• Journal of Korean Society for Quality Management
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• v.35 no.3
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• pp.107-117
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• 2007

The fatigue has been considered the most failure mode of metal, ceramic, and composite materials. In this paper, numerical experiments to asses the usefulness of two Dixon's methods(small and large samples) and 14 S-N methods on assumptions of lognormal fatigue limit distribution under RFL(Random Fatigue Limit) model are conducted for staircase(or up-and-down) test and compared by MSE(Mean Squared Error) and bias for estimates of mean log-fatigue limit. Also, guidelines for staircase test plans to choose initial stress level and step size are recommended from numerical experiments including sensitivity analyses. In addition, the parametric bootstrap method to construct a confidence interval for the mean of log-fatigue limit by the percentile method using a transition probability matrix of Markov chain is presented and illustrated with an example.

• The Korean Journal of Applied Statistics
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• v.34 no.5
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• pp.697-710
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• 2021

Relative error prediction is preferred over ordinary prediction methods when relative/percentile errors are regarded as important, especially in econometrics, software engineering and government official statistics. The relative error prediction techniques have been developed in linear/nonlinear regression, nonparametric regression using kernel regression smoother, and stationary time series models. However, random effect models have not been used in relative error prediction. The purpose of this article is to extend relative error prediction to some of generalized linear mixed model (GLMM) with panel data, which is the random effect models based on gamma, lognormal, or inverse gaussian distribution. For better understanding, the real auto insurance data is used to predict the claim size, and the best predictor and the best relative error predictor are comparatively illustrated.

• The Journal of the Korea institute of electronic communication sciences
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• v.9 no.2
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• pp.187-194
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• 2014

In this paper, we analyze the outage probability of macro diversity combining in cellular networks in consideration of aggregate interference from other mobile stations (MSs). Different from existing works analyzing the outage probability of macro diversity combining, we focus on a diversity gain attained by selecting a base station (BS) subject to relatively low aggregate interference. In our model, MSs are randomly located according to a Poisson point process. The outage probability is analyzed by approximating the multivariate distribution of aggregate interferences on multiple BSs by a multivariate lognormal distribution.

• Earthquakes and Structures
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• v.10 no.2
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• pp.429-450
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• 2016

An attempt has been made to incorporate the concept of collapse safety margin into the procedures proposed in the performance-based earthquake engineering (PBEE) framework for direct earthquake loss estimation, in which the collapse probability curve obtained from incremental dynamic analysis (IDA) is mathematically characterized with the S-type fitting model. The regressive collapse probability curve is then used to identify non-collapse cases and collapse cases. With the assumed lognormal probability distribution for non-collapse damage indexes, the expected direct earthquake loss ratio is calculated from the weighted average over several damage states for non-collapse cases. Collapse safety margin is shown to be strongly related with sustained damage endurance of structures. Such endurance exhibits a strong link with expected direct earthquake loss. The results from the case study on three concrete frames indicate that increase in cross section cannot always achieve a more desirable output of collapse safety margin and less direct earthquake loss. It is a more effective way to acquire wider collapse safety margin and less direct earthquake loss through proper enhancement of reinforcement in structural components. Interestingly, total expected direct earthquake loss ratio seems to be insensitive a change in cross section. It has demonstrated a consistent correlation with collapse safety margin. The results also indicates that, if direct economic loss is seriously concerned, it is of much significance to reduce the probability of occurrence of moderate and even severe damage, as well as the probability of structural collapse.

• Earthquakes and Structures
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• v.7 no.1
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• pp.57-82
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• 2014

The heritage value of the mixed wood-masonry 18th century Pombalino buildings of downtown Lisbon is recognized both nationally and internationally. The present paper focuses on the seismic assessment of global response and retrofitting of a typical Pombalino building by nonlinear static analyses, performed by the research software Tremuri, which is able to model 3D configurations. The structure is modelled using nonlinear beams for masonry panels, while in case of the internal walls (frontal walls) an original formulation has been developed in order to take into account their specific seismic behaviour. Floors are modelled as orthotropic membrane finite elements: this feature allows to simulate the presence of both flexible and rigid diaphragms, being the first ones more representative of the original state while the second ones of retrofitted configurations. Seismic assessment has been evaluated by applying nonlinear static procedure and comparing the performance of different configurations (by considering various retrofitting strategies). Finally, assuming a lognormal cumulative distribution, fragility curves are obtained to be representative of Pombalino buildings: the most important application of such curves is for seismic risk and loss estimation analyses.

• 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.

