Progressive Hybrid Censoring Research Articles

An Analysis of Type-I Generalized Progressive Hybrid Censoring for the One Parameter Logistic-Geometry Lifetime Distribution with Applications

Based on Type-I generalized progressive hybrid censored samples (GPHCSs), the parameter estimate for the unit-half logistic-geometry (UHLG) distribution is investigated in this work. Using maximum likelihood estimation (MLE) and Bayesian estimation, the parameters, reliability, and hazard functions of the UHLG distribution under GPHCSs have been assessed. Likewise, the computation is carried out for the asymptotic confidence intervals (ACIs). Furthermore, two bootstrap CIs, bootstrap-p and bootstrap-t, are mentioned. For symmetric loss functions, like squared error loss (SEL), and asymmetric loss functions, such as linear exponential loss (LL) and general entropy loss (GEL), there are specific Bayesian approximations. The Metropolis–Hastings samplers methodology were used to construct the credible intervals (CRIs). In conclusion, a genuine data set measuring the mortality statistics of a group of male mice with reticulum cell sarcoma is regarded as an application of the methods given.

Inference for depending competing risks from Marshall–Olikin bivariate Kies distribution under generalized progressive hybrid censoring

This paper explores inferences for a competing risk model with dependent causes of failure. When the lifetimes of competing risks are modelled by a Marshall–Olikin bivariate Kies distribution, classical and Bayesian estimations are studied under generalized progressive hybrid censoring. The existence and uniqueness results for maximum likelihood estimators of unknown parameters are established, whereas approximate confidence intervals are constructed using the observed Fisher information matrix. In addition, Bayes estimates are explored based on a flexible Gamma-Dirichlet prior information. Furthermore, when there is a priori order information on competing risk parameters being available, traditional classical likelihood and Bayesian estimates are also established under restricted parameter case. The behavior of the proposed estimators is evaluated through extensive simulation studies, and a real data study is presented for illustrative purposes.

Overlap Analysis in Progressive Hybrid Censoring: A Focus on Adaptive Type-II and Lomax Distribution

This article explores the adaptive type-II progressive hybrid censoring scheme, introduced by Ng et al. (2009), which is used to make inferences about three measures of overlap: Matusita's measure ($\rho $), Morisita's measure ($\lambda $), and Weitzman's measure ($\Delta $) for two Lomax distributions with different parameters. The article derives the bias and variance of these overlap measures' estimators. If sample sizes are limited, the precision or bias of these estimators is difficult to determine because there are no closed-form expressions for their variances and exact sampling distributions, so Monte Carlo simulations are used. Also, confidence intervals for these measures are constructed using both the bootstrap method and Taylor approximation. To demonstrate the practical significance of the proposed estimators, an illustrative application is provided by analyzing real data.

Fuzzy multicomponent stress-strength reliability in presence of partially accelerated life testing under generalized progressive hybrid censoring scheme subject to inverse Weibull model

It typically takes a lot of time to monitor life-testing experiments on a product or material. Units can be tested under harsher conditions than usual, known as accelerated life tests to shorten the testing period. This study's goal is to investigate the issue of partially accelerated life testing that use generalized progressive hybrid censored samples to estimate the stress-strength reliability in the multicomponent case. Also, the fuzziness of the model is considered that gives more sensitive and accurate analyses about the underlying system. Maximum likelihood estimation method under the inverse Weibull distribution and using the generalized progressively hybrid censoring scheme is introduced to obtain an estimator for the fuzzy multicomponent stress-strength reliability. Also, an asymptotic confidence interval is deduced to examine the reliability of the fuzzy multicomponent stress-strength. Simulation study is conducted using maximum likelihood estimates and confidence intervals for the fuzzy multicomponent stress-strength reliability for different values of the parameters and different schemes. A real data application representing the data for the failure times for a certain software model is introduced to obtain the fuzzy multicomponent stress-strength reliability for different schemes.•The fuzzy multicomponent stress-strength reliability is investigated under partially accelerated life testing and the generalized progressively hybrid censored scheme.•An algorithm is introduced to simulate data for the censoring scheme.•A real data application is presented to obtain the fuzzy multicomponent stress-strength reliability at different schemes.

