accepted: 17 Oct 2012
Published online: 28 Jun 2014 *

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