Reliability and Performance Analysis of Two Unit Active Parallel System Attended by Two Repairable Machines

Document Type : Original Article


1 Department of Mathematical Sciences, Bayero University, Kano, Nigeria

2 Department of Mathematics, Kano University of Science and Technology, Wudil, Kano, Nigeria

3 Department of Mathematics, Federal University, Dutse, Nigeria

4 Department of Mathematics College of Arts and Science, Kano, Nigeria

5 Department of Mathematics, Federal University Dutse, Jigawa Nigeria

6 Department of Mathematics, Sokoto State University, Sokoto



The present paper focus on the performance evaluation of an active dissimilar parallel system. The system has two parallel active units. Two repair service stations are set aside to handle unit failure. At failure of a unit, the service station will engage in the repair of the failed unit. The repair machines are systems themselves that are bound to fail. The system of linear differential difference equation is analyzed to obtained expressions of reliability measures of determining the strength of system such as availability, mean time to failure (MTTF) and profit function. Numerical examples such as surface plots and sensitivity analysis are presented to illustrate the obtained results and to analyze the effect of various system parameters. On the basis of numerical experiments, it is observed that the system’s best availability, MTTF and profit results may be achieved on a regular basis when repair machines are deployed.