• East Asian mathematical journal
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• v.35 no.1
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• pp.67-75
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• 2019

We investigate the averaging value of a random sampling of a Dirichlet series with some condition using Poisson distribution. Our result is the following: Let $L(s)={\sum}^{\infty}_{n=1}{\frac{a_n}{n^s}}$ be a Dirichlet series that converges absolutely for Re(s) > 1. If $X_t$ is an increasing random sampling with Poisson distribution and there exists a number $0<{\alpha}<{\frac{1}{2}}$ such that ${\sum}_{n{\leq}u}a_n{\ll}u^{\alpha}$, then we have $${\mathbb{E}}L(1/2+iX_t)=O(t^{\alpha}{\sqrt{{\log}t}})$$, for all sufficiently large t in ${\mathbb{R}}$. As a result, we get the behaviour of $L({\frac{1}{2}}+it)$ such that L is a Dirichlet L-function or a modular L-function, when t is sampled by the Poisson distribution.

• Communications for Statistical Applications and Methods
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• v.25 no.6
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• pp.647-658
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• 2018

In this paper, we study statistical inferences on the maximum likelihood estimation of a normal distribution when data are randomly censored. Likelihood equations are derived assuming that the censoring distribution does not involve any parameters of interest. The maximum likelihood estimators (MLEs) of the censored normal distribution do not have an explicit form, and it should be solved in an iterative way. We consider a simple method to derive an explicit form of the approximate MLEs with no iterations by expanding the nonlinear parts of the likelihood equations in Taylor series around some suitable points. The points are closely related to Kaplan-Meier estimators. By using the same method, the observed Fisher information is also approximated to obtain asymptotic variances of the estimators. An illustrative example is presented, and a simulation study is conducted to compare the performances of the estimators. In addition to their explicit form, the approximate MLEs are as efficient as the MLEs in terms of variances.

• Journal of Ocean Engineering and Technology
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• v.17 no.2
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• pp.54-59
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• 2003

The characteristics of the parameters for the probability distribution of fatigue crack growth life, using the non-Gaussian random process simulation method is investigated. In this paper, the material resistance to fatigue crack growth is treated as a spatial random process, which varies randomly on the crack surface. Using the previous experimental data, the crack length equals the number of cycle curves that are simulated. The results are obtained for constant stress intensity factor range conditions with stress ratios of R=0.2, three specimen thickness of 6, 12 and 18mm, and the four stress intensity level. The probability distribution function of fatigue crack growth life seems to follow the 3-parameter Wiubull,, showing a slight dependence on specimen thickness and stress intensity level. The shape parameter, $\alpha$, does not show the dependency of thickness and stress intensity level, but the scale parameter, $\beta$, and location parameter, ${\gamma}$, are decreased by increasing the specimen thickness and stress intensity level. The slope for the stress intensity level is larger than the specimen thickness.

• Journal of Electrical Engineering and Technology
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• v.12 no.5
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• pp.1743-1753
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• 2017

Since there are multiple random variables in the probabilistic load flow (PLF) calculation of distribution system containing distributed generation (DG) and electric vehicle charging load (EVCL), a Monte Carlo method based on composite sampling method is put forward according to the existing simple random sampling Monte Carlo simulation method (SRS-MCSM) to perform probabilistic assessment analysis of voltage quality of distribution system containing DG and EVCL. This method considers not only the randomness of wind speed and light intensity as well as the uncertainty of basic load and EVCL, but also other stochastic disturbances, such as the failure rate of the transmission line. According to the different characteristics of random factors, different sampling methods are applied. Simulation results on IEEE9 bus system and IEEE34 bus system demonstrates the validity, accuracy, rapidity and practicability of the proposed method. In contrast to the SRS-MCSM, the proposed method is of higher computational efficiency and better simulation accuracy. The variation of nodal voltages for distribution system before and after connecting DG and EVCL is compared and analyzed, especially the voltage fluctuation of the grid-connected point of DG and EVCL.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.11 s.242
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• pp.1472-1479
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• 2005