• Journal of Food Hygiene and Safety
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• v.34 no.2
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• pp.199-204
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• 2019

This study aimed to generate a probability distribution model based on temperature data of frozen food storage facility as input variables for microbial risk assessment (MRA). We visited 8 food-handling businesses to collect temperature data from their cold storage warehouses. The overall mean temperature inside the storage facilities was $-20.48{\pm}3.08^{\circ}C$, with 20.4% of the facilities having above $-18^{\circ}C$, with minimum and maximum temperature values of -10.3 and $-25.80^{\circ}C$ respectively. Temperature distributions by space locations of natural and forced convection were $-22.57{\pm}0.84$ and $-17.81{\pm}1.47^{\circ}C$, $-22.49{\pm}1.05$ and $-17.94{\pm}1.44^{\circ}C$, and $-22.68{\pm}1.03$ and $-18.08{\pm}1.42^{\circ}C$ in the upper (2.4~4 m), middle (1.5~2.4 m), and lower (0.7~1.5 m) shelves, respectively. Probability distributions from the temperature data were obtained using the program @RISK. Statistical ranking was determined using goodness of fit to determine the probability distribution model. Our results show that a log-normal distribution [5.9731, 3.3483, shift (-26.4281)] is most appropriate for relative MRA conduction.

• Structural Engineering and Mechanics
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• v.68 no.6
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• pp.747-760
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• 2018

In the present study, a methodology for developing fragilities of arch concrete dams to assess their performance against seismic hazards is introduced. Firstly, the probability risk and fragility curves are presented, followed by implementation and representation of the way this method is used. Amirkabir arch concrete dam was subjected to non-linear dynamic analyses. A modified three dimensional rotating smeared crack model was used to take the nonlinear behavior of mass concrete into account. The proposed model considers major characteristics of mass concrete. These characteristics are pre-softening behavior, softening initiation criteria, fracture energy conservation, suitable damping mechanism and strain rate effect. In the present analysis, complete fluid-structure interaction is included to account for appropriate fluid compressibility and absorptive reservoir boundary conditions. In this study, the Amirkabir arch concrete dam is subjected to a set of 8 three-component earthquakes each scaled to 10 increasing intensity levels. Using proposed nonlinear smeared crack model, nonlinear analysis is performed where the structure is subjected to a large set of scaled and un-scaled ground motions and the maximum responses are extracted for each one and plotted. Based on the results, fragility curves were plotted according to various and possible damages indexes. Discrete damage probabilities were calculated using statistical methods for each considered performance level and incremental nonlinear analysis. Then, fragility curves were constructed based on the lognormal distribution assumption. Two damage indexes were introduced and compared to one another. The results indicate that the dam has a proper stability under earthquake conditions at MCE level. Moreover, displacement damages index is more conservative and impractical in the fragility analysis than tensional damage index.

• Steel and Composite Structures
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• v.19 no.4
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• pp.811-827
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• 2015

This paper presents a probabilistic investigation of American and European specifications (i.e., AISC and Eurocode 4) for square concrete-filled steel tubular (CFT) stub columns. The study is based on experimental results of 100 axially loaded square CFT stub columns from the literature. By comparing experimental results for ultimate loads with code-predicted column resistances, the uncertainty of resistance models is analyzed and it is found that the modeling uncertainty parameter can be described using random variables of lognormal distribution. Reliability analyses were then performed with/without considering the modeling uncertainty parameter and the safety level of the specifications is evaluated in terms of sufficient and uniform reliability criteria. Results show that: (1) The AISC design code provided slightly conservative results of square CFT stub columns with reliability indices larger than 3.25 and the uniformness of reliability indices is no better because of the quality of the resistance model; (2) The uniformness of reliability indices for the Eurocode 4 was better than that of AISC, but the reliability indices of columns designed following the Eurocode 4 were found to be quite below the target reliability level of Eurocode 4.

• Earthquakes and Structures
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• v.18 no.6
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• pp.709-718
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• 2020

Fragility curves are useful tools to estimate the damage probability of buildings owing to seismic actions. The purpose of this study is to investigate seismic vulnerability of reinforced concrete (RC) buildings, according to the 2007 and 2018 Turkish Seismic Codes, using fragility curves. For the numerical analyses, typical five- and seven-storey RC buildings were selected and incremental dynamic analyses (IDA) were performed. To complete the IDAs, eleven earthquake acceleration records multiplied by various scaling factors from 0.2g to 0.8g were used. To predict nonlinearity, a distributed hinge model that involves material and geometric nonlinearity of the structural members was used. Damages to confined concrete and reinforcement bar of structural members were obtained by considering the unit deformation demands of the 2007 Turkish Seismic Code (TSC-2007) and the 2018 Turkey Building Earthquake Code (TBEC-2018). Vulnerability evaluation of these buildings was performed using fragility curves based on the results of incremental dynamic analyses. Fragility curves were generated in terms of damage levels occurring in confined concrete and reinforcement bar of structural members with a lognormal distribution assumption. The fragility curves show that the probability of damage occurring is more according to TBEC-2018 than according to TSC-2007 for selected buildings.