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Distributed System Reliability Analysis with Two Coverage Factors: A Copula Approach

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Advances in Reliability, Failure and Risk Analysis

Part of the book series: Industrial and Applied Mathematics ((INAMA))

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Abstract

Traditional performance and reliability analysis for distributed systems frequently overestimates the fundamental dependability of their components. To address this quandary, a copula approach for analyzing the performance of distributed system situated to two separate regions employing fault coverage factor in each region is proposed at first. Copula technique is a powerful tool for describing variable dependence and has received much attention in a variety of fields of study. Regions I and II consist of two client and one directory server each. In this chapter, we also introduce coverage factors for each region, such that the failure of each client and directory server for each region is detected by the coverage factor. Each area designed for this system has a constant failure rate. This is prone to two sorts of failure: lower failure and higher failure. When a lower failure occurs, the system is repaired using the general repaired rate; however, a higher failure can be rectified using the copula family of Gumbel-Hougaard distribution. The goal is to obtain explicitly expressed expressions for the dependability, availability, sensitivity, and cost function. As a result of this, in this chapter, we aim at examining the reliability strength of a distributed system in relation to availability, expected profit and reliability. For the sake of generality, we use the Laplace transforms and technique of supplementary variable to establish the partial differential equations related to transition diagram essential to this chapter. The numerical validation of explicit expressions for system availability, reliability, and profit function is performed. Computations for reliability characteristics are evaluated as a specific example by analyzing availability, reliability, and cost in order to reflect the impacts of coverage factor and both failure and repair rates on reliability characteristics. Tables and graphs highlight the computation of the result base on assume numerical values.

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Author information

Authors and Affiliations

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

    Ibrahim Yusuf

  2. Department of Art and Humanities, Kano State Polytechnic, Kano, Nigeria

    Ismail Tukur

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  1. Ibrahim Yusuf
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  2. Ismail Tukur
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Correspondence to Ibrahim Yusuf .

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Editors and Affiliations

  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, Punjab, India

    Harish Garg

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Yusuf, I., Tukur, I. (2023). Distributed System Reliability Analysis with Two Coverage Factors: A Copula Approach. In: Garg, H. (eds) Advances in Reliability, Failure and Risk Analysis. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-19-9909-3_15

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