• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.255-266
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• 2007

A Bayesian estimation of the four-parameter gamma distribution is considered under the noninformative prior. The Bayesian estimators are obtained by the Gibbs sampling. The generation of the shape/power parameter and the power parameter in the Gibbs sampler is implemented using the adaptive rejection sampling algorithm of Gilks and Wild (1992). Also, the location parameter is generated using the adaptive rejection Metropolis sampling algorithm of Gilks, Best and Tan (1995). Finally, the simulation result is presented.

• Journal of Integrative Natural Science
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• v.7 no.2
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• pp.138-144
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• 2014

Fisher information matrix plays an important role in statistical inference of unknown parameters. Especially, it is used in objective Bayesian inference where we calculate the posterior distribution using a noninformative prior distribution, and also in an example of metric functions in geometry. To estimate parameters in a distribution, we can use the Fisher information matrix. The more the number of parameters increases, the more its matrix form gets complicated. In this paper, by using Mathematica programs we derive the Fisher information matrix for 4-parameter generalized gamma distribution which is used in reliability theory.

• Journal of Applied Reliability
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• v.14 no.4
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• pp.220-224
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• 2014

A Bayesian zero-failure reliability demonstration test method for products with Weibull lifetime distribution is presented. Inverted gamma prior distribution for the scale parameter of the Weibull distribution is used to design the Bayesian test plan and selecting a prior distribution using a prior test information is discussed. A test procedure with zero-failure acceptance criterion is developed that guarantee specified reliability of a product with given confidence level. An example is provided to illustrate the use of the developed Bayesian reliability demonstration test method.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.465-471
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• 1997

This paper deals with the problems of obtaining some Bayesian and empirical Bayesian Predictive densities and prediction intervals of a future observation $X_{(\tau+\gamma)}$ in the Rayleigh distribution. Using an inverse gamma prior distribution, some prodictive densities and prodiction intervals are proposed and studied. Also the behaviors of the proposed results are examined via numerical examples.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.861-870
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• 2005

The Bayesian model selection procedures for the shape parameter of gamma distribution are proposed in order to test that the failure rate of gamma distribution is constant, increasing or decreasing. The encompassing intrinsic Bayes factor by Beger and Pericchi (1996) based on Jeffreys prior for shape parameter is used to investigate the usefulness of the proposed Bayesian model selection procedures via both real data and pseudo data.

• Journal of Korea Water Resources Association
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• v.46 no.3
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• pp.315-326
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• 2013

Despite of the importance on the maintenance of a reservoir storage, relatively few studies have addressed the stochastic reliability analysis including uncertainty on the decrease of the reservoir storage by the sedimentation. Therefore, the stochastic gamma process under the reliability framework is developed and applied to estimate the reduction of the Soyang Dam reservoir storage in this paper. Especially, in the estimation of parameters of the stochastic gamma process, the Bayesian MCMC scheme using informative prior distribution is used to incorporate a wide variety of information related with the sedimentation. The results show that the selected informative prior distribution is reasonable because the uncertainty of the posterior distribution is reduced considerably compared to that of the prior distribution. Also, the range of the expected life time of the dead storage in Soyang Dam reservoir including uncertainty is estimated from 119.3 years to 183.5 years at 5% significance level. Finally, it is suggested that the improvement of the assessment strategy in this study can provide the valuable information to the decision makers who are in charge of the maintenance of a reservoir.

• Transactions of Materials Processing
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• v.25 no.4
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• pp.254-260
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• 2016

In this study, hot isostatic pressed Ni-base superalloy was subjected by high-pressure torsion process to improve the dispersion of gamma prime phase, mechanical properties and remove prior particle boundaries. The resulting microstructural size decreases and prior particle boundaries removed with increasing strain by high-pressure torsion process. Moreover, the microhardness values and room temperature tensile strength were enhanced. However, the tensile elongation was decreased as increasing strain due to fast crack propagation along the refined and well dispersed gamma prime particles.

• Journal of Applied Reliability
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• v.13 no.2
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• pp.99-107
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• 2013

One-shot device is required to successfully perform its function only once at the moment of use. The reliability of a one-shot device should be expressed as a probability of success. In this paper, we propose a bayesian approach for estimating reliability of one-shot devices with small sample size. We employ a gamma prior to obtain the posterior distribution. Finally, we compare the accuracy of the proposed method with general maximum likelihood method.

• Transactions of Materials Processing
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• v.28 no.5
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• pp.247-256
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• 2019

In this study, the development of annealing textures in cold rolled and annealed tantalum sheets was analyzed using electron backscatter diffraction. At $900^{\circ}C$, the textures of the recrystallized grains in the partially and completely recrystallized microstructures displayed significant similarities. The average diameter of the recrystallized grains with ${\gamma}-fiber$ orientations exceeded that of grains with different orientations, and the average growth rates were unrelated to the orientations after an initial stage of recrystallization. Additional cold rolling and annealing was done for controlled initial microstructures and textures inherited from various processes of prior cold rolling and annealing. This second cycle of the process resulted in stronger textures with major ${\gamma}-fiber$ orientations as a result of the enhanced ${\gamma}-fiber$ orientations in the preceding textures. A coarse-grained prior microstructure resulted in a weaker annealing texture than a fine grained one regardless of the stronger previous texture, which was occasioned by the sub-structures of the minor orientations at local deformation inhomogeneities such as sharp in-grain shear bands.

• Journal of Applied Reliability
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• v.11 no.2
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• pp.151-165
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• 2011

We consider the problem of estimating the system reliability using noninformative priors when both stress and strength follow generalized gamma distributions with index, scale, and shape parameters. We first derive group-ordering reference priors using the reparametrization. We next provide the sufficient condition for propriety of posterior distributions and provide marginal posterior distributions under those noninformative priors. Finally, we provide and compare estimated values of the system reliability based on the simulated values of parameter of interest in some special cases.