• Earthquakes and Structures
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• v.25 no.6
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• pp.429-442
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• 2023

To study the seismic vulnerability of the composite material structure of adobe and timber, we collected and statistically analysed empirical observation samples of 542,214,937 m² and 467,177 buildings that were significantly impacted during the 179 earthquakes that occurred in mainland China from 1976 to 2010. In multi-intensity regions, combined with numerical analysis and a probability model, a non-linear continuous regression model of the vulnerability, considering the empirical seismic damage area (number of buildings) and the ratio of seismic damage, was established. Moreover, a probability matrix model of the empirical seismic damage mean value was provided. Considering the coupling effect of the annual and seismic fortification factors, an empirical seismic vulnerability curve model was constructed in the multiple-intensity regions. A probability matrix model of the mean vulnerability index (MVI) was proposed, and was validated through the above-mentioned reconnaissance sample data. A matrix model of the MVI of the regions (19 provinces in mainland China) based on the parameter (MVI) was established.

• The Korean Journal of Applied Statistics
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• v.9 no.2
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• pp.83-94
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• 1996

The probability of Yut was calculated by using the physical property in previous study, but this article suggested empirical estimators for probability of Yut. In practice, physics-based probability imposes too strong assumptions, which result in the difference between the calculated probabilies and empirical relative frequencies. Experiment shows the probabilities of Yut depend on the integrated shape of Yut rather than the floor type. Maximum likelihood estimator and empirical Bayes estimators are compared and all turn out to be almost identicla for more than 40 trials. For smaller number of trials, Bayes estimators are recommended for its stability. Regression approach is also adopted as an easy-to-use method without empirical trials.

• International Journal of Reliability and Applications
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• v.14 no.2
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• pp.107-114
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• 2013

Modelling of failures is an important element of reliability modelling. Empirical modelling approach suitable for complex item is explored in this paper. First step of the empirical modelling approach is to plot hazard function, density function, Weibull probability plot as well as cumulative intensity function to see which model fits best for the given data. Next step of the empirical modelling approach is select appropriate model for the data and fit the parametric model accordingly and estimate the parameters.

• Earthquakes and Structures
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• v.22 no.6
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• pp.609-623
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• 2022

To study the empirical seismic fragility of a reinforced concrete girder bridge, based on the theory of numerical analysis and probability modelling, a regression fragility method of a rapid fragility prediction model (Gaussian first-order regression probability model) considering empirical seismic damage is proposed. A total of 1,069 reinforced concrete girder bridges of 22 highways were used to verify the model, and the vulnerability function, plane, surface and curve model of reinforced concrete girder bridges (simple supported girder bridges and continuous girder bridges) considering the number of samples in multiple intensity regions were established. The new empirical seismic damage probability matrix and curve models of observation frequency and damage exceeding probability are developed in multiple intensity regions. A comparative vulnerability analysis between simple supported girder bridges and continuous girder bridges is provided. Depending on the theory of the regional mean seismic damage index matrix model, the empirical seismic damage prediction probability matrix is embedded in the multidimensional mean seismic damage index matrix model, and the regional rapid prediction matrix and curve of reinforced concrete girder bridges, simple supported girder bridges and continuous girder bridges in multiple intensity regions based on mean seismic damage index parameters are developed. The established multidimensional group bridge vulnerability model can be used to quantify and predict the fragility of bridges in multiple intensity regions and the fragility assessment of regional group reinforced concrete girder bridges in the future.

• The Mathematical Education
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• v.48 no.3
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• pp.353-358
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• 2009

The article discusses the independence concept occurring in the learning of probability. The author does not distinguishes the independence in the events from the independence in the trials. Instead, the author suggests the physico-empirical independence and the logico-mathematical independence to distinguish between the two concepts.

• Journal for History of Mathematics
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• v.31 no.5
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• pp.251-269
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• 2018

Empirical probability and classical probability, which are two interpretations of Kolmogorov's axiom, are two ways to recognize the chances of events occurring in the real world. In this paper, I analyzed and suggested the contents of the high school textbooks ${\ll}$Probability and Statistics${\gg}$, associated with two interpretations of probability and experiments on which two interpretations are based. By presenting the cases required expressly stating what the experiment is for supporting students' understanding of some concepts, it was discussed that stating or not stating what the experiment is should be carefully determined by the educational intent. Especially, I suggested that in the textbooks we contrast the good idea of calculating the ratios of two possibilities in the imaginary world of the classical probability with the normal idea of grasping the chances of events through the frequencies in the real world of the empirical probability, with distinguishing the experiments in two interpretations of probability. I also suggested that in the textbooks we make it clear that the Weak Law of Large Numbers justifies our expectations of the frequencies' reflecting the chances of events occurring in the real world under ideal conditions. Teaching and learning about the aesthetic elements and the practicality of imaginary mathematical thinking supported by these textbooks statements could be one form of Humanities education in mathematics as STEAM education.

• Nuclear Engineering and Technology
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• v.45 no.2
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• pp.151-164
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• 2013

A key input for the assessment of Human Error Probabilities (HEPs) with Human Reliability Analysis (HRA) methods is the evaluation of the factors influencing the human performance (often referred to as Performance Shaping Factors, PSFs). In general, the definition of these factors and the supporting guidance are such that their evaluation involves significant subjectivity. This affects the repeatability of HRA results as well as the collection of HRA data for model construction and verification. In this context, the present paper considers the TAsk COMplexity (TACOM) measure, developed by one of the authors to quantify the complexity of procedure-guided tasks (by the operating crew of nuclear power plants in emergency situations), and evaluates its use to represent (objectively and quantitatively) task complexity issues relevant to HRA methods. In particular, TACOM scores are calculated for five Human Failure Events (HFEs) for which empirical evidence on the HEPs (albeit with large uncertainty) and influencing factors are available - from the International HRA Empirical Study. The empirical evaluation has shown promising results. The TACOM score increases as the empirical HEP of the selected HFEs increases. Except for one case, TACOM scores are well distinguished if related to different difficulty categories (e.g., "easy" vs. "somewhat difficult"), while values corresponding to tasks within the same category are very close. Despite some important limitations related to the small number of HFEs investigated and the large uncertainty in their HEPs, this paper presents one of few attempts to empirically study the effect of a performance shaping factor on the human error probability. This type of study is important to enhance the empirical basis of HRA methods, to make sure that 1) the definitions of the PSFs cover the influences important for HRA (i.e., influencing the error probability), and 2) the quantitative relationships among PSFs and error probability are adequately represented.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.195-205
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• 1995

• Communications for Statistical Applications and Methods
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• v.18 no.2
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• pp.245-255
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• 2011

There are two nonparametric methods that use empirical distribution functions and probability density estimators for the test of the distribution change of data. In this paper we investigate the two methods precisely and summarize the results of previous research. We assume several probability models to make a simulation study of the change point analysis and to examine the finite sample behavior of the two methods. Empirical powers are compared to verify which is better for each model.

• Journal for History of Mathematics
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• v.19 no.3
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• pp.43-56
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• 2006

This paper aims to introduce a construction method for the 'Wooden Die for Drinking Game' and to find some geometrical structures and mathematics educational viewpoints. As the results, we get two methods which are eventually same with Figure 5 and Figure 6-3. We proved the ground that classical probability of this Die's each side showing up is one out of fourteen and introduced few other empirical probabilities with Table 1 to Table 3. Also, some Chinese characters were corrected and re-interpreted. In fact, 象人打鼻 changed to 衆人打鼻, and 醜物 is interpreted as 'ugly animal' such as frog, toad, earthworm or pine caterpillar.