Reliability Estimates of Burr XII Components Using Masked Data under Progressive Type-II Censoring

2014 ◽  
Vol 551 ◽  
pp. 626-632
Author(s):  
Mo Chen ◽  
Yi Min Shi ◽  
Li Jin
Keyword(s):  
Latent Variable ◽  
Sampling Method ◽  
Reliability Function ◽  
Maximum Likelihood Estimates ◽  
Lifetime Data ◽  
Series System ◽  
Type Ii ◽  
Reliability Estimates ◽  
Progressive Type ◽  
System Lifetime Data

We consider the series system with three independent and non-identical components, each of which has Burr XII distributed lifetime. Based on progressively type-II censored and masked system lifetime data, the maximum likelihood estimates (MLE) of the components parameters and reliability function are obtained. By introducing a latent variable, Bayesian estimators of the components parameters and the reliability function are also developed using Gibbs sampling method. Furthermore, in the numerical simulation study, the MLE and Bayesian estimates are compared under different removal probabilities and different times.

Reliability Estimation for Cold Standby Series System Based on General Progressive Type II Censored Samples

2013 ◽  
Vol 321-324 ◽  
pp. 2460-2463 ◽  
Author(s):  
Yi Min Shi ◽  
Xiao Lin Shi
Keyword(s):  
Bayesian Estimation ◽  
Reliability Function ◽  
Reliability Estimation ◽  
Likelihood Method ◽  
Series System ◽  
Type Ii ◽  
Censored Samples ◽  
Progressive Type ◽  
Cold Standby ◽  
Two Parameter

Suppose that the life of unit is distributed as two-parameter exponential distribution. The Bayesian estimation for cold standby series system is studied based on general Progressive type II censored samples. Under the different error loss, the Bayesian estimation of the unknown parameter and reliability function are derived where hyper-parameters are estimated by using Maximum likelihood method. At last, a numerical example is given by means of the Monte-Carlo simulation to illustrate the correctness and feasibility for the method proposed in this paper.

Reliability Analysis for Masked Data under Type-II Generalized Progressively Hybrid Censored Scheme

2014 ◽  
Vol 687-691 ◽  
pp. 1198-1201
Author(s):  
Bin Liu ◽  
Yi Min Shi ◽  
Jing Cai ◽  
Mo Chen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Expectation Maximization ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Lifetime Data ◽  
Type Ii ◽  
Distribution Parameters ◽  
System Lifetime Data ◽  
Quasi Newton

The Type-II generalized progressively hybrid censored scheme with masked data is presented. Based on masked system lifetime data, using the expectation maximization algorithm and the Quasi-Newton method, we obtain the Maximum Likelihood Estimation (MLE) of the components distribution parameters in the Weibull case. Finally, Monte Carlo simulation is presented to illustrate the effect.

Reliability Analysis of a Cold Standby System under Progressive Type-II Censoring Date

2012 ◽  
Vol 459 ◽  
pp. 540-543 ◽  
Author(s):  
Feng Li
Keyword(s):  
Confidence Interval ◽  
Empirical Bayes ◽  
Reliability Function ◽  
Type Ii ◽  
Confidence Limits ◽  
Average Life ◽  
Type Ii Censoring ◽  
Progressive Type ◽  
Cold Standby ◽  
Progressive Type Ii Censoring

the exact confidence interval estimations and the approximate confidence interval estimations of the reliability indexes for a cold standby series system are investigated under progressive type-II censoring date, the formulae to calculate the exact confidence limits and the empirical Bayes approximate confidence limits of the failure rate, and the reliability function and average life are given. In order to investigate the accuracy of estimations, an illustrative example is examined numerically by means of Monte-Carlo simulation.

scholarly journals Bayesian Estimation Based on Rayleigh Progressive Type II Censored Data with Binomial Removals

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Reza Azimi ◽  
Farhad Yaghmaei
Keyword(s):  
Censored Data ◽  
Failure Time ◽  
Simulation Method ◽  
Reliability Function ◽  
Rayleigh Distribution ◽  
Type Ii ◽  
Monte Carlo Simulation Method ◽  
Bayesian Procedures ◽  
Progressive Type ◽  
Type Ii Censored Data

This study considers the estimation problem for the parameter and reliability function of Rayleigh distribution under progressive type II censoring with random removals, where the number of units removed at each failure time has a binomial distribution. We use the maximum likelihood and Bayesian procedures to obtain the estimators of parameter and reliability function of Rayleigh distribution. We also construct the confidence intervals for the parameter of Rayleigh distribution. Monte Carlo simulation method is used to generate a progressive type II censored data with binomial removals from Rayleigh distribution, and then these data are used to compute the point and interval estimations of the parameter and compare both the methods used with different random schemes.

scholarly journals E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 626
Author(s):  
Abdalla Rabie ◽  
Junping Li
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Real Life ◽  
Estimation Method ◽  
Reliability Function ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Type Ii ◽  
Credible Intervals ◽  
Generalized Type

