Binomial Removals Research Articles

Analyzing Burr-X competing risk model using adaptive progressive Type-II censored binomial removal data with application to electrodes and electronics

The aim of this paper is to investigate the Burr-X competing risks model in the context of adaptive progressively Type-II censored samples. In this scenario, the removal pattern is assumed to be a random variable that follows the binomial distribution, which is a more realistic assumption compared to assuming a fixed removal pattern. In this study, we explore both classical and Bayesian estimation approaches to estimate the parameters of the Burr-X competing risks model, as well as the reliability parameter and the parameter of the binomial distribution. The interval ranges of different parameters are determined by utilizing the asymptotic normality of the maximum likelihood estimators. Furthermore, the Bayes credible intervals are calculated by sampling from the joint posterior distribution using the Markov Chain Monte Carlo procedure. To assess the efficiency of the acquired estimators, a comprehensive simulation study that considered various types of experimental designs is conducted. Finally, two applications are considered by analyzing data sets of electrodes and electronics.

Stress–Strength Reliability Analysis for Different Distributions Using Progressive Type-II Censoring with Binomial Removal

In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as δ=PW<V, where V and W are the strength and stress random variables, respectively, and δ is reliability parameter. Type-II progressive censoring with binomial removal is used in this study to examine the inference of δ=PW<V for a component with strength V and being subjected to stress W. We suppose that V and W are independent random variables taken from the Burr XII distribution and the Burr III distribution, respectively, with a common shape parameter. The maximum likelihood estimator of δ is derived. The Bayes estimator of δ under the assumption of independent gamma priors is derived. To determine the Bayes estimates for squared error and linear exponential loss functions in the lack of explicit forms, the Metropolis–Hastings method was provided. Utilizing comprehensive simulations and two metrics (average of estimates and root mean squared errors), we compare these estimators. Further, an analysis is performed on two actual data sets based on breakdown times for insulating fluid between electrodes recorded under varying voltages.

Accelerated life test for Pareto distribution under progressive type-II censored competing risks data with binomial removals and its application in electrode insulation system

In this article, based on progressive type-II censored competing risks data with binomial removals, a constant-stress accelerated life testing is discussed when the lifetime of experiment units follows the Pareto distribution. Under the assumption that the failure time of each cause is statistically independent, the estimation of unknown parameters is obtained by maximum likelihood estimation and Bayesian estimators under symmetric and asymmetric loss functions. The corresponding confidence and credible intervals are constructed with approximation theory, bootstrap method, and MCMC technique respectively. Additionally, the log-linear model is established for the life test and two goodness-of-fit test statistics are constructed. Finally, a simulation study is carried out for the power analysis of different censoring ratio schemes and the numerical results verify the feasibility of the constructed test statistics for the censored data with competing risks.

Reliability analysis of two Gompertz populations under joint progressive type-ii censoring scheme based on binomial removal

ABSTRACT Analysis of jointly censoring schemes has received considerable attention in the last few years. In this paper, maximum likelihood and Bayes methods of estimation are used to estimate the unknown parameters of two Gompertz populations under a joint progressive Type-II censoring scheme. Bayesian estimations of the unknown parameters are obtained based on squared error loss functions under the assumption of independent gamma priors. We propose to apply the Markov Chain Monte Carlo technique to carry out a Bayes estimation procedure. The approximate, bootstrap, and credible confidence intervals for the unknown parameters are also obtained. Also, reliability and hazard rate function of the two Gompertz populations under joint progressive Type-II censoring scheme is obtained and the corresponding approximate confidence intervals. Finally, all the theoretical results obtained are assessed and compared using two real-world data sets and Monte Carlo simulation studies.

E-Bayesian inference for xgamma distribution under progressive type II censoring with binomial removals and their applications

ABSTRACT In this article, we propose E-Bayes estimators of the parameter of xgamma distribution under squared error loss function, general entropy loss function, and linear exponential loss function for progressive type II censored data with binomial removals. The proposed estimators, maximum likelihood estimator, and corresponding Bayes estimators are compared in terms of their risks based on simulated samples from xgamma distribution. The proposed methodology is illustrated on two real data sets of bile duct cancer data and the endurance of deep-groove ball bearings data.

On Statistical Inference of Generalized Pareto Distribution with Jointly Progressive Censored Samples with Binomial Removal

A jointly censored sample is a very useful sampling technique in conducting comparative life tests of the products, its efficiency appears in permitting the selection of two samples from two manufacturing lines at the same time and conducting a life‐testing experiment. This article presents estimation information of the joint generalized Pareto distributions parameters using Type‐II progressive censoring scheme, which is carried out with binomial removal. The generalized Pareto distribution has many applications in different fields. We outline the problem of parameter estimation using the frequentest maximum likelihood and the Bayesian estimation methods. Furthermore, different interval estimation methods for estimating the four parameters were used: the asymptotic property of the maximum likelihood estimator, the credible confidence intervals, and the Bootstrap confidence intervals. The detailed numerical simulations have been considered to compare the performance of the proposed estimates. In addition, the applicability of the joint generalized Pareto censored model has been performed by applying a real data example.

