Theoretical framework and inference for fitting extreme data through the modified Weibull distribution in a first-failure censored progressive approach.

The importance of biomedical physical data is underscored by its crucial role in advancing our comprehension of human health, unraveling the mechanisms underlying diseases, and facilitating the development of innovative medical treatments and interventions. This data serves as a fundamental resource, empowering researchers, healthcare professionals, and scientists to make informed decisions, pioneer research, and ultimately enhance global healthcare quality and individual well-being. It forms a cornerstone in the ongoing pursuit of medical progress and improved healthcare outcomes. This article aims to tackle challenges in estimating unknown parameters and reliability measures related to the modified Weibull distribution when applied to censored progressive biomedical data from the initial failure occurrence. In this context, the article proposes both classical and Bayesian techniques to derive estimates for unknown parameters, survival, and failure rate functions. Bayesian estimates are computed considering both asymmetric and symmetric loss functions. The Markov chain Monte Carlo method is employed to obtain these Bayesian estimates and their corresponding highest posterior density credible intervals. Due to the inherent complexity of these estimators, which cannot be theoretically compared, a simulation study is conducted to evaluate the performance of various estimation procedures. Additionally, a range of optimization criteria is utilized to identify the most effective progressive control strategies. Lastly, the article presents a medical application to illustrate the effectiveness of the proposed estimators. Numerical findings indicate that Bayesian estimates outperform other estimation methods by achieving minimal root mean square errors and narrower interval lengths.

Properties, quantile regression, and application of bounded exponentiated Weibull distribution to COVID-19 data of mortality and survival rates.

Well-known continuous distributions such as Beta and Kumaraswamy distribution are useful for modeling the datasets which are based on unit interval [0,1]. But every distribution is not always useful for all types of data sets, rather it depends on the shapes of data as well. In this research, a three-parameter new distribution named bounded exponentiated Weibull (BEW) distribution is defined to model the data set with the support of unit interval [0,1]. Some fundamental distributional properties for the BEW distribution have been investigated. For modeling dependence between measures in a dataset, a bivariate extension of the BEW distribution is developed, and graphical shapes for the bivariate BEW distribution have been shown. Several estimation methods have been discussed to estimate the parameters of the BEW distribution and to check the performance of the estimator, a Monte Carlo simulation study has been done. Afterward, the applications of the BEW distribution are illustrated using COVID-19 data sets. The proposed distribution shows a better fit than many well-known distributions. Lastly, a quantile regression model from bounded exponentiated Weibull distribution is developed, and its graphical shapes for the probability density function (PDF) and hazard function have been shown.

A survey on fractal fractional nonlinear Kawahara equation theoretical and computational analysis.

With the use of the Caputo, Caputo-Fabrizio (CF), and Atangana-Baleanu-Caputo (ABC) fractal fractional differential operators, this study offers a theoretical and computational approach to solving the Kawahara problem by merging Laplace transform and Adomian decomposition approaches. We show the solution's existence and uniqueness through generalized and advanced version of fixed point theorem. We present a precise and efficient method for solving nonlinear partial differential equations (PDEs), in particular the Kawahara problem. Through careful error analysis and comparison with precise solutions, the suggested method is validated, demonstrating its applicability in solving the nonlinear PDEs. Moreover, the comparative analysis is studied for the considered equation under the aforementioned operators.

Efficient estimation of population variance of a sensitive variable using a new scrambling response model.

This study introduces a pioneering scrambling response model tailored for handling sensitive variables. Subsequently, a generalized estimator for variance estimation, relying on two auxiliary information sources, is developed following this novel model. Analytical expressions for bias, mean square error, and minimum mean square error are meticulously derived up to the first order of approximation, shedding light on the estimator's statistical performance. Comprehensive simulation experiments and empirical analysis unveil compelling results. The proposed generalized estimator, operating under both scrambling response models, consistently exhibits minimal mean square error, surpassing existing estimation techniques. Furthermore, this study evaluates the level of privacy protection afforded to respondents using this model, employing a robust framework of simulations and empirical studies.

Reliability analysis of the triple modular redundancy system under step-partially accelerated life tests using Lomax distribution.

