• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.595-610
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• 2021

Recently a few articles have derived robust first-order rotatable and D-optimal designs for the lifetime response having distributions gamma, lognormal, Weibull, exponential assuming errors that are correlated with different correlation structures such as autocorrelated, intra-class, inter-class, tri-diagonal, compound symmetry. Practically, a first-order model is an adequate approximation to the true surface in a small region of the explanatory variables. A second-order model is always appropriate for an unknown region, or if there is any curvature in the system. The current article aims to extend the ideas of these articles for second-order models. Invariant (free of the above four distributions) robust (free of correlation parameter values) second-order rotatable designs have been derived for the intra-class and inter-class correlated error structures. Second-order rotatability conditions have been derived herein assuming the response follows non-normal distribution (any one of the above four distributions) and errors have a general correlated error structure. These conditions are further simplified under intra-class and inter-class correlated error structures, and second-order rotatable designs are developed under these two structures for the response having anyone of the above four distributions. It is derived herein that robust second-order rotatable designs depend on the respective error variance covariance structure but they are independent of the correlation parameter values, as well as the considered four response lifetime distributions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1241-1250
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• 1996

The characteristics of fatigue cumulative damage and fatigue life of 8-harness satin woven CFRP composites with a circular hole under constant amplitude and 2-level block loading are estimated by Stochastic Makov chain model. It is found in this study that the fatigue damage accumulation behavior is very random and the fatigue damage is accumulated as two regions under constant amplitude fatigue loading. In constant amplitude fatigue loading the predicted mean number of cycles to a specified damage state by Markov chain model shows a good agreement with the test result. The predicted distribution of the fatigue cumulative damage by Markov chain model is similar to the test result. The fatigue life predictions under 2-level block loading by Markov chain model revised are good fitted to the test result more than by 2-parameter Weibull distribution function using percent failure rule.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.3
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• pp.509-521
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• 1994

This study is an effort to develop computer simulation model that produce precipitation patterns from stochastic model. A stochastic model is formulated for the process of daily precipitation with considering the sequences of wet and dry days and the precipitation amounts on wet days. This study consists of 2 papers and the process of precipitation occurrence is modelled by an alternate renewal process (ARP) in paper (I). In the ARP model for the precipitation occurrence, four discrete distributions, used to fit the wet and dry spells, were as follows; truncated binomial distribution (TBD), truncated Poisson distribution (TPD), truncated negative binomial distribution (TNBD), logarithmic series distribution (LSD). In companion paper (II) the process of occurrence is developed by Markov chain. The amounts of precipitation, given that precipitation has occurred, are described by a Gamma. Pearson Type-III, Extremal Type-III, and 3 parameter Weibull distribution. Daily precipitation series model consists of two models, A-Wand A-G model, by combining the process of precipitation occurrence and a continuous probability distribution on the precipitation of wet days. To evaluate the performance of the simulation model, output from the model was compared with historical data of 7 stations in the Nakdong and Seomjin river basin. The results of paper (1) show that it is possible to design a model for the synthetic generation of IX)int precipitation patterns.

• Structural Engineering and Mechanics
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• v.63 no.6
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• pp.809-824
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• 2017

