• Title/Summary/Keyword: Weibull Distribution Equation

Search Result 45, Processing Time 0.032 seconds

Data Analysis of Insulating Reliability Properties in Polymer for PCB (PCB용 고분자의 절연 신뢰도 특성 데이터 분석)

  • Park, Geon-Ho
    • Proceedings of the Korean Society of Computer Information Conference
    • /
    • 2015.01a
    • /
    • pp.289-290
    • /
    • 2015
  • 본 연구에서는 인쇄회로기판(PCB)용 재료로 널리 사용되는 고분자에 대해서 와이블 분포 방정식의 시뮬레이션을 수행하여 절연 신뢰도 특성 데이터를 분석하였다. 와이블 분포에 대한 분석 시뮬레이션을 통하여 일반적으로 허용 절연 파괴 확률을 0.1[%] 이하라고 설정하였을 때, 첨가제 배합비를 5종으로 구분한 각 시편에 대해서 인가 전계의 허용치를 각각 계산할 수 있었다.

  • PDF

A Stochastic Analysis of Variation in Fatigue Crack Growth of 7075-T6 Al alloy (7075-T6 A1 합금의 피로균열진전의 변동성에 대한 확률론적 해석)

  • Kim, Jung-Kyu;Shim, Dong-Suk
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.20 no.7
    • /
    • pp.2159-2166
    • /
    • 1996
  • The stochastic properties of variation in fatigue crack growth are important in reliability and stability of structures. In this study,the stochastic model for the variation of fatigue crack growth rate was proposed in consideration of nonhomogeneity of materials. For this model, experiments were ocnducted on 7075-T6 aluminum alloy under the constant stress intensity factor range. The variation of fatigue crack growth rate was expressed by random variables Z and r based on the variation of material coefficients C and m in the paris-Erodogan's equation. The distribution of fatigue life with respect to the stress intensity factor range was evaluated by the stochastic Markov chain model based on the Paris-Erdogan's equation. The merit of proposed model is that only a small number of test are required to determine this this function, and fatigue crack growth life is easily predicted at the given stress intensity factor range.

Development of Diameter Distribution Change and Site Index in a Stand of Robinia pseudoacacia, a Major Honey Plant (꿀샘식물 아까시나무의 지위지수 도출 및 직경분포 변화)

  • Kim, Sora;Song, Jungeun;Park, Chunhee;Min, Suhui;Hong, Sunghee;Yun, Junhyuk;Son, Yeongmo
    • Journal of Korean Society of Forest Science
    • /
    • v.111 no.2
    • /
    • pp.311-318
    • /
    • 2022
  • We conducted this study to derive the site index, which is a criterion for the planting of Robinia pseudoacacia, a honey plant, and to investigate the diameter distribution change by derived site index. We applied the Chapman-Richards equation model to estimate the site index of the Robinia pseudoacacia stand. The site index was distributed within the range of 16-22 when the base age was 30 years. The fitness index of the site index estimation model was low, but we judged that there was no problem in the application because the residual distribution of the equation had not shifted to one side. We used the Weibull diameter distribution function to determine the diameter distribution of the Robinia pseudoacacia stand by site index. We used the mean diameter and the dominant tree height as independent variables to present the diameter distribution, and our analysis procedure was to estimate and recover the parameters of the Weibull diameter distribution function. We used the mean diameter and the dominant tree height of the Robinia pseudoacacia stand to show distribution by diameter class, and the fitness index for dbh distribution estimation was about 80.5%. As a result of schematizing the diameter distribution by site indices as a 30-year-old, we found that the higher the site index, the more the curve of the diameter distribution moved to the right. This suggests that if the plantation were to be established in a high site index stand, considering the suitable trees on the site, the growth of Robinia pseudoacacia woul d become active, and not onl y the production of wood but al so the production of honey would increase. We therefore anticipate that the site index classification table and curve of this Robinia pseudoacacia stand will become the standard for decision making in the plantation and management of this tree.

