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 Estimation for the Two-Parameter Exponential Family Based on Progressively Type-II Censored Data

2018 ◽  
Vol 25 (01) ◽  
pp. 1850005
Author(s):  
Wenhao Gui
Keyword(s):  
Reliability Function ◽  
Reliability Estimation ◽  
Type Ii ◽  
Prior Density ◽  
Monte Carlo Simulation Study ◽  
Censored Samples ◽  
Type Ii Censored Data ◽  
Two Parameters ◽  
Parameter Case ◽  
Two Parameter

In this paper, we deal with the problem of estimating the reliability function of the two-parameter exponential distribution. Classical Maximum likelihood and Bayes estimates for one and two parameters and the reliability function are obtained on the basis of progressively type-II censored samples. The inverted gamma conjugate prior density is assumed for the one-parameter case, whereas the joint prior density of the two-parameter case is composed of the inverted gamma and the uniform densities. A comparison between the obtained estimators is made through a Monte Carlo simulation study. A real example is used to illustrate the proposed methods.

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 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.

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.

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