Computational Intelligence in Sustainable Reliability Engineering

5Series-Parallel Computer System Performance Evaluation with Human Operator Using Gumbel-Hougaard Family Copula

Muhammad Salihu Isa^1,2*, Ibrahim Yusuf³, Uba Ahmad Ali² and Wu Jinbiao¹

¹School of Mathematics and Statistics, Central South University, Changsha, China

²Department of Mathematics, Federal University Dutse, Dutse, Nigeria

³Department of Mathematical Sciences, Bayero University Kano, Kano, Nigeria

Abstract

This chapter examined the performance of a computer network made up of four workstations, three hubs, and two routers. Subsystem 1 consists of workstations A1, A2, A3, and A4 that are parallel and linked to subsystem 2 (hubs B1, B2, and B3), while subsystem 3 router consists of C₁ and C₂ that are also parallel to each other. All subsystems are managed by the human operator H. To analyze the reliability of the system, the partial differential equations are derived from the system’s schematic diagram in which reliability measure of system strength, such as reliability, availability, MTTF, and cost function are computed. Time to failure of devices, such as workstation, hub, and router, obeys exponential distribution, whereas the corresponding repair time follows two different distributions, namely general and copula distribution. Tables and graphs show some of the most important findings.

Keywords: Performance, workstation, Gumbel-Hougaard family copula, hub and routers

5.1 Introduction

Failures in computer systems can be classified as software, hardware, or both. ...