• Communications for Statistical Applications and Methods
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• 제11권1호
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• pp.161-168
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• 2004

A single-index model is useful in fields which employ multidimensional regression models. Many methods have been developed in parametric and nonparametric approaches. In this paper, posterior inference is considered and a wavelet series is thought of as a function approximated to a true function in the single-index model. The posterior inference needs a prior distribution for each parameter estimated. A prior distribution of each coefficient of the wavelet series is proposed as a hierarchical distribution. A direction $\beta$ is assumed with a unit vector and affects estimate of the true function. Because of the constraint of the direction, a transformation, a spherical polar coordinate $\theta$, of the direction is required. Since the posterior distribution of the direction is unknown, we apply a Metropolis-Hastings algorithm to generate random samples of the direction. Through a Monte Carlo simulation we investigate estimates of the true function and the direction.

• International Journal of Reliability and Applications
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• 제17권1호
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• pp.65-84
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• 2016

Motivated by the recent work of Cordeiro and Castro (2011), we study the Kumaraswamy exponentiated Frechet distribution (KEF). We derive some mathematical properties of the (KEF) including moment generating function, moments, quantile function and incomplete moment. We provide explicit expressions for the density function of the order statistics and their moments. In addition, the method of maximum likelihood and least squares and weighted least squares estimators are discuss for estimating the model parameters. A real data set is used to illustrate the importance and flexibility of the new distribution.

• Journal of the Korean Data Analysis Society
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• 제20권6호
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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.

• International Journal of Reliability and Applications
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• 제3권1호
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• pp.1-16
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• 2002

In reliability engineering, the bathtub-shaped hazard rates play an important role in survival analysis and many other applications as well. For the bathtub-shaped, initially the hazard rate decreases from a relatively high value due to manufacturing defects or infant mortality to a relatively stable middle useful life value and then slowly increases with the onset of old age or wear out. In this paper, we present a new two-parameter lifetime distribution function, called the Loglog distribution, with Vtub-shaped hazard rate function. We illustrate the usefulness of the new Vtub-shaped hazard rate function by evaluating the reliability of several helicopter parts based on the data obtained in the maintenance malfunction information reporting system database collected from October 1995 to September 1999. We develop the S-Plus add-in software tool, called Reliability and Safety Assessment (RSA), to calculate reliability measures include mean time to failure, mean residual function, and confidence Intervals of the two helicopter critical parts. We use the mean squared error to compare relative goodness of fit test of the distribution models include normal, lognormal, and Weibull within the two data sets. This research indicates that the result of the new Vtub-shaped hazard rate function is worth the extra function-complexity for a better relative fit. More application in broader validation of this conclusion is needed using other data sets for reliability modeling in a general industrial setting.

• 한국세라믹학회지
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• 제33권5호
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• pp.583-589
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• 1996

In this study a new analytical model which can describe the relationship between the bridging stress and microstructure has beenproposed in order to investigate the microstructural effect on the R-curve behavior in polycrystalline aluminas since the R-curve can be derived via the bridging stress function. In the currently developed model function the distribution of grain size is considered as a microstructural factor in modeling of bridging stress function and thus the bridging stress function including three constants PM, n, and Cx, can be established analytically and quantitatively. The results indicate that the n value is closely related to the grain size distribution thereby providing a reliability of the current model for the bridging stress analysis. Thus this model which explains the correlation of the bridging stress distribution and microstructual parame-ters is useful for the systematic interpretation of microfracture mechanism including the R-curve behavior in polycrystalline aluminas.

• 한국분말재료학회지
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• 제10권3호
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• pp.201-208
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• 2003

Distributions of diamond particles protruding on the surface of worn diamond segments in circular saw has been investigated. Scanning electron microscope was used to examine the worn ,surface and radial saw blade wear and grinding ratio was measured. The number of protruded diamond particle was approximately 50% of the total number of particles, and that was independent of diamond particle concentration and table speed. It was also noted that the inter-particle distance did not follow a symmetric function like Gaussian distribution function, instead it fitted well with a probability density function based on gamma function. The distribution of inter-particle spacing, therefore, was analyzed using a gamma function model.

• 한국자동차공학회논문집
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• 제3권5호
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• pp.1-9
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• 1995

The purpose of this study is to develop a computer simulation program for analyzing load transmission characteristics of a helical gear system in design stage. In this analysis, the rotational delay, load distribution, root stress, and contact area are investigated. That is, the influence function of deflection is obtained by finite element analysis and the influence function of approach and gear tooth error are considered. Load distribution, rotational delay, and contact area are calculated by solving load-deflection equation which includes these influence functions and tooth error, and the influence function of the bending moment is obtained by finite element analysis. The root stress is calculated by the load distribution and the influence function of the bending moment. The results of the simulation are cross-checked through a specially designed experimental set-up.

• 한국강구조학회 논문집
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• 제10권1호통권34호
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• pp.37-45
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• 1998

기계 및 구조물의 안전성과 신뢰성 평가를 위하여 금속재료의 피로강도 데이터베이스 시스템을 구축하고, 이를 이용하여 금속재료의 피로수명 분포특성을 검토하였다. 종속도를 이용하여 구성한 관계형 피로강도 데이터베이스 시스템은 일련의 데이터 관리 및 해석작업을 효율적으로 수행하였다. 또한 Robust 방법과 보상오차함수(complementary error function)를 이용한 3-파라미터 Weibull분포의 파라미터 추정법 및 비파손확률를 검토하기 위하여 제안된 새로운 기준식의 타당성을 검토하였다. 조합분포모델을 이용하여 부하응력비와 Weibull분포의 파라미터 항으로 나타낸 피로수명 분포식은 탄소강의 P-R-N 특성을 해석함에 있어서 좋은 결과를 보였다.

• 대한토목학회논문집
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• 제30권5A호
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• pp.425-431
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• 2010

2가지 이상의 재료로 구성된 다상(multi-phase) 재료는 상 분포에 따라 재료 특성이 다르기 때문에, 상 분포를 묘사할 수 있는 적절한 방법이 필요하다. 본 연구에서는 확률 분포 함수 two-point correlation function과 lineal-path function을 사용하여 재료 내부의 상 분포 상태를 확률적으로 묘사하였다. 수치 계산 방법으로 계산되는 확률 분포 함수를 3개의 매개 변수를 사용한 곡선 접합(curve fitting)을 이용하여 수식으로 표현하고, 적용성을 살펴보기 위하여 2상 합금 미세구조 가상 시편과 지반 모델 시편을 사용하였다. 이를 통해, 확률 분포 함수는 곡선 접합을 이용하여 지수 형태의 수식으로 표현이 가능하며, 이는 시편의 RVE로서의 활용 가능성을 판단하는데 사용될 수 있음을 확인하였다.

• Journal of the Korean Data and Information Science Society
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• 제28권4호
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• pp.875-888
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• 2017

The Rayleigh distribution has been commonly used in life time testing studies of the probability of surviving until mission time. We focus on a reliability function of the Rayleigh distribution and deal with prior distribution on R(t). This paper is an effort to obtain Bayes estimators of rayleigh distribution with three different prior distribution on the reliability function; a noninformative prior, uniform prior and inverse gamma prior. We have found the Bayes estimator and predictive density function of a future observation y with each prior distribution. We compare the performance of the Bayes estimators under different sample size and in simulation study. We also derive the most plausible region, prediction intervals for a future observation.