• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.445-461
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• 1994

This paper deals with the problem of obtaining some Bayes estimators and Bayesian credible regions of a reliability function for the Rayleigh distribution. Using several priors for a reliability function some Bayes estimators and Bayes credible sets are proposed and studied under squared error loss and Harris loss. Also the performances and behaviors of the proposed Bayes estimators are examined via Monte Carlo simulations and some numericla examples are given.

• Journal of the Korean Statistical Society
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• v.32 no.3
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• pp.289-298
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• 2003

We consider the estimation problem for the scale parameter of the Rayleigh distribution using weighted balanced loss function (WBLF) which reflects both goodness of fit and precision. Under WBLF, we obtain the optimal estimator which creates a kind of balance between Bayesian and non-Bayesian estimation. We also deal with the estimation of R ＝ P(Y < X) when Y and X are two independent but not identically distributed Rayleigh distribution under squared error loss function.

• International Journal of Ocean System Engineering
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• v.2 no.4
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• pp.250-258
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• 2012

The distribution of wave heights is assumed to be a Rayleigh distribution, based on the assumption of a narrow band and Gaussian distribution of wave elevation. The present study was started with doubts about the narrow band assumption. We selected the wave spectra widely used to simulate irregular random waves. The wave spectra used in this study included the Pierson-Moskowitz spectrum, Bretschneider-Mitsuyasu spectrum, and JONSWAP spectrum. The directionality of the waves was considered. The cosine 2-l type directional spreading function and mixed form of the half-cosine 2-s type with Mitsuyasu type directional spreading are considered here to investigate the effects of a directional spreading function on random waves. The simulated wave height distribution is compared with a Rayleigh distribution.

• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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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.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.11 no.6
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• pp.800-806
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• 2018

Software efficiency is the probability of failure free use in operating environments, and is the most fundamental factor affecting software system stability. The malfunction of the computer system used in the information technology field may cause a significant loss in the related industry. Therefore, in this study, we analyze the attributes of software reliability models that depend on various hazard functions based on finite fault NHPP model with software failure time data. The hazard function pattern of proposed model is constant for the Goel-Okumoto model, and the Minimax and Rayleigh models follow the incremental pattern, but the hazard function increase value of the Minimax model is smaller than that of the Rayleigh model and the Goel-Okumoto model. Also, the Minimax model was relatively efficient because the true value error of the mean value function m(t) and the mean square error (MSE) of the Minimax model were smaller than those of the Rayleigh and Goel-Okumoto models. The results of this study are expected to be useful for software developers as basic information about the hazard function.

• Journal of Biomedical Engineering Research
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• v.10 no.3
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• pp.323-330
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• 1989

Large bias errors which occur during a numerical evaluation of the Rayleigh's integral is not due to the replicated source problem but due to the coincidence of singularities of the Green's function and the sampling points in Fourier domain. We found that there is no replicated source problem in evaluating the Rayleigh's integral numerically by the reason of the periodic assumption of the input sequence in Dn or by the periodic sampling of the Green's function in the Fourier domain. The wrap around error is not due to an overlap of the individual adjacent sources but berallse of the undersampling of the Green's function in the frequency domain. The replicated and overlApped one is inverse Fourier transformed Green's function rather than the source function.

• Journal of the Korean Data and Information Science Society
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• v.6 no.1
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• pp.39-51
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• 1995

This paper deals with the problem of obtaining some Bayes estimators of Rayleigh reliability function in a time censored sampling with incomplete information. Using the priors about a reliability function some Bayes estimators are proposed and studied under squared error loss and Harris loss.

• Structural Monitoring and Maintenance
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• v.11 no.1
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• pp.19-40
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• 2024

The elastic theory of beams is fundamental in engineering of design and structure. In this study, we construct Green's function for inhomogeneous fourth-order differential operators subjected to associated constraints that arises in dealing with dynamic problems in the Rayleigh beam. We obtain solutions for homogeneous and completely inhomogeneous beam problems using Green's function. This enables us to consider rotational influences in determining the eigenfrequency of beam vibrations. Additionally, we investigate the dynamic vibration model of inhomogeneous beams incorporating rotational effects. The eigenvalues of Rayleigh beams, including first-order correction terms, are also computed and displayed in tabular forms.

• Transactions of the Korean Society of Automotive Engineers
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• v.17 no.4
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• pp.108-117
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• 2009

Leissa claimed in his article that the Rayleigh method is not the same as the Ritz method for determining natural frequencies and its corresponding mode shapes and contended that Rayleigh's name should not be attached to the method. The present article examines the methods in viewpoint of admissible functions and its minimization process, and of the historical developments. It concludes that Leissa's assertion is relevant, although Rayleigh did apply a conceptual theory systematized from the Lagrange method, and given 38 years earlier than Ritz's 'masterly exposition of theory'.

• The KIPS Transactions:PartD
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• v.15D no.2
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• pp.207-212
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• 2008

This paper evaluates software cost estimation models, and presents the most suitable model. First, we transformed a relevant model into variables to make in linear. Second, we evaluated model's performance considering how much suitable the cost data of the actual development software was. In the stage of model performance evaluation criteria, we used MMRE which is the relative error concept rather than the absolute error. Existing software cost estimation model follows Weibull, Gamma, and Rayleigh function. In this paper, Gompertz function model is suggested which is a kind of growth curve. Additionally, we verify the compatability of other different growth curves. As a result of evaluation of model's performance, Gompertz function was considered to be the most suitable for the cost estimation model.