Inference for a competing risks model with Burr XII distributions under generalized progressive hybrid censoring

Inference for a competing risks model with Burr XII distributions under generalized progressive hybrid censoring

Bayesian Analysis of Generalized Inverted Exponential Distribution Based on Generalized Progressive Hybrid Censoring Competing Risks Data

Bayesian Analysis of Generalized Inverted Exponential Distribution Based on Generalized Progressive Hybrid Censoring Competing Risks Data

A New Xgamma–Weibull Model Using Type-II Adaptive Progressive Hybrid Censoring and Its Applications in Engineering and Medicine

This paper is an attempt to study the Xgamma–Weibull distribution using an adaptive progressive type-II censoring plan. This scheme effectively ensures that the experimental time does not exceed a predetermined time limit. Using two classical estimation methods—namely, maximum likelihood and maximum product of spacing—both point and interval estimations for the unknown model parameters, as well as some parameters of life—namely, reliability and hazard rate functions—were obtained. The asymptotic normality of both classical methods was used to determine the approximate confidence intervals for the various parameters. Based on the two conventional methodologies, Bayesian estimations were also investigated using the MCMC technique under the squared error loss function. In addition, the credible intervals of the different parameters were also obtained. To compare the performance of the various approaches, a thorough simulation study was carried out. Furthermore, we propose using several optimality criteria to select the best sampling technique. Finally, two real-world datasets were used to demonstrate how the suggested estimators and optimality criteria operate in real-world circumstances.

Analysis of Muth parameters using generalized progressive hybrid censoring with application to sodium sulfur battery

This study takes into account the estimation concerns of the model parameter, reliability, and hazard rate functions of the Muth distribution when a sample is produced using generalized progressive hybrid censoring. The generalized progressive hybrid censoring scheme is suggested to get around the progressive hybrid censoring scheme's potential drawback of having extremely few failures. The maximum likelihood estimates of the model parameter and some life indices are obtained. The approximate confidence intervals for various parameters are calculated using the asymptotic distribution of the maximum likelihood estimates across the observed Fisher information matrix. Furthermore, the beta prior and squared error loss function are used to offer Bayes point estimates and the highest posterior density credible intervals of the unknown parameters, and the Markov Chain Monte Carlo technique is used to acquire the necessary estimates. We provide thorough simulation results to demonstrate the utility of the suggested methodologies. Finally, one genuine data set is analyzed as an example.

Estimation and prediction of modified progressive hybrid censored data from inverted exponentiated Rayleigh distribution

ABSTRACT In this paper, statistical inference of an inverted exponentiated Rayleigh model is studied when the failure times are obtained under a modified progressive hybrid censoring. The maximum likelihood estimators of the model parameters together with associated existence and uniqueness are established, and approximate confidence intervals are constructed based on asymptotic theory. Alternatively, generalized point and interval estimates for unknown parameters are also constructed based on the proposed pivotal quantities for comparison. In addition, predictive intervals of remaining useful life from the inverted exponentiated Rayleigh distribution are also constructed under classical and generalized inferential approaches, respectively. Finally, extensive simulation studies are carried out to compare the performance of the proposed methods, and two real-life examples are analyzed for illustration. The numerical results indicate that both traditional likelihood and generalized inferential methods work satisfactorily, and that our proposed generalized approach appears much more appealing and are superior to classical results.

On partially observed competing risks model for Chen distribution under generalized progressive hybrid censoring

In this paper, we discuss the inference for the competing risks model when the failure times follow Chen distribution. With assumption of two causes of failures, which are partially observed, are considered as independent. The existence and uniqueness of maximum likelihood estimates for model parameters are obtained under generalized progressive hybrid censoring. Also, we discussed the classical and Bayesian inferences of the model parameters under the assumption of restricted and nonrestricted parameters. Performance of classical point and interval estimators are compared with Bayesian point and interval estimators by conducting extensive simulation study. In addition to that, for illustration purpose, a real life example is discussed. Finally, some concluding remarks, regarding the presented model, are made.