The accurate evaluation of wind characteristics and wind-induced structural responses during a typhoon is of significant importance for bridge design and safety assessment. This paper presents an expectation maximization (EM) algorithm-based angular-linear approach for probabilistic modeling of field-measured wind characteristics. The proposed method has been applied to model the wind speed and direction data during typhoons recorded by the structural health monitoring (SHM) system instrumented on the arch Jiubao Bridge located in Hangzhou, China. In the summer of 2015, three typhoons, i.e., Typhoon Chan-hom, Typhoon Soudelor and Typhoon Goni, made landfall in the east of China and then struck the Jiubao Bridge. By analyzing the wind monitoring data such as the wind speed and direction measured by three anemometers during typhoons, the wind characteristics during typhoons are derived, including the average wind speed and direction, turbulence intensity, gust factor, turbulence integral scale, and power spectral density (PSD). An EM algorithm-based angular-linear modeling approach is proposed for modeling the joint distribution of the wind speed and direction. For the marginal distribution of the wind speed, the finite mixture of two-parameter Weibull distribution is employed, and the finite mixture of von Mises distribution is used to represent the wind direction. The parameters of each distribution model are estimated by use of the EM algorithm, and the optimal model is determined by the values of $R^2$ statistic and the Akaike's information criterion (AIC). The results indicate that the stochastic properties of the wind field around the bridge site during typhoons are effectively characterized by the proposed EM algorithm-based angular-linear modeling approach. The formulated joint distribution of the wind speed and direction can serve as a solid foundation for the purpose of accurately evaluating the typhoon-induced fatigue damage of long-span bridges.

• Progress in Superconductivity and Cryogenics
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• v.17 no.3
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• pp.13-17
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• 2015

In superconducting coil applications particularly in wet wound coils, coated conductor (CC) tapes are subjected to different type of stresses. These include hoop stress acting along the length of the CC tape and the Lorentz force acting perpendicular to the CC tape's surface. Since the latter is commonly associated with delamination problem of multi-layered CC tapes, more understanding and attention on the delamination phenomena induced in the case of coil applications are needed. Difference on the coefficient of thermal expansion (CTE) of each constituent layer of the CC tape, the bobbin, and the impregnating materials is the main causes of delamination in CC tapes when subjected to thermal cycling. The CC tape might also experience cyclic loading due to the energizing scheme (on - off) during operation. In the design of degradation-free superconducting coils, therefore, characterization of the delamination behaviors including mechanism and strength in REBCO CC tapes becomes critical. In this study, transverse tensile tests were conducted under different loading conditions using different size of upper anvils on the GdBCO CC tapes. The mechanical and electromechanical delamination strength behaviors of the CC tapes under transverse tensile loading were examined and a two-parameter Weibull distribution analysis was conducted in statistical aspects. As a result, the CC tape showed similar range of mechanical delamination strength regardless of cross-head speed adopted. On the other hand, cyclic loading might have affected the CC tape in both upper anvil sizes adopted.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.36 no.2
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• pp.50-60
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• 2024

To promote the application of reliability-based design within the Korean coastal engineering community, the author conducted reliability analyses and optimized the design of a vertical-type breakwater, considering multiple limit states in the seas off of Pusan and Gunsan - two representative ports in Korea. In this process, rather than relying on design waves of a specific return period, the author intentionally avoided such constraints. Instead, the author characterized the uncertainties associated with wave force, lift force, and overturning moment - key factors significantly influencing the integrity of a vertical-type breakwater. This characterization was achieved by employing a probabilistic model derived from the frequency analysis results of long-term in-situ wave data. The limit state of the vertical-type breakwater encompassed sliding, overturning, and collapse failure, with the close interrelation between wave force, lift force, and moment described using the Nataf joint probability distribution. Simulation results indicate, as expected, that considering only sliding failure underestimates the failure probability. Furthermore, it was shown that the failure probability of vertical-type breakwaters cannot be consistently secured using design waves with a specific return period. In contrast, breakwaters optimally designed to meet the reliability index requirement of 𝛽-3.5 to 4 consistently achieve a consistent failure probability across all sea areas.

