• Title/Summary/Keyword: Log-normal distribution

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Studies on the Computerization of Reliability Paper (Ⅵ) (신뢰성 확률지의 전산화에 관한 연구 (Ⅵ))

  • 정수일
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.22 no.50
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    • pp.373-380
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    • 1999
  • This paper summerizes the former 5 papers that studied computer programming for the estimation of the Weibull, Extreme value, Hazard, Normal and Log-normal parameters which have a close relation with the reliability of the various kinds of industrial products. Probability paper is very commonly used in estimating the parameters, however, it is very hard to neglect the errors in plotting the data, and especially in drawing the regression line. The main purpose of this paper is to reduce these errors and to help the engineers to use the parameters in improving the reliability of their prod- ucts. The following parts are included in the computer programming with the em- phases on significant digits and rounding of numerical values : $\bullet$ data input part for various cases $\bullet$ parameter estimation part $\bullet$ printing part for input data $\bullet$ printing part for the results $\bullet$ printing part for the graphic(probability paper). And the running results(monitor displays) of the program for a fictitious example of Weibull distribution is given for the interested ones.

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A Comparison of Statistical Prediction Models in Household Water End-Uses (가정용수의 수요량 예측을 위한 통계적 모형 비교)

  • Myoung, Sung-Min;Lee, Doo-Jin;Kim, Hwa-Soo;Jo, Jin-Nam
    • The Korean Journal of Applied Statistics
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    • v.24 no.4
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    • pp.567-573
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    • 2011
  • This study develops a predictive model for household water end-uses based on data that have measured household characteristics, housing characteristics and other items, surveyed over 3 years in Korea. However, the measured data was left-skewed and it was not fitted to normal distribution. The parameter estimate were biased when using a multiple regression model. In addition, the results of the testing for the model were usually of significance due to the tiny residual from a large number of observations. In order to solve the problem, we suggested log-normal regression model and Weibull regression model as alternatives. The results of this study can be utilized in the planning stages of water and waste water facilities.

Effect of Composition on Cutting Characteristics and Reliability Analysis of Ti(C,N) Cermet Tool (Ti(C,N)계 서메트 공구의 조성변화에 따른 절삭성능 및 신뢰도 분석)

  • Park, June-Seuk;Kim, Seong-Won;Kwon, Won-Tae;Kang, Shin-Hoo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.26 no.11
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    • pp.2336-2341
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    • 2002
  • When WC and group IV elements are added to Ti(C,N)-Ni cermet, microstructures of the cermet is changed. The change effects directly on the property of the material. In this study, the amount of WC and group IV elements of Ti(C,N) cermet tool was investigated. The composition of WC was changed from 5 to 20wt% to determine the effect of WC on the cutting performance of cermet tool. The more WC was added, the longer the tool life of the cermet tool was. The cermet with lwt% ZrC and l4wt% WC showed the best cutting performance among the investigated cermet tools. The cutting performance of cermet cutting tools suggests the possibility in interrupted cutting for reliability test experimentation was performed repeatedly with $Ti(C_{0.7},N_{0.3})- l4WC-1ZrC-20Ni$ cermet tool machining SCM440. The flank wear of cermet cutting tool at given time condition is suitable for Normal distribution and Log normal distribution by Chi squared test.

Probabilistic Fatigue Life Evaluation of Rolling Stock Structures (철도차량 구조물의 확률론적 피로수명 평가)

  • 구병춘;서정원
    • Transactions of the Korean Society of Automotive Engineers
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    • v.11 no.5
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    • pp.89-94
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    • 2003
  • Rolling stock structures such as bogie frame and car body play an important role for the support of vehicle leading. In general, more than 25 years' durability is needed for them. A lot of study has been carried out for the prediction of the fatigue life of the bogie frame and car body in experimental and theoretical domains. One of the new methods is a probabilistic fatigue lift evaluation. The objective of this paper is to estimate the fatigue lift of the bogie frame of an electric car, which was developed by the Korea Railroad Research Institute (KRRI). We used two approaches. In the first approach probabilistic distribution of S-N curve and limit state function of the equivalent stress of the measured stress spectra are used. In the second approach, limit state function is also used. And load spectra measured by strain gauges are approximated by the two-parameter Weibull distribution. Other probabilistic variables are represented by log-normal and normal distributions. Finally, reliability index and structural integrity of the bogie frame are estimated.

Durability Analysis of Underground Structure based on Limit State Function Considering Carbonation (탄산화 기반의 한계상태함수를 활용한 지하구조물의 내구성 평가)

  • Choo, Jin-Ho;Lee, Tae-Jong;Yoon, Tae-Gook;Lee, Sang-Chul
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.18 no.3
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    • pp.69-75
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    • 2014
  • The priority of repair areas are chosen with the probability distribution of 0.3mm wide crack and carbonation induced corrosion. Data is analyzed and evaluated based on the 28 section of Precise Inspection for Safety and Diagnosis (PISD) in seoul. As the crack is distributed in log-normal, the carbonation and cover are in normal distribution. To have rational in repair sections among 503 sheets of underground structure, it is adopted the reliability index as well as the environment factors: strength, sonic speed, $CO_2$ concentration, corrosion, and content of chloride.

