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"Yousef, Manal M."
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Statistical inference for a constant-stress partially accelerated life tests based on progressively hybrid censored samples from inverted Kumaraswamy distribution
In this article, we investigate the problem of point and interval estimations under constant-stress partially accelerated life tests. The lifetime of items under use condition is assumed to follow the two-parameter inverted Kumaraswamy distribution. Based on Type-I progressively hybrid censored samples, the maximum likelihood and Bayesian methods are applied to estimate the model parameters as well as the acceleration factor. Under linear exponential, general entropy and squared error loss functions, Bayesian method outcomes are obtained. In addition, interval estimation is achieved by finding approximately confidence intervals for the parameters, as well as credible intervals. To investigate the accuracy of the obtained estimates and to compare the performance of confidence intervals, a Monte Carlo simulation is developed. Finally, a set of real data is analyzed to demonstrate the estimation procedures.
Journal Article
Parametric inference on partially accelerated life testing for the inverted Kumaraswamy distribution based on Type-II progressive censoring data
This article discusses the problem of estimation with step stress partially accelerated life tests using Type-II progressively censored samples. The lifetime of items under use condition follows the two-parameters inverted Kumaraswamy distribution. The maximum likelihood estimates for the unknown parameters are computed numerically. Using the property of asymptotic distributions for maximum likelihood estimation, we constructed asymptotic interval estimates. The Bayes procedure is used to calculate estimates of the unknown parameters from symmetrical and asymmetric loss functions. The Bayes estimates cannot be obtained explicitly, therefor the Lindley's approximation and the Markov chain Monte Carlo technique are used to obtaining the Bayes estimates. Furthermore, the highest posterior density credible intervals for the unknown parameters are calculated. An example is presented to illustrate the methods of inference. Finally, a numerical example of March precipitation (in inches) in Minneapolis failure times in the real world is provided to illustrate how the approaches will perform in practice.
Journal Article
Utilizing unified progressive hybrid censored data in parametric inference under accelerated life tests
Progressive-stress accelerated life testing (PSALT) is a specialized experimental method that evaluates the longevity of a product under continuously fluctuating stress levels. Due to the constraints of testing equipment and expenses, the lifetime data collected by PSALT are typically censored. This paper introduces the PSALT model that utilizes Type-II unified progressive hybrid censoring to address this data characteristic, specifically when the lifespan of test units follows a truncated Cauchy power exponential (TCPE) distribution. The distribution’s scale parameter follows the inverse power law, and the cumulative exposure model is relevant for the effects of differing stress levels. The estimation methods for the TCPE parameters and the acceleration factor are examined, including maximum likelihood and Bayesian estimation techniques. Bayesian estimates are generated using the Markov chain Monte Carlo technique based on symmetric and asymmetric loss functions. The highest posterior density intervals are assessed, as well as asymptotic confidence intervals. A simulation study is conducted to evaluate the efficacy of the proposed point and interval estimators. Ultimately, a real data set is applied to the TCPE distribution, and the proposed estimators are assessed.
Journal Article
Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling
The current work focuses on ranked set sampling and a simple random sample as sampling approaches for determining stress–strength reliability from the inverted Topp–Leone distribution. Asymptotic confidence intervals are established, along with a maximum likelihood estimator of the parameters and stress–strength reliability. The reliability of such a system is assessed using the Bayesian approach under symmetric and asymmetric loss functions. The highest posterior density credible interval is constructed successively. The results are extracted using Monte Carlo simulation to compare the proposed estimators performance with different sample sizes. Finally, by looking at waiting time data and failure times of insulating fluid, the usefulness of the suggested technique is demonstrated.
Journal Article
Utilizing Empirical Bayes Estimation to Assess Reliability in Inverted Exponentiated Rayleigh Distribution with Progressive Hybrid Censored Medical Data
This study addresses the issue of estimating the shape parameter of the inverted exponentiated Rayleigh distribution, along with the assessment of reliability and failure rate, by utilizing Type-I progressive hybrid censored data. The study explores the estimators based on maximum likelihood, Bayes, and empirical Bayes methodologies. Additionally, the study focuses on the development of Bayes and empirical Bayes estimators with balanced loss functions. A concrete example based on actual data from the field of medicine is used to illustrate the theoretical insights provided in this study. Monte Carlo simulations are employed to conduct numerical comparisons and evaluate the performance and accuracy of the estimation methods.
Journal Article
Bayesian and Non-Bayesian Analysis of Exponentiated Exponential Stress–Strength Model Based on Generalized Progressive Hybrid Censoring Process
In many real-life scenarios, systems frequently perform badly in difficult operating situations. The multiple failures that take place when systems reach their lower, higher, or extreme functioning states typically receive little attention from researchers. This study uses generalized progressive hybrid censoring to discuss the inference of R=P(X
Journal Article
Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation
It is highly common in many real-life settings for systems to fail to perform in their harsh operating environments. When systems reach their lower, upper, or both extreme operating conditions, they frequently fail to perform their intended duties, which receives little attention from researchers. The purpose of this article is to derive inference for multi reliability where stress-strength variables follow unit Kumaraswamy distributions based on the progressive first failure. Therefore, this article deals with the problem of estimating the stress-strength function, R when X,Y, and Z come from three independent Kumaraswamy distributions. The classical methods namely maximum likelihood for point estimation and asymptotic, boot-p and boot-t methods are also discussed for interval estimation and Bayes methods are proposed based on progressive first-failure censored data. Lindly’s approximation form and MCMC technique are used to compute the Bayes estimate of R under symmetric and asymmetric loss functions. We derive standard Bayes estimators of reliability for multi stress–strength Kumaraswamy distribution based on progressive first-failure censored samples by using balanced and unbalanced loss functions. Different confidence intervals are obtained. The performance of the different proposed estimators is evaluated and compared by Monte Carlo simulations and application examples of real data.
Journal Article
Simulation Techniques for Strength Component Partially Accelerated to Analyze Stress–Strength Model
Based on independent progressive type-II censored samples from two-parameter Burr-type XII distributions, various point and interval estimators of δ=P(Y
Journal Article
Bayesian Estimation of Exponentiated Weibull Distribution Under Partially Acceleration Life Tests
This paper presents statistical methods for analyzing partially accelerated life test from constant-stress test. The lifetime of items under use condition follows the two-parameter exponentiated Weibull distribution. Based on progressively Type-II censored sample, the classical maximum likelihood method as well as a fully Bayesian method based on Lindley (Trabajos de Estadistica 31:223–237, 1980) approximation form and the Markov chain Monte Carlo technique are developed for inference about model parameters and acceleration factor. Furthermore, approximate confidence intervals and credible intervals are presented. A Monte Carlo simulation is given to study the precision of different estimators.
Journal Article
Statistical inference for a constant-stress partially accelerated life tests based on progressively hybrid censored samples from inverted Kumaraswamy distribution
In this article, we investigate the problem of point and interval estimations under constant-stress partially accelerated life tests. The lifetime of items under use condition is assumed to follow the two-parameter inverted Kumaraswamy distribution. Based on Type-I progressively hybrid censored samples, the maximum likelihood and Bayesian methods are applied to estimate the model parameters as well as the acceleration factor. Under linear exponential, general entropy and squared error loss functions, Bayesian method outcomes are obtained. In addition, interval estimation is achieved by finding approximately confidence intervals for the parameters, as well as credible intervals. To investigate the accuracy of the obtained estimates and to compare the performance of confidence intervals, a Monte Carlo simulation is developed. Finally, a set of real data is analyzed to demonstrate the estimation procedures.
Journal Article