International Journal of Engineering & Technology, 7 (1) (2018) 135-139 International Journal of Engineering & Technology Website: www.sciencepubco.com/index.php/IJET doi: 10.14419/ijet.v7i1.8037 Research paper Some reliability characteristics of a linear consecutive 2-out-of-4 system connected to 2-out-of-4 supporting device for operation Ibrahim Yusuf 1* , Bashir Yusuf 2 , Mansur Babagana 3 , Baffa Sani 3 and Muhammad Auwal Lawan 4 1 Department of Mathematical Sciences, Bayero University, Kano, Nigeria 2 Department of Mathematics, Federal University, Dutse, Nigeria 3 Department of Computer Science, Bayero University, Kano, Nigeria 4 Department of Mathematics, Kano State University of Science and Technology, Wudil, Kano, Nigeria * Corresponding author E-mail: iyusuf.mth@buk.edu.ng Abstract 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. Keywords: availability; external supporting device; Linear consecutive; operation; profit. 1. Introduction Systems are usually studied with intention to the evaluation of their reliability measures in terms of busy period of repairman, availability and generated revenue. In real-life situations, we often encounter cases where systems that cannot work without the help of exter- nal supporting devices connect to such systems. These external supporting devices are systems themselves that are bound to fail. Such systems are found in power plants, manufacturing systems, and industrial systems. Improving the reliability and availability of such systems with their supporting device is vital in ensuring quality of products. Due to their importance in promoting and sustaining industries and economy, reliability and economic analysis of such systems have become an area of interest. Among the reliability measures of interest are the steady-state availability, busy period, profit function and mean time to system failure (MTSF). Improving the availability of such systems leads to an increase in production and associated profit. Large volumes of literature exist on the is- sue relating to prediction of reliability characteristics of consecutive k-out-of-n systems. Parashar and Taneja [1] deals with reliability and profit evaluation of hot standby PLC system. Singh and Taneja [2] analyzed the reliability of power generating system with random inspection. Yusuf [3] performed the reliability comparison between redundant systems requiring supporting device for operation. Yusuf and Bala [4] analyzed the reliability characteristics of parallel system with external supporting device for operation. Yusuf and Hussaini [5] studied the reliability characteristics of 2-out-of-3 standby system under perfect repair condition. Aliyu et. al.[6] studied the optimiza- tion of availability and profit of series-parallel system with linear consecutive cold standby units. Krishnan and Somasundaram [7] analyzed the reliability and profit of Repairable K-Out-of-N System with Sensor. Bhardwaj and chander [8] analyzed the reliability and profit of 2-out-of-3 redundant system with general repair distribution. Bharwaj and Malik [9] studied cost effectiveness of 2-out-of-3 cold standy system with repair and inspection. Chander and Bhardwaj [10] analyzed the reliability of 2-out-of-3 redundant system with repair priority. Existing literatures ignores the impact of having more redundant supporting device connected to the system or where each unit is connected to its supporting device to improve the reliability of the system. Such literature works laid emphasis on reliability of the system with one supporting device whose failure retards the opera- tion of the system. More sophisticated models of redundant systems connected to multi redundant external supporting device should be developed to assist in reliability of the system, reducing operating costs and the risk of a catastrophic breakdown. This paper presents availability and profit analysis of a linear con- secutive 2-out-of-4 system that worked with the aid of an external linear consecutive 2-out-of-4 supporting device and derived its cor- responding mathematical models. The objectives of our analysis are twofold. First is to capture the effect of failure and repair rates on steady-state availability and profit. Second is to capture the impact of steady-state availability on profit. The organization of the paper is as follows. Section 2 contains the description of the system under study. Section 3 present Material and method while section 4 present formulations of the models. The results of our numerical simulations are presented in section 5. Finally, we make a concluding remark in Section 6. Copyright © 2018 Author. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.