Availability Analysis of Hybrid Systems Consisting of Main Units and Cold Standby Processors

  • Ibrahim Yusuf Department of Mathematical Sciences, Bayero University, Kano, Nigeria
  • Nafisatu Muhammad Usman Department of Arts and Humanity, School of General Studies, Kano State Polytechnic, Kano, Nigeria
  • Saminu Iliyasu Bala Department of Mathematical Sciences, Bayero University, Kano, Nigeria
Keywords: Availability, processor, configuration, main unit, series parallel

Abstract

The present paper studies availability of four hybrid systems configured as series-parallel systems. Each system or configuration consisting of main units and their corresponding processors. Configuration I consist of three processors is a 2-out-of-3 unit connected to 2-out-of-3 processors, Configuration II is a 2-out-of-3 unit connected to 2-out-of-4 processors, Configuration III is a 2-out-of-4 unit connected to 2-out-of-4 processors while Configuration IV is a 2-out-of-4 unit connected to 2-out-of-3 processors. The failure and repair times of units and their processors are assumed to be exponentially distributed. Explicit expressions for steady state availability are developed for each system using first order linear differential difference equations and validated by performing numerical experiments. Analysis of the effect of various system parameters on availability was performed. Graphical illustrations are given to highlight important results. The systems are ranked based on their availability and found that Configuration IV is better. Sensitivity analysis on the model’s outcomes are performed using partial rank correlation coefficients (PRCC) to determine the most critical parameters leading to increase (decrease) in the value of availability.

Author Biographies

Ibrahim Yusuf, Department of Mathematical Sciences, Bayero University, Kano, Nigeria

Ibrahim Yusuf is an Associate Professor in the Department of Mathematical Sciences, Bayero University Kano, Nigeria. He obtained his PhD in the University of Bayero University Kano, Nigeria. He has taught in BUK for more than 18 years. He is currently the Dean Faculty of Computer Science and Information Technology, Bayero University Kano, Nigeria. His research interest includes operation research, stochastic analysis, statistics and reliability modelling. He has published a number of research articles in both local and international journals.

Nafisatu Muhammad Usman, Department of Arts and Humanity, School of General Studies, Kano State Polytechnic, Kano, Nigeria

Nafisa Muhammad Usman is a lecturer in the Department of Arts and Humanity, School of General Studies, Kano State Polytechnic, Kano, Nigeria. She received her M.Sc in Mathematics the Department of Mathematical Sciences, Bayero University Kano, Nigeria. She is currently a Phd candidate in the Department of Mathematical Sciences, Bayero University Kano, Nigeria. She has 8 years of teaching and research experience. Her research interest includes operation research and reliability.

Saminu Iliyasu Bala, Department of Mathematical Sciences, Bayero University, Kano, Nigeria

Saminu Iliyasu Bala is a Professor in the Department of Mathematical Sciences, Bayero University Kano, Nigeria.He obtained his B.Sc and M.Sc degree in Mathematics from Bayero University Kano, Nigeria. Mr Bala obtained his PhD from the University of Liverpool in the year 2009. He has since been lecturer in Bayero University Kano where he supervised and still supervising many students.

Published
2021-01-08
Section
Articles