• 품질경영학회지
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• 제24권2호
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• pp.65-76
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• 1996

In general, most industrial products exhibit bath-tub shaped curve for their failure rate functions. This distributional life model can be obtained by the Piecewise Weibull distribution. The least squares, maximum likelihood, and mixed methods of estimating the parameters of the Piecewise Weibull distribution are compared. The comparison is made by using the empirical mean squared errors of (a) the parameter estimates and (b) the estimated change-points, to summarize the results of 1000 simulated samples of three sizes - each 100, 150 and 200. The results are that the mixed method estimation comes to be the best as the sample sizes increase.

• Communications for Statistical Applications and Methods
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• 제31권1호
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• pp.55-64
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• 2024

In this study, we consider the sample size determination problem for clustered count data with many zeros. In general, zero-inflated Poisson and binomial models are commonly used for zero-inflated data; however, in real data the assumptions that should be satisfied when using each model might be violated. We calculate the required sample size based on a discrete Weibull regression model that can handle both underdispersed and overdispersed data types. We use the Monte Carlo simulation to compute the required sample size. With our proposed method, a unified model with a low failure risk can be used to cope with the dispersed data type and handle data with many zeros, which appear in groups or clusters sharing a common variation source. A simulation study shows that our proposed method provides accurate results, revealing that the sample size is affected by the distribution skewness, covariance structure of covariates, and amount of zeros. We apply our method to the pancreas disorder length of the stay data collected from Western Australia.

• 한국농공학회논문집
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• 제55권3호
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• pp.105-111
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• 2013

Probability distribution of microbes in wastewater is a crucial factor to be determined for microbial risk assessment associated with its reuse. The objective of this study was to investigate probability distribution of an indicator microorganism in wastewater. Daily total coliform counts measured from nationwide wastewater treatment plants in 2010 by the Ministry of Environment were used for statistical analysis. Basic statistics and probability distributions were estimated in the three different spatial scales using the MS Excel software and FARD2006 model. Overall, wastewater from manure and livestock treatment plants demonstrated greater median coliform counts than from sewage and village treatment plants. Generalized logistic (GLO) and 2-parameter Weibull (WBU2) appeared to be the two probability distributions that fitted best for total coliform numbers in wastewater. The study results of microbial statistics and probability distributions would provide useful data for quantitative assessment of microbial risk from agricultural wastewater reuse.

• Journal of the Korean Statistical Society
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• 제30권3호
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• pp.467-480
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• 2001

This paper considers the use of local $\phi$-divergence measures between posterior distributions under classes of perturbations in order to investigate the inherent robustness of certain classes. The smaller value of the limiting local $\phi$-divergence implies more robustness for the prior or the likelihood. We consider the cases when the likelihood comes form the class of weighted distribution. Two kinds of perturbations are considered for the local sensitivity analysis. In addition, some numerical examples are considered which provide measures of robustness.

• International Journal of Reliability and Applications
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• 제2권3호
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• pp.199-207
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• 2001

The failure rate functions between successive failures are of concatenated form. We allow the parameters of failure rate function change after a certain failure and its fixing. We confine out attention to a model wherein the interfailure times are described by its failure rate function. We suggest an adaptive failure rate function with a change-point under the assumption that interfailure times are record value statistics from a Weibull distribution. The proposed model will be applied through a practical example of software failure data.

• Journal of the Korean Data and Information Science Society
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• 제8권2호
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• pp.231-237
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• 1997

The Koziol-Green(KG) model has become an important topic in industrial life testing. In this paper we suggest MLE of the reliability function for the Weibull distribution under the KG model. Futhermore, we compare Kaplan-Meier estimator, Nelson estimator, Cheng & Chang estimator, and Ebrahimi estimator with proposed estimator for the reliability function under the KG model.

• Communications for Statistical Applications and Methods
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• 제8권3호
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• pp.711-717
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• 2001

Two imperfect repair models for system are considered, one introduced by Brown and Proschan(1983) and the other by Lee and Seoh(1999). We, in this paper, after assigning repair costs to the system, optimize both repair models, when the underlying life distributions of the system are exponential, uniform and Weibull.

• Communications for Statistical Applications and Methods
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• 제19권2호
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• pp.219-224
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• 2012

This article considers the mean time to failure(MTTF) of a dependent parallel system. We study how the degree of dependency components influences the increase in the mean lifetime for this system. The results are illustrated by tables and figures.

• Communications for Statistical Applications and Methods
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• 제28권1호
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• pp.1-19
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• 2021

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.

• 한국해안해양공학회지
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• 제19권4호
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• pp.313-319
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• 2007

장기간의 극치 및 평상시 파고는 연안 및 항만구조물의 계획 및 설계에서 매우 중요한 환경인자이다. 그러나, 한국 연안 심해파의 관측 자료가 한정되어 있기 때문에, 심해설계파의 정보는 기상정보로부터 사후추정 한 장기간의 파랑자료를 이용하고 있다. 본 연구에서는 한국해양연구원(2003)에서 제시한 1979년부터 1998년까지의 한국연안 67개 지점의 16방향별 최대 유의파 산출자료를 이용하여 극치분포 분석을 수행하였다. 특성분석에 사용된 극치분포함수는 FT-I과 Weibull 분포이며, 각 분포함수의 매개변수는 Goda(2004)의 방법을 이용하여 추정하였다. 또한 Goda and Gobune(1990)가 제안한 MIR 값을 산정하여 가장 적합한 확률분포형을 결정하였다. 분석결과 FT-I 분포가 886개 지점, Weibull(k=0.75) 분포가 81개 지점 및 Weibull(k=1.00) 분포가 105개 지점의 확률분포형으로 적합한 것으로 판단된다.