Reliability Analysis of Gas Turbine Engine Blades (가스터빈 블레이드의 신뢰성 해석)

  • Lee, Kwang-Ju;Rhim, Sung-Han;Hwang, Jong-Wook;Jung, Yong-Wun;Yang, Gyae-Byung
    • Journal of the Korean Society for Aeronautical & Space Sciences
    • /
    • v.36 no.12
    • /
    • pp.1186-1192
    • /
    • 2008
  • The reliability of gas turbine engine blades was studied. Yield strength, Young’s modulus, engine speed and gas temperature were considered as statistically independent random variables. The failure probability was calculated using five different methods. Advanced Mean Value Method was the most efficient without significant loss in accuracy. When random variables were assumed to have normal, lognormal and Weibull distributions with the same means and standard deviations, the CDF of limit state equation did not change significantly with the distribution functions of random variables. The normalized sensitivity of failure probability with respect to standard deviations of random variables was the largest with gas temperature. The effect of means and standard deviations of random variables was studied. The increase in the mean of gas temperature and the standard deviation of engine speed increased the failure probability the most significantly.

Lifetime Prediction of Geogrids for Reinforcement of Embankments and Slopes through Time-Temperature Superposition

  • Koo, Hyun-Jin;Kim, You-Kyum;Kim, Dong-Whan
    • Corrosion Science and Technology
    • /
    • v.4 no.4
    • /
    • pp.147-154
    • /
    • 2005
  • The creep resistance of geogrids is one of the most significant long-term safety characteristics used as the reinforcement in slopes and embankments. The failure of geogrids is defined as creep strain greater than 10%. In this study, the accelerated creep tests were applied to polyester geogrids at various loading levels of 30, 50% of the yield strengths and temperatures using newly designed test equipment. Also, the new test equipment permitted the creep testing at or above glass transition temperature($T_g$) of 75, 80, $85^{\circ}C$. The time-dependent creep behaviors were observed at various temperatures and loading levels. And then the creep curves were shifted and superposed in the time axis by applying time-temperature supposition principles. The shifting factors(AFs) were obtained using WLF equation. In predicting the lifetimes of geogrids, the underlying distribution for failure times were determined based on identification of the failure mechanism. The results confirmed that the failure distribution of geogrids followed Weibull distribution with increasing failure rate and the lifetimes of geogrids were close to 100 years which was required service life in the field with 1.75 of reduction factor of safety. Using the newly designed equipment, the creep test of geogrids was found to be highly accelerated. Furthermore, the time-temperature superposition with the newly designed test equipment was shown to be effective in predicting the lifetimes of geogrids with shorter test times and can be applied to the other geosynthetics.

Estimation of Stand Yield and Carbon Stock for Robinia pseudoacacia Stands in Korea (아까시나무 임분의 임목수확량 및 탄소저장량 추정)

  • Son, Yeong Mo;Kim, So Won;Lee, Sun Jeoung;Kim, Jeong Soo
    • Journal of Korean Society of Forest Science
    • /
    • v.103 no.2
    • /
    • pp.264-269
    • /
    • 2014
  • The aim of this study was to determine the current distribution area of Robinia pseudoacacia habitat and to estimate its stand yield as well as its carbon stocks. In order to do so, the area of R. pseudoacacia distribution is obtained based on the large-scaled forest type map (1:5,000). Also, Weibull diameter distribution model is used to predict the yield of R. pseudoacacia stands. In addition, carbon emission factor is applied to calculate carbon stocks and removals. To obtain the stand yield of R. pseudoacacia, we developed estimation equation considering growth factors of the stand, e.g. mean diameter, the basal area, maximum and minimun diameter and etc. and tested it to ensure accuracy. Consequently, estimation equation derived from all growth factors have shown significance that could also be used for analysis. Site index was also established to determine the productivity of the forestland that later turned out to be ranging from 16 to 22. Based on these results, stand yield tables were drawn up. R. pseudoacacia is widely distributed in inland areas of Gyeongsang, Chungcheong and Gyeonggi provinces which covers total area of 26,770 ha. And when it is converted into carbon stocks, it amounts to 2,517,598tC with annual carbon uptake of 3.76tC/ha which is comparable to Querqus species that is known to storer large amounts of carbon. Therefore, R. pseudoacacia is also expected to serve as a viable carbon pool that would contribute to the mitigation of climate change. Furthermore, stand yield tables, an outcome of this survey would assist not only in proper management but also in sustainable management policy of R. pseudoacacia.