Concentrations of lead, iron, and zinc in blood of coal wokers' pneumoconiosis patients (탄광부 진폐증자의 혈액 중 납, 철 및 아연 농도)

  • Choi, Ho-Chun;Chung, Ho-Keun;Kim, Hae-Jeong
    • Journal of Preventive Medicine and Public Health
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    • v.22 no.4 s.28
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    • pp.486-494
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    • 1989
  • Lead, iron, and zinc concentrations in whole blood were determined by atomic absorption spectrophotometry, using a simple one-step dilution procedure, which were measured in 3 groups, 98 officers unexposed to dust or to metal, 58 coal miners without pneumoconiosis, and 113 coal workers' pneumoconiosis (CWP) patients. The results were as follows : 1. The precisions (C. V.%) of lead, iron, and zinc in blood were $12.65{\pm}6.95%,\;1.47{\pm}1.25%\;and\;6.35{\pm}3.34%$, respectively. 2. Lead and zinc in blood showed the log-normal distribution unlike iron in blood which showed normal distribution. 3. Lead, iron, and zinc concentrations in blood of 3 groups were follows : There was significant difference of concentration for zinc in blood by groups statistically. 4. The difference of lead, iron, and zinc concentrations in blood was not significant (p>0.05) by profusion on chest radiographs.

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Analysis of BOD Mean Concentration and Confidence Interval using Bootstrap Technique (Bootstrap 기법을 이용한 BOD 평균 농도 및 신뢰구간 분석)

  • Kim, Kyung Sub
    • Journal of Korean Society on Water Environment
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    • v.26 no.2
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    • pp.297-302
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    • 2010
  • It is very important to know mean and confidence interval of water-quality constituents such as BOD for water-quality control and management of rivers and reservoirs effectively. The mean and confidence interval of BOD at Anseong2 and Hwangguji3 sampling stations which are located at the border of local governments in Anseong Stream were estimated and analyzed in this paper using Bootstrap technique which is one of non-parametric statistics. The results of Bootstrap were compared with arithmetic mean, geometric mean, Biweight method mean as a point estimator and distribution mean came from the appropriate probability distribution of Log-normal. In Bootstrap technique 12 data set was randomly selected in each year and 1000 samples was produced to get parameter of population. Visual Basic for Applications (VBA) of Microsoft Excel was utilized in Bootstrap. It was revealed that the Bootstrap technique can be used to explain more rigorously and robustly the achievement or violation of BOD target concentration in Total Maximum Daily Load (TMDL).

The Step Stress Life Testing for the Parallel System with Censored Data (절단된 자료가 있는 병렬형 시스템의 단계적 충격수명검사)

  • Park, Hee-Chang;Lee, Suk-Hoon
    • Journal of Korean Society for Quality Management
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    • v.23 no.1
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    • pp.15-28
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    • 1995
  • We consider a step-stress life testing which is devised for a two-component parallel system with considerably long life time. To describe such a system, we use an exponential distribution as the survival function. The lift distribution is assumed between the log mean life time and the stress with the cumulative exposure model. The criterion for optimality is to minimize the sum of the variances of the maximum likelihood estimators of the mean life times of each part under the normal stress.

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Collection Efficiency of Electrostatic Precipitator using Moment Method (모멘트 방법을 이용한 전기집진기의 집진 효율)

  • 정창훈;이규원
    • Journal of Korean Society for Atmospheric Environment
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    • v.18 no.5
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    • pp.345-353
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    • 2002
  • A study of polydispersed aerosol dynamics by Electrostatic Precipitator (ESP) was carried out. The log-normal particle size distribution was assumed and moment method was considered. In order to apply moment method in Deutsch-Anderson equation, Cunningham slip correction factor and Cochet's charge equation were simplified for certain range of particle size. The three parameters, which explain the particle size distribution, such as total number concentration, geometric mean diameter, and geometric standard deviation were considered to derive the analytic solution. The obtained solution was compared with available numerical results (Bai et al., 1995). The comparison of the numerical and analytic results showed a good agreement.

MWD of Fractionated Polystyrene in Ultrasound Induced High Pressure Reactor (초음파가 조사된 고압반응기에서 분획된 Polystyrene의 분자량 분포특성)

  • Kim, H.H.;Lee, S.B.;Hong, I.K.
    • Elastomers and Composites
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    • v.32 no.3
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    • pp.173-178
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    • 1997
  • In this study, the ultrasonic irradiation in elevated pressure was used to alter the molecular weight and MWD of polystyrene. The high pressure reactor was filled with 0.5w/v% polystyrene solution, and then it was pressurized from 500psi to 4000psi. The ultrasound was irradiated in 10 minutes at each pressure, and the extract was collected and analyzed by GPC. Molecular weight distribution was predicted by log-normal and Schulz distribution function. The average molecular weight and polydispersity of polystyrene were decreased, as the pressure applied during the ultrasonic irradiation was increase. It was able to fractionate polymer material and control polydispersity by adjusting pressure in the ultrasonic irradiation.

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