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The proportional hazard regression models are widely used statistical tools for analyzing survival data and estimating the effects of covariates on survival times. It is assumed that the effects of the covariates are constant across the time. In this paper, we propose a novel extension of the proportional hazard model by incorporating an exponentiated-Weibull distribution to model the baseline line hazard function. The proposed model offers more flexibility in capturing various shapes of failure rates and accommodates both monotonic and non-monotonic hazard shapes. The performance evaluation of the proposed model and comparison with other commonly used survival models including the generalized log–logistic, Weibull, Gompertz, and exponentiated exponential PH regression models are explored using simulation results. The results demonstrate the ability of the introduced model to capture the baseline hazard shapes and to estimate the effect of covariates on the hazard function accurately. Furthermore, two real survival medical data sets are analyzed to illustrate the practical importance of the proposed model to provide accurate predictions of survival outcomes for individual patients. Finally, the survival data analysis reveal that the model is a powerful tool for analyzing complex survival data. [ABSTRACT FROM AUTHOR]

The paper presents a novel statistical approach for analyzing the daily coronavirus case and fatality statistics. The survival discretization method was used to generate a two-parameter discrete distribution. The resulting distribution is referred to as the "Discrete Marshall–Olkin Length Biased Exponential (DMOLBE) distribution". Because of the varied forms of its probability mass and failure rate functions, the DMOLBE distribution is adaptable. We calculated the mean and variance, skewness, kurtosis, dispersion index, hazard and survival functions, and second failure rate function for the suggested distribution. The DI index demonstrates that the proposed model can represent both over-dispersed and under-dispersed data sets. We estimated the parameters of the DMOLBE distribution. The behavior of ML estimates is checked via a comprehensive simulation study. The behavior of Bayesian estimates is checked by generating 10,000 iterations of Markov chain Monte Carlo techniques, plotting the trace, and checking the proposed distribution. From simulation studies, it was observed that the bias and mean square error decreased with an increase in sample size. To show the importance and flexibility of DMOLBE distribution using two data sets about deaths due to coronavirus in China and Pakistan are analyzed. The DMOLBE distribution provides a better fit than some important discrete models namely the discrete Burr-XII, discrete Bilal, discrete Burr-Hatke, discrete Rayleigh distribution, and Poisson distributions. We conclude that the new proposed distribution works well in analyzing these data sets. The data sets used in the paper was collected from 2020 year. [ABSTRACT FROM AUTHOR]

The reliability analysis is usually concerned with failures in the time domain which show the difference between the quality control and reliability engineering. Also, It is very common in engineering or biological science units are falling under different causes of failure, which is known by competing risks model. In this paper, we have adopted the competing risks model when the lifetime of units distributed with generalized half-logistic (GHL) distribution. This model is formulated under consideration the failure done with two independent causes of failure. Also, to balance in statistical inference between the minimum number of failure and ideal test time, we are using, the type-I generalized hybrid censoring scheme (GHCS). The model parameters are estimated by maximum likelihood (ML) and Bayes approaches. The approximate confidence intervals, bootstrap confidence intervals and credible intervals are constructed. The developed results are discussed and assessed through Monte Carlo simulation study. A real data set is used and analyzed to report and illustrate the developed results. [ABSTRACT FROM AUTHOR]

A fully parametric accelerated failure time (AFT) model with a flexible, novel modified exponential Weibull baseline distribution called the extended exponential Weibull accelerated failure time (ExEW-AFT) model is proposed. The model is presented using the multi-parameter survival regression model, where more than one distributional parameter is linked to the covariates. The model formulation, probabilistic functions, and some of its sub-models were derived. The parameters of the introduced model are estimated using the maximum likelihood approach. An extensive simulation study is used to assess the estimates' performance using different scenarios based on the baseline hazard shape. The proposed model is applied to a real-life right-censored COVID-19 data set from Sudan to illustrate the practical applicability of the proposed AFT model. [ABSTRACT FROM AUTHOR]