Determination of No-Failure Test Times for the Life Test of Hydraulic System Components (유압시스템 구성품의 수명시험을 위한 무고장 시험시간의 산출)

  • Lee, S.R.;Kim, H.E.
    • Transactions of The Korea Fluid Power Systems Society
    • /
    • v.3 no.3
    • /
    • pp.8-13
    • /
    • 2006
  • It is very important for the manufacturers to predict the life of hydraulic system components according to the results of life tests. Since it takes too much time to test the hydraulic system components until failure, the no-failure test method is applied for the life test of them. If the shape parameter of Weibull distribution, the number of samples, the confidence level, and the assurance life are given, the no-failure test times of hydraulic system components can be calculated by given equation. Here, the procedures to obtain the no-failure test times of the hydraulic system components such as hydraulic motors and pumps, hydraulic cylinders, hydraulic valves, hydraulic accumulators, hydraulic hoses, and hydraulic filters are described briefly.

  • PDF

Estimation and Application of Reliability Values for Strength of Material Following Gamma Distribution (감마분포를 따르는 재료강도의 신뢰도 예측과 응용)

  • Park, Sung-Ho;Kim, Jae-Hoon
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.36 no.2
    • /
    • pp.223-230
    • /
    • 2012
  • The strength of brittle material has commonly been characterized by a normal distribution or Weibull distribution, but it may fit the gamma distribution for some material. The use of an extreme value distribution is proper when the largest values of a set of stresses dominate the failure of the material. This paper presents a formula for reliability estimation based on stress-strength interference theory that is applicable when the strength of material is distributed like a gamma distribution and the stress is distributed like an extreme value distribution. We verified the validity of the equation for the reliability estimation by examining the relationships among the factor of safety, the coefficient of variation, and the reliability. The required minimum factor of safety and the highest allowable coefficient of variation of stress can be estimated by choosing an objective reliability and estimating the reliabilities obtained for various factors of safety and coefficients of variation.

Strength Evaluation and Eailure Analysis of Unidirectional Composites Using Monte-Carlo Simulation (몬테카를로 시뮬레이션을 이용한 일방향 복합재의 강도평가 및 파손 해석)

  • Kim, Jeong-Gyu;Park, Sang-Seon;Kim, Cheol-Su;Kim, Il-Hyeon
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.24 no.12
    • /
    • pp.2917-2925
    • /
    • 2000
  • Tensile strength and failure process of composite materials depend on the variation in fiber strength, matrix properties and fiber-matrix interfacial shear strength. A Monte-Carlo simulation considering variation in these factors has been widely used to analyze such a complicated phenomenon as a strength and simulated the failure process of unidirectional composites. In this study, a Monte Carlo simulation using 2-D and 3-D(square and hexagonal array) model was performed on unidirectional graphite/epoxy and glass/polyester composites. The results simulated by using 3-D hexagonal array model have a good agreement with the experimental data which were tensile strength and failure process of unidirectional composites.

Statistical Analysis for Creep Crack Growth Behavior of Modified 9Cr-1Mo Steel (Modified 9Cr-1Mo 강의 크리프 균열성장 거동에 관한 통계적 해석)

  • Jung, Ik-Hee;Kim, Woo-Gon;Yin, Song-Nan;Ryu, Woo-Seog;Kim, Seon-Jin
    • Korean Journal of Metals and Materials
    • /
    • v.47 no.5
    • /
    • pp.283-289
    • /
    • 2009
  • This paper dealt with a statistical analysis for evaluating the creep crack growth rate (CCGR) for Modified 9Cr-1Mo (ASTM Grade 91) steel. The CCGR data was obtained by the creep crack growth (CCG) tests conducted under various applied loads at $600^{\circ}C$. To obtain logically the B and q values used in the CCGR equation, three methods such as the least square fitting method (LSFM), the mean value method (MVM) and the probabilistic distribution method (PDM) were adopted and their CCGR lines were compared, respectively. In addition, a number of random variables were generated by using the Monte Carlo simulation (MCS), and the CCGR lines were predicted probabilistically. It was found that both the B and q coefficients followed a 2-parameter Weibull distribution well. In the case of the ranges of 10-90% for the probability variables, P(B, q), the CCGR lines were predicted. Fractographic study was conducted from the specimen after the CCG tests.