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

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.

Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings

“…They devised statistical inference techniques encompassing bivariate random censoring, semi-competing risks, and competing risks, alongside maximum likelihood estimation procedures. Haj Ahmed et al [27] introduced a novel bivariate model based on the FGM copula and the univariate modified extended exponential distribution, named the bivariate modified extended exponential distribution. They estimated the unknown parameters using both maximum likelihood and Bayesian estimation methods within a Type II censored sampling scheme.…”