Progressive Type-II Censoring Research Articles

Inference for the Two Parameter Reduced Kies Distribution under Progressive Type-II Censoring

In this paper, we obtained several recurrence relations for the single and product moments under progressively Type-II right censored order statistics and then use these results to compute the means and variances of two parameter reduced Kies distribution. Besides, these moments are then utilized to derived best linear unbiased estimators of the scale and location parameters of two parameter reduced Kies distribution. The parameters of the two parameter reduced Kies distribution are estimated under progressive type-II censoring scheme. The model parameters are estimated using the maximum likelihood estimation method. Further, we explore the asymptotic confidence intervals for the model parameters. Monte Carlo simulations are performed to compare between the proposed estimation methods under progressive type-II censoring scheme. Based on our study, we can conclude that maximum likelihood estimators is decreasing with respect to an increase of the schemes and comparing the three censoring schemes, it is clear that the mean sum of squares, confidence interval lengths are smaller for scheme 1 than schemes 2 and 3.

Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.

Inference of Process Capability Index Cpy for 3-Burr-XII Distribution Based on Progressive Type-II Censoring

In this paper, we discussed the estimation of the index Cpy for a 3-Burr-XII distribution based on Progressive Type-II censoring. The maximum likelihood and Bayes method have been used to obtain the estimating of the index Cpy. The Fisher information matrix has been used to construct approximate confidence intervals. Also, bootstrap confidence intervals (CIs) of the estimators have been obtained. The Bayesian estimates for the index Cpy have been obtained by the Markov Chain Monte Carlo method. Also, the credible intervals are constructed by using MCMC samples. Two real-datasets have been discussed using the proposed index.

New Approach for a Weibull Distribution under the Progressive Type-II Censoring Scheme

This paper proposes a new approach based on the regression framework employing a pivotal quantity to estimate unknown parameters of a Weibull distribution under the progressive Type-II censoring scheme, which provides a closed form solution for the shape parameter, unlike its maximum likelihood estimator counterpart. To resolve serious rounding errors for the exact mean and variance of the pivotal quantity, two different types of Taylor series expansion are applied, and the resulting performance is enhanced in terms of the mean square error and bias obtained through the Monte Carlo simulation. Finally, an actual application example, including a simple goodness-of-fit analysis of the actual test data based on the pivotal quantity, proves the feasibility and applicability of the proposed approach.

Progressive Type-II Censoring Schemes of Extended Odd Weibull Exponential Distribution with Applications in Medicine and Engineering

In this paper, the parameters of the extended odd Weibull exponential distribution are estimated under progressive type-II censoring scheme with random removal. The model parameters are estimated using the maximum product spacing and maximum likelihood estimation methods. Further, we explore the asymptotic confidence intervals and bootstrap confidence intervals for the model parameters. Monte Carlo simulations are performed to compare between the proposed estimation methods under progressive type-II censoring scheme. An empirical study using two real datasets form engineering and medicine fields to validate the introduced methods of inference. Based on our study, we can conclude that the maximum product of spacing method outperforms the maximum likelihood method for estimating the extended odd Weibull exponential (EOWE) parameters under a progressive type-II censoring scheme in both numerical and empirical cases.

Statistical inference based on progressively type-II censored data from the Burr X distribution under progressive-stress accelerated life test

ABSTRACT In this article, estimation problems for the Burr X distribution under a progressive-stress accelerated life test with progressive type-II censoring are studied. The stress is assumed to be a linearly increasing function of time. The inverse power law and the cumulative exposure model are considered. The classical and Bayesian estimations for the model parameters are obtained by using maximum likelihood method and Markov chain Monte Carlo technique,respectively. The asymptotic confidence intervals are constructed and highest posterior density intervals are also established. A simulation study is conducted to investigate the performance of the proposed point and interval estimations. Finally, a real data set is analysed for illustration.

Different Approaches to Estimation of the Gompertz Distribution under the Progressive Type-II Censoring Scheme

This paper provides an estimation method for an unknown parameter by extending weighted least-squared and pivot-based methods to the Gompertz distribution with the shape and scale parameters under the progressive Type-II censoring scheme, which induces a consistent estimator and an unbiased estimator of the scale parameter. In addition, a way to deal with a nuisance parameter is provided in the pivot-based approach. For evaluation and comparison, the Monte Carlo simulations are conducted, and real data are analyzed.