Analysis of adaptive type-II progressively hybrid censoring with binomial removals

Adaptive Type-II progressive hybrid censoring scheme has quite popular in a life-testing problem and reliability analysis due to it ensures more efficiency of inference procedures and saves total testing time. In this paper, an adaptive Type-II progressive hybrid censored sampling with random removals is considered, where the removals of the survival units at each stage from a life-test follows a binomial distribution during the execution of the experiment. The classical and Bayesian approaches are used to obtain the point and interval estimates of the unknown parameters of Weibull distribution, when the lifetimes are collected under the proposed censoring scheme. Different Bayesian estimates relative to various balanced type loss functions are obtained. Due to the complexity of the proposed estimators, some numerical techniques are implemented to obtain them. Using Markov chain Monte Carlo methods, the different Bayes estimates and associate credible intervals are developed. Extensive simulation study is performed to examine the efficiency of the proposed estimators. To show the applicability of the proposed methods in a real-life scenario, two real data sets coming from clinical and engineering areas are analysed.

Classical and Bayesian Estimation in Exponential Power Distribution under Type-I Progressive Hybrid Censoring with Binomial Removals

This article deals with the classical and Bayesian estimation in exponential power distribution based on Type-I progressive hybrid censoring with binomial removals at each stage. Based on the considered censoring scheme, the maximum likelihood estimates and their coverage probabilities are computed by the Monte Carlo simulation technique. MCMC technique is used to obtain the Bayes estimates under the informative priors. The performance of both the approaches is evaluated in terms of their absolute bias and mean square error (MSE) as well as the width of the confidence interval. Applicability of the suggested approach is illustrated by analysis of a real-life dataset.

Single and Multiple Ramp Progressive Stress with Binomial Removal: Practical Application for Industry

The objective of this article is to conduct a full study on the failure times of items when subjected to a progressive-stress accelerated life test. These failure times follow the Modified Kies exponential distribution. We performed the experiments under a type-II censoring scheme with binomial removal. The stress design has two ways to be applied either the simple ramp-stress test or the multiple ramp-stress level design of acceleration. We made a comparison between these two designs to decide which design is better. When the lifetime of test units follows the Modified Kies distributions, the cumulative exposure model has been used to apply the acceleration on the failure times to produce early failures. The simulation study was done to compare two types of progressive-stress designs. Different estimation techniques such as maximum likelihood estimation and Bayes estimation are employed to estimate the model parameters. The Metropolis Hasting method is used to derive the Bayesian estimates under symmetric and asymmetric loss functions. We also developed interval estimation as well as point estimation, and we estimated the asymptotic confidence intervals, bootstrap, and credible for the distribution parameters. We made a comparison between different estimation methods. We used real data from a practical experiment as a real data set example to assess the performance of the estimations methods. These data are analyzed to demonstrate the adequacy and superiority of the distribution to fit accelerated failure times. Also, we studied the existence and uniqueness of the roots and we used graphs to assure that the estimates used are unique and global maximum. Finally, some noteworthy conclusions are reached.

Bayesian inference for Maxwell Boltzmann distribution on step-stress partially accelerated life test under progressive type-II censoring with binomial removals

Bayesian inference for Maxwell Boltzmann distribution on step-stress partially accelerated life test under progressive type-II censoring with binomial removals

Accelerated life tests for modified Kies exponential lifetime distribution: binomial removal, transformers turn insulation application and numerical results

<abstract> This paper is concerned with statistical inference of multiple constant-stress testing for progressive type-II censored data with binomial removal. The failure times of the test units are assumed to be independent and follow the modified Kies exponential (MKEx) distribution. The maximum likelihood method as well as Bayes method are used to derive both point and interval estimates of the parameters. Furthermore, a real data application for transformers turn insulation is used to illustrate the proposed methods. Moreover, this real data set is used to show that MKEx distribution can be a possible alternative model to the exponential, generalized exponential and Weibull distributions. Finally, simulation studies are carried out to investigate the accuracy of the different estimation methods. </abstract>

Inference on a new distribution under progressive-stress accelerated life tests and progressive type-II censoring based on a series-parallel system