Parameters and Reliability Estimation of Alpha Power Exponential Distribution under Type-II Progressive Hybrid Censoring with Applications of Engineering and Management Fields

Parameters and Reliability Estimation of Alpha Power Exponential Distribution under Type-II Progressive Hybrid Censoring with Applications of Engineering and Management Fields

Analysis of Two Generalized Exponential Populations Under Joint Type-I Progressive Hybrid Censoring Scheme

Analysis of Two Generalized Exponential Populations Under Joint Type-I Progressive Hybrid Censoring Scheme

Computational Analysis for Fréchet Parameters of Life from Generalized Type-II Progressive Hybrid Censored Data with Applications in Physics and Engineering

Generalized progressive hybrid censored procedures are created to reduce test time and expenses. This paper investigates the issue of estimating the model parameters, reliability, and hazard rate functions of the Fréchet (Fr) distribution under generalized Type-II progressive hybrid censoring by making use of the Bayesian estimation and maximum likelihood methods. The appropriate estimated confidence intervals of unknown quantities are likewise built using the frequentist estimators’ normal approximations. The Bayesian estimators are created using independent gamma conjugate priors under the symmetrical squared-error loss. The Bayesian estimators and the associated greatest posterior density intervals cannot be computed analytically since the joint likelihood function is obtained in complex form, but they may be assessed using Monte Carlo Markov chain (MCMC) techniques. Via extensive Monte Carlo simulations, the actual behavior of the proposed estimation methodologies is evaluated. Four optimality criteria are used to choose the best censoring scheme out of all the options. To demonstrate how the suggested approaches may be utilized in real scenarios, two real applications reflecting the thirty successive values of precipitation in Minneapolis–Saint Paul for the month of March as well as the number of vehicle fatalities for thirty-nine counties in South Carolina during 2012 are examined.

Estimating the Parameters of an Exponentiated Logistic Distribution under Progressive Hybrid Censoring Scheme

As the progressive hybrid censoring scheme (PHCS) and exponentiated logistic distribution (ELD) are widely employed in reliability and survival analysis, it is necessary to infer on ELD parameters under PHCS. The maximum product spacings estimator (MPSE) is effective and authors advocated the use of this method as an alternative to maximum likelihood estimator (MLE), and found that MPSE provides better estimates than MLE in various situations. In this paper, we propose the MPSEs for the parameters of the ELD under PHCS. Also, we derive the approximate MPSEs for the parameters of ELD using Talyor series expansion. And we compare the proposed estimators (MPSEs and approximate MPSEs) in the sense of mean squared error (MSE) under PHCS. The progressive hybrid censored data (PHCD) from the ELD are generated for data size = 25, 30, 35, 40, 45 and various PHCS. Using this generated data, the MSEs and biases of MPSE and approximate MPSE are simulated by the Monte Carlo method based on 1,000 times for = 25, 30, 35, 40, 45 and various PHCD. As a result, approximate MPSEs are better than the corresponding MPSEs. Further, a real data set (strength on GPA for single carbon fibers of 10mm in gauge lengths) has been analyzed.

Bayes and Maximum Likelihood Estimation of Uncertainty Measure of the Inverse Weibull Distribution under Generalized Adaptive Progressive Hybrid Censoring

The inverse Weibull distribution (IWD) can be applied to a various situations, including applications in reliability and medicine. In a reliability and medicine test, it is generally known that the results of test units may not be recorded. Recently, the generalized adaptive progressive hybrid censoring (GAPHC) scheme was introduced. In this paper, therefore, we consider the classical estimators (maximum likelihood estimator (MLE) and maximum product spacings estimator (MPSE)) and Bayes estimators (BayEsts) of the uncertainty measure of the IWD under GAPHC scheme. We derive the BayEsts of the uncertainty measure based on flexible (symmetrical and asymmetrical) priors. Additionally, we derive the Bayes estimators using the Tierney and Kadane approximation (TiKa) and importance sampling methods. In particular, the importance sampling method is used to obtain the credible interval for the uncertainty measure of the IWD under the GAPHC scheme. To compare the proposed estimators (classical and BayEsts), the Monte Carlo simulation method is conducted. Finally, the real dataset based on GAPHC scheme is analyzed.

