In 2019, a new lethal and mutant virus (COVID-19) spread around the world, causing the deaths of millions of people. COVID-19 demonstrates that scientists are involved in significant research efforts to face bacteria with less effort than that dedicated to viruses. Since then, engineers and bio-materials scientists have been trying to develop antiviral research and find a suitable effective medication. Strategies and opportunities for interference diagnostics, treatment strategies, and predicting future factors became mandatory. From a statistical point of view, estimating and modelling these factors play an important role in preventing future viral epidemics. In this article, modelling the recovery rate of COVID-19 is investigated through a new distribution which is called the unit exponential Pareto distribution. The new continuous distribution with three parameters displays a prominent level of flexibility to model decreasing, symmetric, and asymmetric data with a monotone failure rate. The recovery rates of COVID-19 in Turkey and France were examined; moreover, milk production data and components’ failure rates are presented for data modeling. The obtained results proved the superiority of the newly suggested model compared to other unit-based distributions. Several statistical features are studied such as the quantile function, the moments, the moment-generating function, some entropy measures, the ordered statistics, the stress–strength, and stochastic ordering. Two classical estimation methods are used in addition to the Bayesian method. The statistical features and estimation analysis are evaluated using numerical and simulation techniques. As a result, we obtain the efficiency of using the Bayesian method over the classical ones, with respect to the bias, average squared error, and the length of confidence intervals for the unknown parameters.

Accurate estimation and modeling of infant mortality rates are crucial for public health planning, medical research, and policy-making. Many biological, environmental, and socio-economic factors influence infant mortality. It is essential to employ robust statistical models that can detect the underlying failure patterns. Traditional lifetime models are incapable of capturing infant mortality patterns due to their complexity, particularly when decreasing failure rates occur over time. We introduce the Inverse Power Ailamujia (IPA) and Truncated Inverse Power Ailamujia (TIPA) distributions as a generalizable lifetime model specifically designed to represent decreasing failure rates, making it highly suitable for analyzing infant mortality data. For the mortality studies, it is often not possible to complete data gathering due to the limitations in cost and time, and hence one resorts to a progressive censoring scheme where only a subset of the observed failures is recorded while the remaining units are progressively censored. Progressive censoring with the IPA and TIPA framework is employed to facilitate data collection. The maximum likelihood estimation (MLE) and Bayesian inference are employed to estimate the IPA and TIPA model's unknown parameters under progressive censoring. The Bayesian approach is explored under symmetric squared error and asymmetric LINEX loss functions, providing robust estimation techniques that account for different levels of parameter uncertainty. Additionally, confidence intervals and credible intervals are constructed using bootstrap methods, asymptotic approximations, and Markov Chain Monte Carlo (MCMC) simulations, ensuring the reliability of parameter estimates. The effectiveness of the proposed approach is demonstrated through a two real-world dataset, where the IPA and TIPA models predicts. The findings highlight the advantages of integrating progressive censoring with the IPA and TIPA distributions, offering a practical and computationally efficient tool for modeling.

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.

This study explores a new dimension of accelerated life testing by analyzing competing risk data through Tampered Random Variable (TRV) modeling, a method that has not been extensively studied. This method is applied to simple step-stress life testing (SSLT), and it considers multiple causes of failure. The lifetime of test units under changeable stress levels is modeled using Power Rayleigh distribution with distinct scale parameters and a constant shape parameter. The research introduces unique tampering coefficients for different failure causes in step-stress data modeling through TRV. Using SSLT data, we calculate maximum likelihood estimates for the parameters of our model along with the tampering coefficients and establish three types of confidence intervals under the Type-II censoring scheme. Additionally, we delve into Bayesian inference for these parameters, supported by suitable prior distributions. Our method’s validity is demonstrated through extensive simulations and real data application in the medical and electrical engineering fields. We also propose an optimal stress change time criterion and conduct a thorough sensitivity analysis.

The issue of this paper is the inference about the parameters of modified extended exponential distribution (MExED) planned on the progressively type-II censored (Prog -II- C) samples. The maximum likelihood and Bayesian estimates are procured for the parameters of MExED. Approximate confidence intervals (ACIs), the reliability and risk functions are estimated based on the asymptotic distribution of maximum likelihood estimates (MLEs) and delta method approach. Moreover, Bayesian estimates are obtained for symmetric and asymmetric loss functions such as squared error loss (SEL) and LINEX loss functions. Gibbs within Metropolis–Hasting samplers procedure is applied for using the Markov chain Monte Carlo (MCMC) technique to get on the Bayes estimates of the unknown parameters and their credible intervals (CRIs). Finally, a real-life data set, which represents the breakdown of some mechanical components, is considered an application of the proposed methods.