Multiple surface crack distributed randomly along a weld toe influences strongly on the fatigue crack propagation life of welded joint. It is investigated by using statistical approaches based on series of systematic experiments. From the statistical results, initial crack numbers and its locations follow the normal distribution, and the probability of initial crack depths and lengths can be described well by tile Weibull distribution. These characteristics are used to calculate the fatigue crack propagation life, in which the mechanisms of mutual interaction and coalescence of the multiple cracks are considered as well as the Mk-factors obtained from a parametric study on the crack depths and lengths. The automatic calculation is achieved by the NESUSS, where the parameters such as the number, location and size of the cracks are all treated as random variables. The random variables are dealt through the Monte-Carlo simulation with sampling random numbers of 2,000. The simulation results show that the multiple cracks lead to much shorter crack propagation life compared with those in single crack situation. The sum of the simulation and tile fatigue crack initiation life derived by the notch strain approach agrees well with the experiments.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2002.10a
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• pp.301-306
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• 2002

The characteristics of parameters for the probability distribution of fatigue crack growth lives by the non-Gaussian random process simulation method is investigated. In this paper, the material resistance to fatigue crack growth is treated as a spatial random process, which varies randomly on the crack surface. Using the previous experimental data, the crack length - the number of cycles curves are simulated. The results are obtained for constant stress intensity factor range conditions with stress ratio of R=0.2, three specimen thickness of 6, 12 and 18mm, and the four stress intensity level. The probability distribution function of fatigue crack growth lives seems to follow the 3-parameter Wiubull and shows a slight dependence on specimen thickness and stress intensity level. The shape parameter, ${\alpha}$, does not show the dependency of thickness and stress intensity level, but the scale parameter, ${\beta}$, and location parameter, ${\upsilon}$, are decreased by increasing the specimen thickness and stress intensity level. The slope for the stress intensity level is larger than the specimen thickness.

• Geotechnical Engineering
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• v.1 no.2
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• pp.67-74
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• 1985

A study is made on the determination of the total head distribution using the random walk theory within a confined flow system with complicated boundary conditions. Both nonhomogeniety and anisotropy of the aquifer are considered. The overlying on the aquifer may have sheet piles and the impervious boundary may be inclined. Use is made of the Monte Carlo simulation based on the random walk theory to determine the total head at a given Point. A computer program is developed for practical use. The proposed method was evaluated by comparing the results with those obtained by other method, i.e., the conventional flow net, the finite difference method, and the method of fragment. It is found that all the values are in reasonable agreement and the method is sufficiently accurate for practical use.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.461-472
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• 2015

The existence of initial imperfections in manufacturing or assembly of double-layer space structures having hundreds or thousands of members is inevitable. Many of the imperfections, such as the initial curvature of the members and residual stresses in members, are all random in nature. In this paper, the probabilistic effect of initial curvature imperfections in the load bearing capacity of double-layer grid space structures with different types of supports have been investigated. First, for the initial curvature imperfection of each member, a random number is generated from a gamma distribution. Then, by employing the same probabilistic model, the imperfections are randomly distributed amongst the members of the structure. Afterwards, the collapse behavior and the ultimate bearing capacity of the structure are determined by using nonlinear push down analysis and this procedure is frequently repeated. Ultimately, based on the maximum values of bearing capacity acquired from the analysis of different samples, structure's reliability is obtained by using Monte Carlo simulation method. The results show the sensitivity of the collapse behavior of double-layer grid space structures to the random distribution of initial imperfections and supports type.

• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.265-271
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• 2005

Randomness exists in engineering. Tolerance, assemble-error, environment temperature and wear make the parameters of a mechanical system uncertain. So the behavior or response of the mechanical system is uncertain. In this paper, the uncertain parameters are treated as random variables. So if the probability distribution of a random parameter is known, the simulation of mechanical multibody dynamics can be made by Monte-Carlo method. Thus multibody dynamics simulation results can be obtained in statistics. A new concept called functional reliability is put forward in this paper, which can be defined as the probability of the dynamic parameters(such as position, orientation, velocity, acceleration etc.) of the key parts of a mechanical multibody system belong to their tolerance values. A flexible mechanical arm with random parameters is studied in this paper. The length, width, thickness and density of the flexible arm are treated as random variables and Gaussian distribution is used with given mean and variance. Computer code is developed based on the dynamic model and Monte-Carlo method to simulate the dynamic behavior of the flexible arm. At the same time the end effector's locating reliability is calculated with circular tolerance area. The theory and method presented in this paper are applicable on the dynamics modeling of general multibody systems.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.04a
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• pp.59-62
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• 2000

In this study, the distribution of the effective modulus was investigated statistically Plain weave structures were modeled with random stacking phase shift angles and the effective modulus was calculated by the unit cell analysis. The analysis results indicated that the effect of random phase shift angles was significant on the modulus distribution. As the number of layers increased, the coefficient of variation decreased and higher degree of homogeneity was attained.