Triple modular redundancy (TMR) is a robust technique utilized in safety-critical applications to enhance fault-tolerance and reliability. This article focuses on estimating the distribution parameters of a TMR system under step-stress partially accelerated life tests, where each component included in the system follows a Lomax distribution. The study aims to analyze the system's reliability and mean residual lifetime based on the estimated parameters. Various estimation techniques, including maximum likelihood, percentile, least squares, and maximum product of spacings, are explored. Additionally, the optimal stress change time is determined using two criteria. An illustrative example supported by two actual data sets is presented to showcase the methodology's application. By conducting Monte Carlo simulations, the assessment of the estimation methods' effectiveness reveals that the maximum likelihood method outperforms the other three methods in terms of both accuracy and performance, as indicated by the numerical outcomes. This research contributes to the understanding and practical implementation of TMR systems in safety-critical industries, potentially saving lives and preventing catastrophic events.

Comparative dynamics of mixed convection heat transfer under thermal radiation effect with porous medium flow over dual stretched surface.

Due to enhanced heat transfer rate, the nanofluid and hybrid nanofluids have significant industrial uses. The principal objective of this exploration is to investigate how thermal radiation influences the velocity and temperature profile. A water-based rotational nanofluid flow with constant angular speed [Formula: see text] is considered for this comparative study. A similarity conversion is applied to change the appearing equations into ODEs. Three different nanoparticles i.e., copper, aluminum, and titanium oxide are used to prepare different nanofluids for comparison. The numerical and graphical outputs are gained by employing the bvp-4c procedure in MATLAB. The results for different constraints are represented through graphs and tables. Higher heat transmission rate and minimized skin friction are noted for triple nanoparticle nanofluid. Skin coefficients in the x-direction and y-direction have reduced by 50% in trihybrid nanofluid by keeping mixed convection levels between the range [Formula: see text]. The heat transmission coefficient with raising the levels of thermal radiation between [Formula: see text] and Prandlt number [Formula: see text] has shown a 60% increase.

Effect of inclined magnetic field on radiative heat and mass transfer in chemically reactive hybrid nanofluid flow due to dual stretching.

This research analyzes the three-dimensional magneto hydrodynamic nanofluid flow through chemical reaction and thermal radiation above the dual stretching surface in the presence of an inclined magnetic field. Different rotational nanofluid and hybrid nanofluids with constant angular velocity [Formula: see text] for this comparative study are considered. The constitutive relations are used to gain the equations of motion, energy, and concentration. This flow governing extremely non-linear equations cannot be handled by an analytical solution. So, these equations are transformed into ordinary differential equalities by using the similarity transformation and then handled in MATLAB by applying the boundary values problem practice. The outcomes for the considered problem are accessed through tables and graphs for different parameters. A maximum heat transfer amount is observed in the absence of thermal radiation and when the inclined magnetic field and axis of rotation are parallel.

Elimination of aspirin and paracetamol from aqueous media using Fe/N-CNT/ß-cyclodextrin nanocomposite polymers: theoretical comparative survey via advanced physical models.

The main purpose of this research is to theoretically investigate the adsorption of two pharmaceutical molecules, i.e. aspirin and paracetamol, using two composite adsorbents, i.e. N-CNT/ß-CD and Fe/N-CNT/ß-CD nanocomposite polymers. A multilayer model developed by statistical physics is implemented to explain the experimental adsorption isotherms at the molecular scale, so as to overpass some limitations of the classical adsorption models. The modelling results indicate that the adsorption of these molecules is almost accomplished by the formation of 3 to 5 adsorbate layers, depending on the operating temperature. A general survey of the number of adsorbate molecules captured by the adsorption site (npm) suggested that the adsorption process of pharmaceutical pollutants is multimolecular and that each adsorption site can capture several molecules simultaneously. Furthermore, the npm values demonstrated the presence of aggregation phenomena of aspirin and paracetamol molecules during adsorption. The evolution of the adsorbed quantity at saturation confirmed that the presence of Fe in the adsorbent enhanced the removal performance of the investigated pharmaceutical molecules. In addition, the adsorption of the pharmaceutical molecules aspirin and paracetamol on the N-CNT/ß-CD and Fe/N-CNT/ß-CD nanocomposite polymer surface involved weak physical type interactions, since the interaction energies do not overcome the threshold of 25 000 J mol-1.