In this article, we are concerned with the E-Bayesian (the expectation of Bayesian estimate) method, the maximum likelihood and the Bayesian estimation methods of the shape parameter, and the reliability function of one-parameter Burr-X distribution. A hybrid generalized Type-II censored sample from one-parameter Burr-X distribution is considered. The Bayesian and E-Bayesian approaches are studied under squared error and LINEX loss functions by using the Markov chain Monte Carlo method. Confidence intervals for maximum likelihood estimates, as well as credible intervals for the E-Bayesian and Bayesian estimates, are constructed. Furthermore, an example of real-life data is presented for the sake of the illustration. Finally, the performance of the E-Bayesian estimation method is studied then compared with the performance of the Bayesian and maximum likelihood methods.

scholarly journals Minimum Variance Unbiased Estimation in the Gompertz Distribution under Progressive Type II Censored Data with Binomial Removals

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Ashok Shanubhogue ◽  
N. R. Jain
Keyword(s):  
Censored Data ◽  
Hazard Function ◽  
Shape Parameter ◽  
Reliability Function ◽  
Minimum Variance ◽  
Unbiased Estimation ◽  
Type Ii ◽  
Gompertz Distribution ◽  
Progressive Type ◽  
Type Ii Censored Data

This paper deals with the problem of uniformly minimum variance unbiased estimation for the parameter of the Gompertz distribution based on progressively Type II censored data with binomial removals. We have obtained the uniformly minimum variance unbiased estimator (UMVUE) for powers of the shape parameter and its functions. The UMVUE of the variance of these estimators is also given. The UMVUE of (i) pdf, (ii) cdf, (iii) reliability function, and (iv) hazard function of the Gompertz distribution is derived. Further, an exact % confidence interval for the th quantile is obtained. The UMVUE of pdf is utilized to obtain the UMVUE of . An illustrative numerical example is presented.

Bayesian estimation of reliability indexes for cold standby system under general progressive Type II censored data

2014 ◽  
Vol 31 (3) ◽  
pp. 311-343 ◽  
Author(s):  
D.R. Barot ◽  
M.N. Patel
Keyword(s):  
Empirical Bayes ◽  
Series System ◽  
Type Ii ◽  
Confidence Limits ◽  
Content Type ◽  
Type Ii Censoring ◽  
Progressive Type ◽  
Cold Standby ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

Purpose – This paper aims to deal with the estimation of the empirical Bayesian exact confidence limits of reliability indexes of a cold standby series system with (n+k−1) units under the general progressive Type II censoring scheme. Design/methodology/approach – Assuming that the lifetime of each unit in the system is identical and independent random variable with exponential distribution, the exact confidence limits of the reliability indexes are derived by using an empirical Bayes approach when an exponential prior distribution of the failure rate parameter is considered. The accuracy of these confidence limits is examined in terms of their coverage probabilities by means of Monte-Carlo simulations. Findings – The simulation results show that accuracy of exact confidence limits of reliability indexes of a cold standby series system is efficient. Therefore, this approach is good enough to use for reliability practitioners in order to improve the system reliability. Practical implications – When items are costly, the general progressive Type II censoring scheme is used to reduce the total test time and the associated cost of an experiment. The proposed method provides the means to estimate the exact confidence limits of reliability indexes of the proposed cold standby series system under this scheme. Originality/value – The application of the proposed technique will help the reliability engineers/managers/system engineers in various industrial and other setups where a cold standby series system is widely used.

scholarly journals Estimation and Prediction for Nadarajah-Haghighi Distribution under Progressive Type-II Censoring

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 999
Author(s):  
Mingjie Wu ◽  
Wenhao Gui
Keyword(s):  
Loss Function ◽  
Maximum Likelihood Estimates ◽  
Type Ii ◽  
Unknown Parameters ◽  
Estimation And Prediction ◽  
Error Loss ◽  
Squared Error ◽  
Progressive Type ◽  
Metropolis Hasting Algorithm ◽  
Highest Posterior Density

The paper discusses the estimation and prediction problems for the Nadarajah-Haghighi distribution using progressive type-II censored samples. For the unknown parameters, we first calculate the maximum likelihood estimates through the Expectation–Maximization algorithm. In order to choose the best Bayesian estimator, a loss function must be specified. When the loss is essentially symmetric, it is reasonable to use the square error loss function. However, for some estimation problems, the actual loss is often asymmetric. Therefore, we also need to choose an asymmetric loss function. Under the balanced squared error and symmetric squared error loss functions, the Tierney and Kadane method is used for calculating different kinds of approximate Bayesian estimates. The Metropolis-Hasting algorithm is also provided here. In addition, we construct a variety of interval estimations of the unknown parameters including asymptotic intervals, bootstrap intervals, and highest posterior density intervals using the sample derived from the Metropolis-Hasting algorithm. Furthermore, we compute the point predictions and predictive intervals for a future sample when facing the one-sample and two-sample situations. At last, we compare and appraise the performance of the provided techniques by carrying out a simulation study and analyzing a real rainfall data set.

Sign in / Sign up

Export Citation Format

Share Document