• Journal of the Korean Statistical Society
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• 제34권4호
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• pp.331-344
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• 2005

Inference on current data could be more reliable if there exist similar data based on previous studies. Ibrahim and Chen (2000) utilize these data to characterize the power prior. The power prior is constructed by raising the likelihood function of the historical data to the power $a_o$, where $0\;{\le}\;a_o\;{\le}\;1$. The power prior is a useful informative prior in Bayesian inference. However, for model selection or model comparison problems, the propriety of the power prior is one of the critical issues. In this paper, we suggest two joint power priors for the power law process and show that they are proper under some conditions. We demonstrate our results with a real dataset and some simulated datasets.

• Journal of the Korean Data and Information Science Society
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• 제18권2호
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• pp.535-541
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• 2007

The Non-homogeneous Poisson process is probably the most popular model since it can model systems that are deteriorating or improving. The renewal process is a model that is often used to describe the random occurrence of events in time. But both these models are based on too restrictive assumptions on the effect of the repair action. The Modulated Power Law Process is a suitable model for describing the failure pattern of repairable systems when both renewal-type behavior and time trend are present. In this paper we propose maximum likelihood estimation of the next failure time after the system has experienced some failures, that is, Mean Time Between Failure for the MPLP model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제10권2호
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• pp.41-47
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• 2006

The Renewal process and the Non-homogeneous Poisson process (NHPP) process are probably the most popular models for describing the failure pattern of repairable systems. But both these models are based on too restrictive assumptions on the effect of the repair action. For these reasons, several authors have recently proposed point process models which incorporate both renewal type behavior and time trend. One of these models is the Modulated Power Law Process (MPLP). The Modulated Power Law Process is a suitable model for describing the failure pattern of repairable systems when both renewal-type behavior and time trend are present. In this paper we propose Bayes estimation of the next failure time after the system has experienced some failures, that is, Mean Time Between Failure for the MPLP model. Numerical examples illustrate the estimation procedure.

• Computers and Concrete
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• 제29권4호
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• pp.255-262
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• 2022

The present study investigates the effects of Cattaneo-Christov thermal effects of stagnation point in Walters-B nanofluid flow through lubrication of power-law fluid by taking the slip at the interfacial condition. The impacts of thermophoresis and Brownian motions are further accounted. The fluid impinging orthogonally on the surface is due to power-law slim coating liquid. The generalized newtonian fluid equation is used that obeys the power law constitutive equation to model our problem. The effect of velocity profiles, temperature for different values of n are investigated. The prandtl on the temperature distribution for partial slip and no slip cases is also observed. It is found that for larger values of prandtl number thermal diffusivity of fluid reduces and it enhance the decrease in temperature and boundary layer thickness.

• 한국신뢰성학회지:신뢰성응용연구
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• 제9권2호
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• pp.121-130
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• 2009

The power law process model the Rate of occurrence of failures(ROCOF) with monotonic trend during the operating time. However, the power law process is inappropriate when a non-monotonic trend in the failure data is observed. In this paper we deals with the reliability modeling of the failure process of large and complex repairable system whose rate of occurrence of failures shows the non-monotonic trend. We suggest a sectional model and a change-point test based on the Schwarz information criterion(SIC) to describe the non-monotonic trend. Maximum likelihood is also suggested to estimate parameters of sectional model. The suggested methods are applied to field data from an repairable system.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.483-496
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• 2005

We consider the power law process which is assumed to have multiple changepoints. We propose a binary segmentation procedure for locating all existing changepoints. We select one model between the no-changepoints model and the single changepoint model by the Bayes factor. We repeat this procedure until no more changepoints are found. Then we carry out a multiple test based on the Bayes factor through the intrinsic priors of Berger and Pericchi (1996) to investigate the system behaviour of failure times. We demonstrate our procedure with a real dataset and some simulated datasets.

