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Investigating the Relationship between Processor and Memory Reliability in Data Science: A Bivariate Model Approach

Author

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  • Hanan Haj Ahmad

    (Department of Basic Science, Preparatory Year Deanship, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia)

  • Ehab M. Almetwally

    (Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, Egypt)

  • Dina A. Ramadan

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

Modeling the failure times of processors and memories in computers is crucial for ensuring the reliability and robustness of data science workflows. By understanding the failure characteristics of the hardware components, data scientists can develop strategies to mitigate the impact of failures on their computations, and design systems that are more fault-tolerant and resilient. In particular, failure time modeling allows data scientists to predict the likelihood and frequency of hardware failures, which can help inform decisions about system design and resource allocation. In this paper, we aimed to model the failure times of processors and memories of computers; this was performed by formulating a new type of bivariate model using the copula function. The modified extended exponential distribution is the suggested lifetime of the experimental units. It was shown that the new bivariate model has many important properties, which are presented in this work. The inferential statistics for the distribution parameters were obtained under the assumption of a Type-II censored sampling scheme. Therefore, point and interval estimation were observed using the maximum likelihood and the Bayesian estimation methods. Additionally, bootstrap confidence intervals were calculated. Numerical analysis via the Markov Chain Monte Carlo method was performed. Finally, a real data example of processors and memories failure time was examined and the efficiency of the new bivariate distribution of fitting the data sample was observed by comparing it with other bivariate models.

Suggested Citation

  • Hanan Haj Ahmad & Ehab M. Almetwally & Dina A. Ramadan, 2023. "Investigating the Relationship between Processor and Memory Reliability in Data Science: A Bivariate Model Approach," Mathematics, MDPI, vol. 11(9), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2142-:d:1138524
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    References listed on IDEAS

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    1. Silvia Angela Osmetti & Paola Maddalena Chiodini, 2011. "A method of moments to estimate bivariate survival functions: the copula approach," Statistica, Department of Statistics, University of Bologna, vol. 71(4), pages 469-488.
    2. repec:bot:journl:v:71:y:2011:i:4:p:469-488 is not listed on IDEAS
    3. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
    4. Ehab Mohamed Almetwally & Hiba Zeyada Muhammed & El-Sayed A. El-Sherpieny, 2020. "Bivariate Weibull Distribution: Properties and Different Methods of Estimation," Annals of Data Science, Springer, vol. 7(1), pages 163-193, March.
    5. Christian Genest & Jean‐François Quessy & Bruno Rémillard, 2006. "Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366, June.
    6. M. El-Morshedy & Ziyad Ali Alhussain & Doaa Atta & Ehab M. Almetwally & M. S. Eliwa, 2020. "Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples," Mathematics, MDPI, vol. 8(2), pages 1-31, February.
    7. Steve P. Verrill & James W. Evans & David E. Kretschmann & Cherilyn A. Hatfield, 2015. "Asymptotically Efficient Estimation of a Bivariate Gaussian–Weibull Distribution and an Introduction to the Associated Pseudo-truncated Weibull," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(14), pages 2957-2975, July.
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    Cited by:

    1. Aisha Fayomi & Ehab M. Almetwally & Maha E. Qura, 2023. "Exploring New Horizons: Advancing Data Analysis in Kidney Patient Infection Rates and UEFA Champions League Scores Using Bivariate Kavya–Manoharan Transformation Family of Distributions," Mathematics, MDPI, vol. 11(13), pages 1-37, July.
    2. Ehab M. Almetwally & Aisha Fayomi & Maha E. Qura, 2024. "Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings," Mathematics, MDPI, vol. 12(12), pages 1-35, June.

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