In a reliability theory, the statistical inference under accelerated competing risks model have a great significance. This model proposes the assumption of independence of variables for convenience. But, in general this assumption doesn't agree with the nature of the problem at hand. In this paper, we proposed a step stress accelerated life testing (ALT) model on the dependent competing risk modes of life Lomax distribution (LD). The structural problem of the dependence between variables discussed copula approach. Also, we are considering the units of the product fails under two dependent fatal risks and the failure times accelerated under step stress ALTs and censored with type-I generalized hybrid censoring scheme (GHCS). The parameters of this model are estimated by maximum likelihood method. Also, the confidence intervals are discussed with asymptotic and two bootstrap confidence intervals. The Monte Carlo simulation study conducted to measure the quality of the proposed methods. Finally, we report some points to describe the numerical results. [ABSTRACT FROM AUTHOR]

In this paper, we develop statistical inference of competing risks samples which are collected under a joint Type-II censoring scheme of products with Weibull lifetime distributions. These inferences are drawn from two independent fatal risks and come from two different lines of production with the same facility. The model parameters and the parameters of life (reliability and hazard rate functions) are estimated using maximum likelihood (ML), bootstrap and Bayes methods. Additionally, we constructed asymptotic ML confidence intervals, bootstrap confidence intervals and Bayes credible intervals. Furthermore, the theoretical results are assessed and compared through Monte Carlo simulations. Finally, one real data set is analyzed under the proposed model for illustrative purpose. [ABSTRACT FROM AUTHOR]

For the first time and by using an entire sample, we discussed the estimation of the unknown parameters θ 1 , θ 2 , and β and the system of stress-strength reliability R = P Y < X for exponentiated inverted Weibull (EIW) distributions with an equivalent scale parameter supported eight methods. We will use maximum likelihood method, maximum product of spacing estimation (MPSE), minimum spacing absolute-log distance estimation (MSALDE), least square estimation (LSE), weighted least square estimation (WLSE), method of Cramér-von Mises estimation (CME), and Anderson-Darling estimation (ADE) when X and Y are two independent a scaled exponentiated inverted Weibull (EIW) distribution. Percentile bootstrap and bias-corrected percentile bootstrap confidence intervals are introduced. To pick the better method of estimation, we used the Monte Carlo simulation study for comparing the efficiency of the various estimators suggested using mean square error and interval length criterion. From cases of samples, we discovered that the results of the maximum product of spacing method are more competitive than those of the other methods. A two real‐life data sets are represented demonstrating how the applicability of the methodologies proposed in real phenomena. [ABSTRACT FROM AUTHOR]

This paper is concerned with estimating the parameters of the modified Kies exponential (MKEx) distribution using the classical estimation method, based on ranked set sampling (RSS), Likelihood estimation method is used for estimating the MKEx parameters. The maximum likelihood estimators (MLEs) are then investigated and compared to the corresponding ones based on simple random sampling (SRS) and RSS designs. A Monte Carlo simulation is used to obtain the absolute relative biases, mean square errors for the MKEx distribution. Efficiencies are compared for the different designs. The relative efficiency of RSS design was found to increase with increasing the number of cycles, compared with other designs for the MKEx distribution. [ABSTRACT FROM AUTHOR]

In reliability engineering and lifetime analysis, many units of the product fail with different causes of failure, and some tests require stress higher than normal stress. Also, we need to design the life experiments which present methodology for formulating scientific and engineering problems using statistical models. So, in this paper, we adopted a partially constant stress accelerated life test model to present times to failure in a small period of time for Gompertz life products. Also, considering that, units are failing with the only two independent causes of failure and tested under type-I generalized hybrid censoring scheme the data built. Obtained data are analyzed with two methods of estimations, maximum likelihood and Bayes methods. These two methods are used to construct the point and interval estimators with the help of the MCMC method. The developed results are measured and compared under Monte Carlo studying. Also, a data set is analyzed for illustration purposes. Finally, some comments are presented to describe the numerical results. [ABSTRACT FROM AUTHOR]