&lt;abstract&gt;&lt;p&gt;It is of great importance for physicists and engineers to assess a lifetime distribution of a series-parallel system when its components' lifetimes are subject to a finite mixture of distributions. The present article addresses this problem by introducing a new distribution called "Poisson-geometric-Lomax distribution". Important properties of the proposed distribution are discussed. When the stress is an increasing nonlinear function of time, the progressive-stress model is considered and the inverse power-law model has suggested a relationship between the stress and the scale parameter of the proposed distribution. Based on the progressive type-II censoring with binomial removals, estimation of the included parameters is discussed using maximum likelihood and Bayes methods. An example, based on two real data sets, demonstrates the superiority of the proposed distribution over some other known distributions. To compare the performance of the implemented estimation methods, a simulation study is carried out. Finally, some concluding remarks followed by certain features and motivations to the proposed distribution are presented.&lt;/p&gt;&lt;/abstract&gt;

Bayesian inference: Weibull Poisson model for censored data using the expectation–maximization algorithm and its application to bladder cancer data

This article focuses on the parameter estimation of experimental items/units from Weibull Poisson Model under progressive type-II censoring with binomial removals (PT-II CBRs). The expectation–maximization algorithm has been used for maximum likelihood estimators (MLEs). The MLEs and Bayes estimators have been obtained under symmetric and asymmetric loss functions. Performance of competitive estimators have been studied through their simulated risks. One sample Bayes prediction and expected experiment time have also been studied. Furthermore, through real bladder cancer data set, suitability of considered model and proposed methodology have been illustrated.

Assessing the effect of E-Bayesian inference for Poisson inverse exponential distribution parameters under different loss functions and its application

This paper present E-Bayesian and Bayesian estimators of parameters of Poisson inverse exponential distribution (PIED) under Squared error loss function (SELF), General entropy loss function (GELF) and Linear Exponential loss function (LINEX) for progressive type-II censored data with binomial removals (PT-II CBRs). The E-Bayesian and corresponding Bayesian estimators are compared in terms of their risks based on simulated samples from PIED. The proposed methodology is applied to survival time of multiple myeloma patients data.

Statistical inference of Burr-XII distribution under progressive Type-II censored competing risks data with binomial removals

In this paper, we consider the analysis of Burr XII distribution based on the competing risks model under progressive Type-II censoring, where the amount of units withdrawn at each stage is assumed to be random and subject to a binomial distribution. The maximum likelihood estimations of unknown parameters are derived and their existence and uniqueness are proved as well. Furthermore, approximate confidence intervals are also constructed by using the observed Fisher information matrix and delta method. Moreover, Bayes estimators and associated credible intervals under different loss functions are obtained based on MCMC method. In addition, simulation study used to evaluate the performance of all estimators proposed is included. Finally, a practical data example is given to illustrate all the inferential processes developed here.

Statistical inference for Kumaraswamy-exponential distribution based on progressive Type-II censored data with binomial removals

In this paper, estimation of parameters of Kumaraswamy-exponential distribution with shape parameters α and β is considered based on a progressively type-II censored sample with binomial removals. Together with the unknown parameters, the removal probability p is also estimated. Bayes estimators are obtained using different loss functions such as squared error, LINEX loss function and entropy loss function. All Bayesian estimates are compared with the corresponding maximum likelihood estimates numerically in terms of their bias and mean square error values and found that Bayes estimators perform better than MLE’s for β and p and MLEs perform better than Bayes estimators for α. A real data set is also used for illustration.

Bayesian Estimation of Inverted Exponentiated Weibull Distribution under Progressive Type II Censoring with Binomial Removal

Bayesian Estimation of Inverted Exponentiated Weibull Distribution under Progressive Type II Censoring with Binomial Removal

Optimal Design of Step Stress Partially Accelerated Life Test under Progressive Type-II Censored Data with Random Removal for Inverse Lomax Distribution

Step Stress-Partially Accelerated Life Test SS-PALT under Type-II progressive censoring with Binomial or uniform removal assuming Inverse Lomax distribution has been presented. A comparison between both removals is shown. The Newton-Raphson method is applied to obtain maximum likelihood estimators MLE of the parameters and the optimal stress-change time which minimizes the generalized asymptotic variance. A simulation study is performed to illustrate the statistical properties of the parameters.

Parameter Estimation of Lindley Distribution Based on Progressive Type-II Censored Competing Risks Data with Binomial Removals

The competing risk model based on Lindley distribution is discussed under the progressive type-II censored sample data with binomial removals. The maximum likelihood estimation of the unknown parameters of the distribution is established. Using the Lindley approximation method, we also obtain the Bayesian estimation of the unknown parameters of the distribution under different loss functions. The performance of different estimates is studied in this article. A real practical dataset is analyzed for illustration.

Empirical Bayes estimator of parameter, reliability and hazard rate for Kumaraswamy distribution

This paper proposes empirical Bayes estimators of parameter, reliability and hazard function for Kumaraswamy distribution under the linear exponential loss function for progressively type II censored samples with binomial removal and type II censored samples. The proposed estimators have been compared with the corresponding Bayes estimators for their simulated risks. The applicability of the proposed estimators have been illustrated through ulcer patient data.