Probabilistic Assessment of Computer-Based Test (CBT) Network System Consists of Four Subsystems in Series Configuration Using Copula Linguistic Approach

  • Vijay Vir Singh Department of Mathematics, Yusuf Maitama Sule University, Kano, Nigeria
  • Abdul Kareem Lado Ismail Department of Mathematics, Kano State College of Education, Kano, Nigeria
  • Ibrahim Yusuf Department of Mathematical Sciences, Bayero University, Kano, Nigeria
  • Ameer Hassan Abdullahi Department of Mathematics Kano University of Science and Technology Kano, Nigeria
Keywords: Repairable systems, availability, MTTF, sensitivity MTTF, cost analysis, general repair, copula repair

Abstract

A complex repairable computer-based test (CBT) network system studied in this paper consists of three client computers, a load balancer, two database servers, with the centralized server structured in a series configuration. Subsystem 1 consists of three homogeneous clients arranged in parallel configuration, subsystem 2 comprises a load balancer, subsystem 3 is comprised of two distributed homogeneous database servers in parallel arrangement and subsystem 4 consists of a centralized database server. Through the transition diagram, the first-order differential equations are derived. The model has solved using supplementary variables, with implications of Laplace transforms. Reliability metrics of system effects such as availability, reliability, MTTF, MTTF sensitivity, and the cost function is estimated to see the impact of failure and repair patterns on reliability evaluations. The results of this study indicated that system performance could be improved when the copula repair is employed.

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Author Biographies

Vijay Vir Singh, Department of Mathematics, Yusuf Maitama Sule University, Kano, Nigeria

Vijay Vir Singh currently working as Professor Mathematics at Yusuf Maitama Sule University, Kano, Nigeria. He received Ph.D., from Chaudhary Charan Singh University campus Meerut, India. Prof. Singh’s research filed is in Operation Research specialized in Reliability Theory with copula linguistic approach. He has supervised four Ph.D., six MSc students for their research projects in Reliability and other Applied Mathematics area. Dr. Singh has participated in many international conferences in India, Thailand, and Nigeria as a Presenters, Technical advisory board member, and session chairperson. Prof. V. V. Singh is a member of the editorial board several Journals in India and abroad. He has reviewed many research articles from Springer, Elsevier, Inderscience, and other SCI journals in Reliability and Applied Mathematics areas.

Abdul Kareem Lado Ismail , Department of Mathematics, Kano State College of Education, Kano, Nigeria

Abdul Kareem Lado Ismail is a lecturer in the Department of Mathematics, Kano State College of Education and Preliminary Studies, Kano, Nigeria. He received his M.Sc., in Mathematics from Kano University of Science and Technology, Kano. He has more than 6 years of teaching and research experience. His research interest includes operation research, fuzzy availability analysis, statistics and reliability.

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. 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.

Ameer Hassan Abdullahi, Department of Mathematics Kano University of Science and Technology Kano, Nigeria

Ameer Hassan Abdullahi is a lecturer in the Department of Mathematics Kano University of Science & Technology Wudil, Kano State, Nigeria. Ameer Abdullahi received his M.Sc., in Mathematics from Sharda University, Greater Noida Uttar Pradesh India under sponsorship of Kano State government merit scholarship. He has more than 6 years of teaching experience at Federal polytechnic at Kano state and Kano University of Science and Technology, Wudil, Nigeria. Ameer Hassan Abdullahi research area is System reliability modeling and stochastic analysis.

Published
2021-01-08
Section
Articles