• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.633-641
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• 2014

The exponential distibution is one of the most popular distributions in analyzing the lifetime data. In this paper, we propose multiply Type I hybrid censoring. And this paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply Type I hybrid censoring. The scale parameter is estimated by approximate maximum likelihood estimation methods using two different Taylor series expansion types ($AMLE_I$, $AMLE_{II}$). We also obtain the maximum likelihood estimator (MLE) of the scale parameter ${\sigma}$ under the proposed multiply Type I hybrid censored samples. We compare the estimators in the sense of the root mean square error (RMSE). The simulation procedure is repeated 10,000 times for the sample size n=20 and 40 and various censored schemes. The $AMLE_{II}$ is better than $AMLE_I$ in the sense of the RMSE.

• 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.

• 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.28 no.3
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• pp.659-668
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• 2017

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

• Communications for Statistical Applications and Methods
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• v.29 no.6
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• pp.665-677
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• 2022

This paper proposes a new estimation method based on the maximum product of spacings for estimating unknown parameters of the three-parameter Weibull distribution under a generalized Type-II progressive hybrid censoring scheme which guarantees a constant number of observations and an appropriate experiment duration. The proposed approach is appropriate for a situation where the maximum likelihood estimation is invalid, especially, when the shape parameter is less than unity. Furthermore, it presents the enhanced performance in terms of the bias through the Monte Carlo simulation. In particular, the superiority of this approach is revealed even under the condition where the maximum likelihood estimation satisfies the classical asymptotic properties. Finally, to illustrate the practical application of the proposed approach, the real data analysis is conducted, and the superiority of the proposed method is demonstrated through a simple goodness-of-fit test.

• Journal of the Korean Data and Information Science Society
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• v.26 no.1
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• pp.271-280
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• 2015

In this paper, the maximum likelihood estimators for parameters are derived under three step-stress accelerated life tests for Type-I hybrid censored data. The exponential distribution and the cumulative exposure model are considered based on the assumption that a log quadratic relationship exits between stress and the mean lifetime ${\theta}$. The test plan to search optimal stress change times minimizing the asymptotic variance of maximum likelihood estimators are presented. A numerical example to illustrate the proposed inferential procedures and some simulation results to investigate the sensitivity of the optimal stress change times by the guessed parameters are given.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.256-259
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• 1996

수명시험에서는 시험기간을 단축하기 위해 중도절단(consoring) 방법을 사용한다. 혼합 관측중단방법은 정시에 시험을 끝낼 수 있으며 고장시간을 관찰할 필요가 없다는 장점 때문에 널리 사용되고 있다. 본 논문에서는 제품의 수명이 와이블 분포를 따르고 형상모수를 알고 있다는 가정아래, 혼합 관측중단하에서 생산자 위험과 소비자 위험을 고려한 신뢰도 합격판정 샘플링 계획을 개발하였다. 아울러, 형상모수값에 개재된 불확실성이 실제 생산자 위험과 소비자 위험, 그리고 의사결정까지의 평균 고장개수에 미치는 영향을 민감도 분석을 통해 파악하였다.

• Journal of Korean Society for Quality Management
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• v.39 no.2
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• pp.313-319
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• 2011

In design verification and process validation stages, reliability demonstration tests(RDT's) are common practice in industry, A new two-stage RDT that is known to be more efficient than a corresponding single-stage one in terms of expected test duration for Weibull distribution is proposed. Zero or one failure two-stage plans to minimize expected test duration under Type I and hybrid censoring subject to satisfying consumer's risk at a specified reliability target are developed and a numerical example is provided to illustrate the proposed two-stage RDT plans and compared with other one- and two-stage plans.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.519-531
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• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.