• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.105-121
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• 2019

One of the main objective of manufacturing industries is to assess the capability performance of different processes. In this paper, we use the lifetime performance index $C_L$ as a criterion to measure larger-the-better type quality characteristic for evaluating the product performance. The lifetimes of products are assumed to follow a general class of inverted exponentiated distributions. We use maximum likelihood estimator to estimate the lifetime performance index under the assumption that data are progressive type I interval censored. We also obtain asymptotic distribution of this estimator. Based on this estimator, a new hypothesis testing procedure is developed with respect to a given lower specification limit. Finally, two numerical examples are discussed in support of the proposed testing procedure.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.1
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• pp.597-605
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• 2019

This paper proposes a novel method for efficient prediction of joint distributions of heights and periods of nonlinear ocean waves. The proposed novel method utilizes a transformed linear simulation which is based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial, calibrated such that the first four moments of the transformed model match the moments of the true process. This proposed novel method is utilized to predict the joint distributions of wave heights and periods of a sea state with the surface elevation data measured at the Gulfaks C platform in the North Sea, and the novel method's accuracy and efficiency are favorably validated by using comparisons with the results from an empirical joint distribution model, from a linear simulation model and from a second-order nonlinear simulation model.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.1
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• pp.165-177
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• 2019

This paper considers corrosion wastage of two ship hull structure members as a part of investigated fuel oil tanks of 25 aging bulk carriers. Taking into account that many factors which influence corrosion wastage of ship hull structures are of uncertain nature, the related corrosion rate ($c_1$) is considered here as a real-valued continuous distribution, assuming that the corrosion wastage starts after 5, 6 or 7 years. In all considered cases, by using available data and applying three basic statistical tests, it is established that between two-parameter continuous distributions, normal, Weibull and logistic distributions are best fitted distributions for the mentioned corrosion rate ($c_1$). Note that the presented statistical, numerical and graphical results concerning two mentioned ship hull structure members allow to compare and discuss the corresponding probabilistic estimates for the corrosion rate ($c_1$).

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.431-450
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• 2023

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n-means and the nth quantization errors for different values of n with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise [2], which says that for a Borel probability measure P with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.380-385
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• 2001

In the present study, flow characteristics of turbulent oscillatory flow in a square-sectional $180^{\circ}$ curved duct are investigated experimentally. In order to measure wall shear stress and pressure distributions, experimental studies for air flow are conducted in a square-sectional $180^{\circ}$ curved duct by using the LDV system with the data acquisition and the processing system. The wall shear stress measuring point bend angle of the $150^{\circ}$ and pressure distribution of the inlet (${\phi}=0^{\circ}$) to the outlet (${\phi}=180^{\circ}$) at $10^{\circ}$ intervals of the duct. The results obtained from the experimentation are summarized as follows: A wall shear stress value in an inner wall is larger than that in an outer wall, except for the phase angle (${\omega}t/{\pi}/6$) of 3, because of the intensity of secondary flow. The pressure distributions are the largest in accelerating and decelerating regions at the bend angle(${\phi}$) of $90^{\circ}$ and pressure difference of inner and outer walls is the largest before and after the ${\phi}=90^{\circ}$.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.519-531
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• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.

• Water for future
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• v.28 no.5
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• pp.191-203
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• 1995

In this study, the past flood levels of Goan station, which is one of major gaging stations and located at downstream of Paldang dam, were converted based on the 1994's cross section and the flood quantiles were estimated from flood frequency analysis. The recently established rating curve was used to convert flood levels. And the parameters of the several probability distributions commonly used in hydrologic analysis were estimated based on the method of probability weighted moments and the goodness of fit tests were applied to those distributions. As a result, the gamma-2 and gamma-3 distributions were selected as the appropriate models. The flood lovels and quantiles for selected return periods were calculated based on those distributions. Furthermore, frequency analysis using historical flood information was performed to overcome the misleading caused by missing data.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.10
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• pp.1378-1386
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• 2002

In the present study, velocity profile and wall shear stress distributions of developing turbulent oscillatory flows in an oscillator connected to straight duct located in exit region of a curved duct was investigated experimentally. The experimental study for air flows was conducted to measure axial velocity profiles, shear stress distributions by using the Laser Doppler Velocimetry(LDV) system with the data acquisition and processing system of Rotating Machinery Resolver(R.M.R) and PHASE software. The results obtained from experimental studies are summarized as follows. The critical Reynolds number for a change from transitional oscillatory flow to turbulent flow was about 7500, in the 60region of dimensionless axial position which was considered as a fully developed flow region. The turbulent oscillatory flow, velocity profiles of the inflow period in the entrance region were gradually developed, but those of the outflow period were not changed nearly. Velocity profiles of inflow and outflow were shown as a symmetric form in a fully developed flow region. The wall shear stress distributions of turbulent oscillatory flow increase rapidly as the flow proceeds to downstream and flow was in good agreement with the theoretically.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.8
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• pp.1131-1139
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• 2001

Experimental results are presented, which describe the effect of blowing ratio on film cooling from two rows of holes with opposite orientation angles. The inclination angle is fixed at 35°, and the orientation angles are set to be 45°for the downstream row, and -45°for the upstream row. The studied blowing ratios are 0.5, 1.0 and 2.0. The boundary layer temperature distributions are measured using thermocouple at two downstream locations. Detailed adiabatic film cooling effectiveness and heat transfer coefficient distributions are measured with TLC(Thermochromic Liquid Crystal). The adiabatic film cooling effectiveness and heat transfer coefficient distributions are discussed in connection with the injectant behaviors inferred from the boundary layer temperature distributions. Film cooling performance, represented by heat flux is evaluated from the adiabatic film cooling effectiveness and heat transfer coefficient data. The results show that the investigated geometry provides improved film cooling performance at the high blowing ratios of 1.0 and 2.0.

• Journal of Power System Engineering
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• v.3 no.1
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• pp.16-22
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• 1999

The purpose of this study is to prevent the stick, scuffing, scratch between piston and cylinder, is to contribute the piston design such as piston profile, clearance by calculating reaction force by over-lap of piston skirt, as measuring the temperature distributions of cylinder wall. The experiment has been peformed to obtain data during actual engine operation. Temperature gradient in peripheral and axial distributions of cylinder wall according to torque and speed of engine were measured by use of an 800cc class gasoline engine. The results obtained are summarized as follows ; 1) The temperature of cylinder wall at TDC was about $50{\sim}75^{\circ}C$ higher than temperature of cooling water. 2) The rear side temperature of top dead center was $141^{\circ}C$(1/4 load) in axial distribution, whereas the rear side of midway position temperature was $98^{\circ}C$. 3) The temperature of cylinder wall increased in according to rising temperature of cooling water. 4) The thrust side temperature of cylinder wall was about $15^{\circ}C$ in all load test. 5) The rear side temperature of top dead center was $159^{\circ}C$ (1/2 load) in peripheral distribution, it was about $39^{\circ}C$ higher than thrust side temperature.