Some reliability characteristics of a linear consecutive 2-out-of-4 system connected to 2-out-of-4 supporting device for operation


  • Yusuf Ibrahim Bayero University, Kano
  • Bashir Yusuf Federal University, Dutse
  • Mansur Babagana Bayero University, Kano
  • Baffa Sani Bayero University, Kano
  • Muhammad Auwal Lawan Kano State University of Science and Technology, Wudil,Kano





Availability, External Supporting Device, Linear Consecutive, Operation, Profit


This paper presents the Markov model for the reliability analysis of a linear consecutive 2-out-of-4 repairable system operating with the help of a linear consecutive 2-out-of-4 external supporting device. The system is analyzed using first order linear differential equation to develop the explicit expression for steady-state availability, busy period and profit function. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. In addition, the effect of failure and repair on availability and profit are researched.


[1] B. Parashar and G. Taneja. Reliability and profit evaluation of a PLC hot standby system based on a master slave concept and two types of repair facilities. IEEE Trans. Reliab, 56: , (2007),534-539. DOI: 10.1109/TR.2007.903151.

[2] D. Singh and G. Taneja. Reliability and economic analysis of a power generating system comprising one gas and one steam turbine with random inspection, J. Math. Stat, 10 (4), (2014).

[3] I. Yusuf. Comparison of some reliability characteristics between redundant systems requiring supporting units for their operation. J Math Comput Sci 3(1): (2013), 216–232.

[4] 1. Yusuf, and S.I. Bala. Analysis of reliability characteristics of a parallel system with external supporting devices for operation, International Journal of Information and Management Sciences, 24, (2013), 297-306.

[5] I. Yusuf and N. Hussaini. (2012). Evaluation of reliability and availability characteristics of 2-out-of-3 standby system under a perfect repair condition. American Journal of Mathematics and Statistics,2(5): 114-119.

[6] M.S. Aliyu, I. Yusuf and U. A. Ali. Availability and profit optimization of series-parallel system with linear consecutive cold standby units, Applied Mathematics, 6, (2015),332-344.

[7] R. Krishnan and S. Somasundaram. Reliability and Profit Analysis of Repairable K-Out-of-N System with Sensor. European Journal of Scientific Research, 67, (2012),215-222.

[8] R.K., Bhardwaj and S. Chander. (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.

[9] R.K., Bhardwaj 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.

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