• 공업화학
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• 제23권2호
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• pp.204-209
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• 2012

상업용 루테늄 촉매 상에서 에탄의 수증기 개질 반응에 대한 kinetics 데이터를 얻기 위하여 반응온도, 에탄의 분압, 수증기/에탄의 비 등을 변화시키면서 반응 실험을 수행하였다. Kinetics 데이터를 사용하여 Power rate law kinetic model 과 Langmuir-Hinshelwood model의 parameter를 구하였다. 또한 kinetic model식을 적용하여 PRO/II를 이용한 공정 모사를 통해서 에탄의 수증기 개질 반응기 sizing을 수행하였다. 동일한 전환율을 얻기 위해서는 Power rate law model을 적용하였을 경우가 Langmuir-Hinshelwood model을 적용하였을 경우보다 개질 반응기의 부피가 더 큼을 알 수 있었다. Langmuir-Hinshelwood model에 의해 계산된 반응 속도가 반응 실험 결과에 의해 구해진 반응 속도와 더 잘 일치했기 때문에 Langmuir-Hinshelwood model을 적용하여 계산된 반응기의 크기가 실제 반응기 설계에 더 적절하다고 판단된다.

• 한국전산유체공학회지
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• 제15권4호
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• pp.1-8
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• 2010

This article describes the numerical investigation of turbulent blood flow in the stenosed artery bifurcation under periodic acceleration of the human body. Numerical analyses for turbulent blood flow were performed with different magnitude of periodic accelerations using a modified turbulence model which was considering drag reduction of non-Newtonian fluid. The blood was considered to be a non-Newtonian fluid which was based on the power-law viscosity. In order to validate the modified $k-{\varepsilon}$ model, numerical simulations were compared with the standard $k-{\varepsilon}$ model and the Malin's low Reynolds number turbulence model for power-law fluid. As results, the modified $k-{\varepsilon}$ model represents intermediate characteristics between laminar and standard $k-{\varepsilon}$ model, and the modified $k-{\varepsilon}$ model showed good agreements with Malin's verified power law model. Moreover, the computing time and computer resource of the modified $k-{\varepsilon}$ model were reduced about one third than low Reynolds number model including Malin's model.

• 생태와환경
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• 제45권4호
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• pp.420-443
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• 2012

An Individual-Based Model (IBM) was developed by employing natural and toxic survival rates of individuals to elucidate the community responses of benthic macroin-vertebrates to anthropogenic disturbance in the streams. Experimental models (dose-response and relative sensitivity) and mathematical models (power law and negative exponential distribution) were applied to determinate the individual survival rates due to acute toxicity in stressful conditions. A power law was additionally used to present the natural survival rate. Life events, covering movement, exposure to contaminants, death and reproduction, were simulated in the IBM at the individual level in small (1 m) and short (1 week) scales to produce species abundance distributions (SADs) at the community level in large (5 km) and long (1~2 years) scales. Consequently, the SADs, such as geometric series, log-series, and log-normal distribution, were accordingly observed at severely (Biological Monitoring Working Party (BMWP<10), intermediately (BMWP<40) and weakly (BMWP${\geq}50$) polluted sites. The results from a power law and negative exponential distribution were suitably fitted to the field data across the different levels of pollution, according to the Kolmogorov-Smirnov test. The IBMs incorporating natural and toxic survival rates in individuals were useful for presenting community responses to disturbances and could be utilized as an integrative tool to elucidate community establishment processes in benthic macroin-vertebrates in the streams.

• 한국추진공학회지
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• 제16권6호
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• pp.23-31
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• 2012

본 연구에서는 $SiO_2$ 계열 젤화제로 알려진 Aerosil(R) R972, Silica 230, Silica 530을 사용하여 케로신 기반 젤 연료를 제작하였다. 케로신 계열 연료로는 Jet A-1을 사용하였으며 젤화(gelification) 여부를 확인하기 위한 전단박화(shear thinning) 현상은 멱법칙(power-law) 모델을 이용하여 검증하였고 제작된 모든 젤 연료는 전단박화 효과와 함께 $SiO_2$ 젤화제의 함유량이 증가할수록 젤의 점도가 높게 형성됨을 확인하였다. 본 연구에서 사용된 젤화제 중 Aerosil(R) R972를 첨가한 젤 연료의 점성계수가 전단률 전 영역에 걸쳐 멱법칙 모델을 따르는 것이 확인되었으며 상대적으로 Silica 230과 Silica 530을 첨가한 젤 연료는 전단률 150 [1/s] 근방 이하에서 멱법칙이 유효하지 않음을 알 수 있었다. 또한, 젤화제 함유량이 증가할수록 vortex 혼합법과 수동 혼합법 간의 유변학적 특성이 크게 차이 나는 것이 관찰되었다.