• Communications for Statistical Applications and Methods
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• v.26 no.2
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• pp.131-148
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• 2019

Constant stress partially accelerated life tests are studied according to exponentiated Weibull distribution. Grounded on multiple censoring, the maximum likelihood estimators are determined in connection with unknown distribution parameters and accelerated factor. The confidence intervals of the unknown parameters and acceleration factor are constructed for large sample size. However, it is not possible to obtain the Bayes estimates in plain form, so we apply a Markov chain Monte Carlo method to deal with this issue, which permits us to create a credible interval of the associated parameters. Finally, based on constant stress partially accelerated life tests scheme with exponentiated Weibull distribution under multiple censoring, the illustrative example and the simulation results are used to investigate the maximum likelihood, and Bayesian estimates of the unknown parameters.

• Journal of the Korean Data Analysis Society
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• v.20 no.6
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• pp.2747-2757
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• 2018

We consider the MLE (maximum likelihood estimate) and Bayesian estimates of three-parameter bathtub-shaped lifetime distribution based on the progressive type II censoring with binomial removal. Jung, Chung (2018) proposed the three-parameter bathtub-shaped distribution which is the extension of the two-parameter bathtub-shaped distribution given by Zhang (2004). Jung, Chung (2018) investigated its properties and estimations. The maximum likelihood estimates are computed using Newton-Raphson algorithm. Also, Bayesian estimates are obtained under the balanced loss function using MCMC (Markov chain Monte Carlo) method. In particular, BSEL (balanced squared error loss) function is considered as a special form of balanced loss function given by Zellner (1994). For comparing theirs MLEs with the corresponding Bayes estimates, some simulations are performed. It shows that Bayes estimates is better than MLEs in terms of risks. Finally, concluding remarks are mentioned.

• Industrial Engineering and Management Systems
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• v.10 no.2
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• pp.154-160
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• 2011

In this paper, a reliability sampling plan under progressively type-1 interval censoring is proposed when the lifetime of products follows the Pareto distribution of second kind. We use the maximum likelihood estimator for the median life and its asymptotic distribution. The cost model is proposed and the design parameters are determined such that the given producer's and the consumer's risks are satisfied. Tables are given and the results are explained with examples.

• Journal of the Korean Data and Information Science Society
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• v.22 no.5
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• pp.977-989
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• 2011

The half logistic distribution has been used intensively in reliability and survival analysis especially when the data is censored. In this paper, we provide Bayesian estimation of the shape parameter and reliability function in the generalized half logistic distribution based on progressively Type-II censored data under various loss functions. We here consider conjugate prior and noninformative prior and corresponding posterior distributions are obtained. As an illustration, we examine the validity of our estimation using real data and simulated data.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.597-603
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• 2011

The half logistic distribution has been used intensively in reliability and survival analysis especially when the data is censored. In this paper, we provide prole likelihood estimation of the shape parameter and scale parameter in the generalized half logistic distribution based on progressively Type-II censored data. We also introduce approximate maximum prole likelihood estimates for the scale parameter. As an illustration, we examine the validity of our estimation using real data and simulated data.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.565-574
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• 2011

The exponenetiated distribution has been used in reliability and survival analysis especially when the data is censored. In this paper, we derive Bayesian estimation of shape parameter and reliability function in the exponenetiated half triangle distribution based on Type-I hybrid censored data. Here we consider conjugate prior and noninformative prior and obtained corresponding posterior distributions. As an illustration, the mean square errors of the estimates are computed. Comparisons are made between these estimators using Monte Carlo simulation study.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.961-969
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• 2009

A hybrid censoring is a mixture of Type-I and Type-II censoring schemes. This paper deals with estimation based on Type-I hybrid censored samples from the half triangle distribution. We derive some estimators of the scale parameter of the half triangle distribution based on Type-I hybrid censored samples. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.603-613
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• 2011

Exponentiated distribution has been used in reliability and survival analysis especially when the data is censored. In this paper, we derive Bayesian estimation of the shape parameter, reliability function and failure rate function in the exponentiated distribution family based on Type-II right censored data. We here consider conjugate prior and noninformative prior and corresponding posterior distributions are obtained. As an illustration, the mean square errors of the estimates are computed. Comparisons are made between these estimators using Monte Carlo simulation study.

• Journal of the Korean Data and Information Science Society
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• v.5 no.2
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• pp.19-27
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• 1994

It is known that the maximum likelihood method does not provide explicit estimator for the scale parameter of the Weibull distribution based on Type-II censored samples. In this paper we provide an approximate maximum likelihood estimator (AMLE) of the scale parameter of the Weibull distribution with Type-II censoring. We obtain the asymptotic variance and simulate the values of the bias and the variance of this estimator based on 3000 Monte Carlo runs for n = 10(10)30 and r,s = 0(1)4. We also simulate the absolute biases of the MLE and the proposed AMLE for complete samples. It is found that the absolute bias of the AMLE is smaller than the absolute bias of the MLE.

• Journal of the Korean Data and Information Science Society
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• v.20 no.6
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• pp.1169-1175
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• 2009

In this paper, the inferences of data obtained from periodic inspection and type I censoring for the step-stress accelerated life test are studied. The exponential distribution with a failure rate function that a log-linear function of stress and the tampered failure rate model are considered. The maximum likelihood estimators of the model parameters are estimated and also the optimal stress change time which minimize the asymptotic variance of maximum likelihood estimators of parameters is determined. A numerical example will be given to illustrate the proposed inferential procedures and the sensitivity of the asymptotic variance of the estimated mean by the guessed parameters is investigated.