Estimation of the stress-strength reliability for the inverse Weibull distribution under adaptive type-II progressive hybrid censoring.

In this article, we compare the maximum likelihood estimate (MLE) and the maximum product of spacing estimate (MPSE) of a stress-strength reliability model, θ = P(Y < X), under adaptive progressive type-II progressive hybrid censoring, when X and Y are independent random variables taken from the inverse Weibull distribution (IWD) with the same shape parameter and different scale parameters. The performance of both estimators is compared, through a comprehensive computer simulation based on two criteria, namely bias and mean squared error (MSE). To demonstrate the effectiveness of our proposed methods, we used two examples of real-life data based on Breakdown Times of an Insulated Fluid by (Nelson, 2003) and Head and Neck Cancer Data by (Efron, 1988). It is concluded that the MPSE method outperformed the MLE method in terms of bias and MSE values.

Reliability Inferences of the Inverted NH Parameters via Generalized Type-II Progressive Hybrid Censoring with Applications

Generalized progressive hybrid censored mechanisms have been proposed to reduce the test duration and to save the cost spent on testing. This paper considers the problem of estimating the unknown model parameters and the reliability time functions of the new inverted Nadarajah–Haghighi (NH) distribution under generalized Type-II progressive hybrid censoring using the maximum likelihood and Bayesian estimation approaches. Utilizing the normal approximation of the frequentist estimators, the corresponding approximate confidence intervals of unknown quantities are also constructed. Using independent gamma conjugate priors under the symmetrical squared error loss, the Bayesian estimators are developed. Since the joint likelihood function is obtained in complex form, the Bayesian estimators and their associated highest posterior density intervals cannot be obtained analytically but can be evaluated via Monte Carlo Markov chain techniques. To select the optimum censoring scheme among different censoring plans, five optimality criteria are used. Finally, to explain how the proposed methodologies can be applied in real situations, two applications representing the failure times of electronic devices and deaths from the coronavirus disease 2019 epidemic in the United States of America are analyzed.

Statistical inference for Gompertz distribution under adaptive type-II progressive hybrid censoring

Gompertz distribution is a significant and commonly used lifetime distribution, which plays an important role in reliability engineering. In this paper, we study the statistical inference of Gompertz distribution based on adaptive Type-II hybrid progressive censored schemes. From the perspective of frequentist, we derive the point estimations through the method of maximum likelihood estimation (MLE) and the existence of MLE is proved. Besides MLE, we propose the stochastic EM algorithm to reduce complexity and simplify computing. We also apply the method of Bootstraps (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are evaluated by applying the MCMC method, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error loss function and LINEX loss function. Furthermore, a numerical simulation is conducted to assess the performance of the proposed methods. Finally, a real-life example is considered to illustrate the application and development of the inference methods. In summary, the Bayesian method seems to perform the best among all approaches, while other approaches also present different advantages.

Estimation for Kies distribution with generalized progressive hybrid censoring under partially observed competing risks model

In this paper, estimation of a competing risks model is discussed with partially observed modes of failure. When latent lifetimes of competing risks follow the Kies distribution under a generalized progressive hybrid censoring, estimation of the unknown parameters is explored under non-order and order restrictions via classical and Bayesian approaches, respectively. The uniqueness and existence of maximum likelihood estimators of parameters are established, and subsequently interval estimators are also derived. Bayesian estimates as well as highest posterior density credible intervals are developed for the model parameters. In addition, when extra order information for the competing risks parameters is available, classical and Bayesian estimates are also established. Extensive simulation studies are conducted to investigate the performance of different methods, and a numerical example is also presented for illustrative purposes.

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.