• Progress in Superconductivity and Cryogenics
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• v.7 no.2
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• pp.21-26
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• 2005

Breakdown characteristics and survival probability of turn-to-turn models were investigated under ac and impulse voltage at 77K. For experiments, two test electrode models were fabricated: One is point contact model and the other is surface contact model. Both are made of copper wrapped by O.025mm thick polyimide film(Kapton). The experimental results were analyzed statistically using Weibull distribution in order to examine the wrapping number effects on voltage-time characteristics under ac voltage as well as under impulse voltage in LN$_{2}$. Also survival analysis were performed according to the Kaplan-Meier method. The breakdown voltages of surface contact model are lower than that of point contact model, because the contact area of surface contact model is wider than that of point contact model. Besides, the shape parameter of point contact model is a little bit larger than that of surface contact model. The time to breakdown t$_{50}$ is decreased as the applied voltage is increased, and the lifetime indices slightly are increased as the number of layers is increased. According to the increasing applied voltage and decreasing wrapping number, the survival probability is increased.

• Journal of the Korean Data Analysis Society
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• v.20 no.6
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• pp.2813-2827
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• 2018

Progressive censoring schemes have become quite popular in reliability study. Under progressive censored data, however, some units can be failed between two points of observation with exact times of failure of these units unobserved. For example, loss may arise in life-testing experiments when the failure times of some units were not observed due to mechanical or experimental difficulties. Therefore, multiply progressive censoring scheme was introduced. So, we derives a maximum likelihood estimator of the parameter of exponential distribution. And we introduced the goodness-of-fit test statistics using order statistic and Lorenz curve. We carried out Monte Carlo simulation to compare the proposed test statistics. In addition, real data set have been analysed. In Weibull and chi-squared distributions, the test statistics using Lorenz curve are more powerful than test statistics using order statistics.

• Korean journal of applied entomology
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• v.55 no.1
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• pp.35-43
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• 2016

The temperature-dependent development of Metcalfa pruinosa overwintering eggs was investigated at ten constant temperatures (12.5, 15, 17.5, 20, 22.5, 25, 27.5, 30, 32.5, and $35{\pm}1^{\circ}C$, Relative Humidity 20~30%). All individuals collected before April 13, 2012 failed to develop into first instar larvae. In contrast, some individuals that were collected on April 11, 2013 successfully developed when reared under $20{\sim}32.5^{\circ}C$ temperature regimes. The developmental duration was shortest at $30^{\circ}C$ (13.3 days) and longest at $15^{\circ}C$ (49.6 days) in the fourth collected colony (April 26 2013). Developmental duration decreased with increasing temperature up to $30^{\circ}C$ and development was retarded at high-temperature regimes ($32.5^{\circ}C$). The lower developmental threshold was $10.1^{\circ}C$ and the thermal constant required to complete egg overwintering was 252DD. The Lactin 2 model provided the best statistical description of the relationship between temperature and the developmental rate of M. pruinosa overwintering eggs ($r^2=0.99$). The distribution of the developmental completion of overwintering eggs was well described by the 2-parameter Weibull function ($r^2=0.92$) based on the standardized development duration. However, the estimated cumulative 50% spring emergence dates of overwintering eggs were best predicted by poikilotherm rate model combined with the 2-parameter Weibull model (average difference of 1.7days between observed and estimated dates).

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2004.11a
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• pp.356-362
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• 2004

Using multi wrapped copper by polyimide film for HTS transformer, the breakdown and V-t characteristics of two type models for turn-to-turn, one is point contact model, the other is surface contact model, were investigated under ac and impulse voltage at 77 K. A material that is Polyimide film (Kapton) 0.025 mm thickness is used for multi wrapping of the electrode. Statistical analysis of the results using Weibull distribution to examine the wrapping number effects on V-t characteristics under at voltage as well as breakdown voltage under ac and impulse voltage in $LN_2$ was carried. Also, survival analysis was performed according to the Kaplan-Meier method. The breakdown voltages for surface contact model are lower than that of the point contact model, because the contact area of surface contact model is wider than that of point contact model. At the same time, the shape parameter of the point contact model is a little bit larger than the of the surface contact model. The time to breakdown tn is decreased as the applied voltage is increased, and the lifetime indices slightly are increased as the number of layers is increased. According to the increasing applied voltage and decreasing wrapping number, the survival probability is increased.