Inference of progressively type-II censored competing risks data from Chen distribution with an application

In this paper, the estimation of unknown parameters of Chen distribution is considered under progressive Type-II censoring in the presence of competing failure causes. It is assumed that the latent causes of failures have independent Chen distributions with the common shape parameter, but different scale parameters. From a frequentist perspective, the maximum likelihood estimate of parameters via expectation–maximization (EM) algorithm is obtained. Also, the expected Fisher information matrix based on the missing information principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. We also apply the bootstrap methods (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are computed by applying the Markov chain Monte Carlo (MCMC) procedure, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error, LINEX, and general entropy loss functions. The performance of point estimators and confidence intervals is evaluated by a simulation study. Finally, a real-life example is considered for illustrative purposes.

Stage life testing with random stage changing times

In progressive Type-II censoring, it is often claimed that the withdrawn items are further tested under different conditions but a model incorporating this information has not been discussed so far. Introducing the model of Type-II stage life testing, we propose an approach to include information from progressively censored units subject to additional life testing by assuming a cumulative exposure model. Postulating exponentially distributed lifetimes, we establish the exact (conditional) distribution of the maximum likelihood estimators which is applied to construct (exact) confidence intervals for the distribution parameters. Further, we investigate the model with Weibull distributed lifetimes as well as the problem of missing information about the stage of failure. The study is supplemented by illustrative simulations.

Bayesian Inference on Progressive-Stress Accelerated Life Testing for the Exponentiated Weibull Distribution under Progressive Type-II Censoring

Bayesian Inference on Progressive-Stress Accelerated Life Testing for the Exponentiated Weibull Distribution under Progressive Type-II Censoring

Estimation of Reliability in a Multicomponent Stress–Strength Model for a General Class of Inverted Exponentiated Distributions Under Progressive Censoring

We consider estimation of the multicomponent stress–strength reliability for a general class of inverted exponentiated distributions under progressive type-II censoring. We assume that both stress and strength variables follow this general class of distributions with a common parameter. Different point and interval estimates for the reliability of this system are obtained by using maximum likelihood and Bayesian approaches when the common parameter is known and unknown. The uniformly minimum variance unbiased estimate and exact Bayes estimate under the squared error loss function are derived when the common parameter is known. Bayes estimates are also obtained by using Lindley, Tierney–Kadane and Markov chain Monte Carlo methods. The asymptotic confidence and highest posterior density credible intervals are constructed. Proposed methods are compared numerically using Monte Carlo simulations. Finally, a progressively censored real data set is analyzed for illustration purposes.

Estimation of the Parameters for the Exponentiated Weibull Distribution Based on Progressive Type-II Censoring Scheme

The main objective of the present study is to find the estimation of the two Exponentiated Weibull distribution parameters, based on progressive Type II censored samples. The maximum likelihood and Bayes estimators for the two shape parameters and the scale parameter of the exponentiated Weibull lifetime model were derived. Bayes estimators was obtained by using both the symmetric and asymmetric loss functions via squared error loss and linex loss functions This was done with respect to the conjugate priors for two shape parameters. We used an approximation based on the Lindley (Trabajos de Estadistca) method for obtaining Bayes estimates under these loss functions. The different proposed estimators have been compared through an extensive simulation studies. Bayes ratings also turned out to be better than MLE. Whatever the sample sizes are, we get the same results.

Bayesian Inference for Logarithmic Transformed Exponential Distribution in Presence of Adaptive Progressive Type-II Censoring

In this paper, estimations problem (point and interval) are studied for the logarithmic transformed exponential (LTE) distribution based on an adaptive progressive Type-II (APTII ) censoring scheme. In point estimation; the maximum likelihood estimate (MLE) and Bayesian estimates (BE) based on squared error and Linex loss functions are obtained. The Markov Chain Monte Carlo (MCMC) technique is used to compute Bayes estimates by using gamma prior for the unknown parameter under two different loss functions. Metropolis-Hasting (M-H) algorithm has been applied to generate MCMC samples from the posterior density. In case of interval estimation; asymptotic confidence interval (CI) and two different bootstrap CI’s namely; Boot-p and Boot-t are obtained. Also, we have computed posterior credible interval for the unknown parameter. The performance of these estimates are studied on the basis of their risks. Finally, a real dataset has been taken for different censoring schemes and times under APTII censoring.

Development of Preliminary Test Estimators and Preliminary Test Confidence Intervals for Measures of Reliability of Kumaraswamy-G Distributions Based on Progressive Type-II Censoring

Classical estimators and preliminary test estimators (PTEs) of the powers of model parameter and the two measures of reliability, namely $$R\left( t \right) = P(X > t)$$ and $$P = P(X > Y)$$ of Kumaraswamy-G distribution, are developed under progressive type-II censoring. The preliminary test confidence intervals (PTCIs) are also developed based on uniformly minimum variance unbiased estimators (UMVUEs) and maximum likelihood estimators (MLEs). Merits of PTEs and PTCIs are established. Simulation results are presented, and real-life data set is also analysed.

Step Stress Partially Accelerated Life Tests and Estimating Costs of Maintenance Service Policy for the Power Function Distribution under Progressive Type-II Censoring

Step Stress Partially Accelerated Life Tests and Estimating Costs of Maintenance Service Policy for the Power Function Distribution under Progressive Type-II Censoring

Estimation of Generalized Inverted Exponential Distribution based on Adaptive Type-II Progressive Censoring Data

Estimation of Generalized Inverted Exponential Distribution based on Adaptive Type-II Progressive Censoring Data

Reliability Estimation for Hybrid System under Constant-stress Partially Accelerated Life Test with Progressively Hybrid Censoring

Background: Reliability analysis for the systems with masked data had been studied by many scholars. However, most researches focused on a system that is either series or parallel only, and the component in the system is mainly exponential or Weibull. In engineering practice, it is often seen that the structure of a system is a combination of series and parallel system, and other types of components are also used in the system. So it is important to study the reliability analysis of hybrid systems with modified Weibull components. Objective: For the hybrid system with masked data, the constant stress partial accelerated life test is performed under type-II progressive hybrid censoring. These data from life test are used to estimate unknown parameters and reliability index of system. The research results will not only provide theoretical basis and reference for system reliability assessment but also favor the patents on partial accelerated life test. Methods: Maximum likelihood estimates of unknown parameters are investigated with the numerical method. The approximate confidence intervals, and bootstrap confidence intervals for parameters are constructed by the asymptotic theory and the bootstrap method, respectively. Results: Maximum likelihood estimations of unknown parameters and reliability index of system are derived. The approximate confidence intervals and bootstrap confidence intervals for unknown parameters are proposed. The performance of estimation of unknown parameters and reliability index are evaluated numerically through Monte Carlo method. Conclusion: The performance on maximum likelihood estimation method is effective and satisfying. For the confidence intervals of parameters, bootstrap method outperforms the approximate method.

Statistical Inference for the Inverted Scale Family under General Progressive Type-II Censoring

Two estimation problems are studied based on the general progressively censored samples, and the distributions from the inverted scale family (ISF) are considered as prospective life distributions. One is the exact interval estimation for the unknown parameter θ , which is achieved by constructing the pivotal quantity. Through Monte Carlo simulations, the average 90 % and 95 % confidence intervals are obtained, and the validity of the above interval estimation is illustrated with a numerical example. The other is the estimation of R = P ( Y < X ) in the case of ISF. The maximum likelihood estimator (MLE) as well as approximate maximum likelihood estimator (AMLE) is obtained, together with the corresponding R-symmetric asymptotic confidence intervals. With Bootstrap methods, we also propose two R-asymmetric confidence intervals, which have a good performance for small samples. Furthermore, assuming the scale parameters follow independent gamma priors, the Bayesian estimator as well as the HPD credible interval of R is thus acquired. Finally, we make an evaluation on the effectiveness of the proposed estimations through Monte Carlo simulations and provide an illustrative example of two real datasets.

On Step-Stress Accelerated Life Testing for Power Generalized Weibull Distribution Under Progressive Type-II Censoring

In this paper, step-stress accelerated life testing is studied when the lifetime of test units follows power generalized Weibull distribution (PGW). Maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are obtained under type-II progressive censoring. Moreover, the approximate and credible confidence intervals of the parameters are derived. Also, simulation studies are conducted to check the precision of the MLEs and BEs for the parameters of PGW distribution. Finally, some interesting conclusions are obtained.

Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring

In this paper, the estimation problem of two parameters of a lifetime distribution with a bathtub-shaped failure rate function based on adaptive progressive type-II censored data is discussed. This censoring scheme allows the experiment to be more efficient in the use of time and cost while ensuring the statistical inference efficiency based on the experimental results. Maximum likelihood estimators are proposed and the approximate confidence intervals for two parameters are computed using the asymptotic normality. Lindley approximation and Gibbs sampling are used to obtain Bayes point estimates and the latter is also used to generate Bayes two-sided credible intervals. Finally, the performance of various estimation methods is evaluated through simulation experiments, and the proposed estimation method is illustrated through the analysis of a real data set.