• Korean Journal of Agricultural and Forest Meteorology
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• v.12 no.2
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• pp.83-94
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• 2010

The objective of this study was to determine the best probability distributions of annual, seasonal and monthly precipitation in Korea. Data observed at 32 stations in Korea were analyzed using the L-moment ratio diagram and the average weighted distance (AWD) to identify the best probability distributions of each precipitation. The probability distribution was best represented by 3-parameter Weibull distribution (W3) for the annual precipitation, 3-parameter lognormal distribution (LN3) for spring and autumn seasons, and generalized extreme value distribution (GEV) for summer and winter seasons. The best probability distribution models for monthly precipitation were LN3 for January, W3 for February and July, 2-parameter Weibull distribution (W2) for March, generalized Pareto distribution (GPA) for April, September, October and November, GEV for May and June, and log-Pearson type III (LP3) for August and December. However, from the goodness-of-fit test for the best probability distributions of the best fit, GPA for April, September, October and November, and LN3 for January showed considerably high reject rates due to computational errors in estimation of the probability distribution parameters and relatively higher AWD values. Meanwhile, analyses using data from 55 stations including additional 23 stations indicated insignificant differences to those using original data. Further studies using more long-term data are needed to identify more optimal probability distributions for each precipitation.

• Journal of Power System Engineering
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• v.21 no.5
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• pp.13-19
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• 2017

The effect of heat treatment temperature (HTT) on the mechanical properties of polyacrylonitrile (PAN)-based carbon fiber had been investigated. The heat treatment on the carbon fiber was conducted under high vacuum atmosphere of $10^{-6}mmHg$, and the range of temperature of $1,000^{\circ}C$ to $2,000^{\circ}C$. As a results, The tensile strength of carbon fiber and carbon fiber composites showed increasing tendency with the rise of heat treatment temperature. And, the shape parameter of Weibull distribution for the strength of carbon single fiber showed an increasing trend until $1,800^{\circ}C$. But the shape parameter of Weibull distribution for the strength of carbon fiber composites showed no clear tendency with the rise of heat treatment temperature. The cause of reinforcement effect of the carbon fiber by the heat treatment was regarded as the carbonization of carbon single fiber.

• Proceedings of the Korea Concrete Institute Conference
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• 2003.05a
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• pp.311-314
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• 2003

Concrete structures such as bridge, pavement, airfield, and offshore structure are normally subjected to repeated load. This paper proposes a failure probability models of concrete subjected to split tension repeated-loads, based on experimental results. The fatigue tests were performed at the stress ratio of 0.1, the loading shape of sine, the frequency of 20Hz, and the stress levels of 90, 80 and 70%. The fatigue test specimen was 150mm in diameter and 75mm in thickness. The fatigue analysis did not include which exceeded 0.9 of statistical coefficient of determination values or did not failure at 2$\times$$10^6$ cycles. The graphical method, the moment method, and maximum likelihood estimation method were used to obtain Weibull distribution parameters. The goodness-of-fit test by Kolmogorov-Smirnov test was acceptable 5% level of significance. As a result, the proposed failure probability model based on the two-parameter($\alpha and \mu$) Weibull distribution was good enough to estimate accurately the fatigue life subjected to tension mode.

• Journal of Korean Society for Quality Management
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• v.24 no.2
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• pp.65-76
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• 1996

In general, most industrial products exhibit bath-tub shaped curve for their failure rate functions. This distributional life model can be obtained by the Piecewise Weibull distribution. The least squares, maximum likelihood, and mixed methods of estimating the parameters of the Piecewise Weibull distribution are compared. The comparison is made by using the empirical mean squared errors of (a) the parameter estimates and (b) the estimated change-points, to summarize the results of 1000 simulated samples of three sizes - each 100, 150 and 200. The results are that the mixed method estimation comes to be the best as the sample sizes increase.

• Journal of Ocean Engineering and Technology
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• v.10 no.4
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• pp.38-50
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• 1996

Recently carbon fiber reinforced plastic (CFRP) has been used structural materials in corrosive environment such as for water, chemical tank and pipes. However, mechanical properties of such materials may be change when CFRP and exposed to corrosive environment for long periods of time. The degradation behavior of carbon fiber/epoxy resin composite material in distilled water is investigated using acoustic emission (AE) technique, Fracture toughness tests are performed on the compact tension specimens that are pilled by two types of $[O_2/9O_2]_{3s}$ and $[O/9O]_6s$. During the testes, AE test was carried out to monitor the damage of CFRP by moisture absorption. The data was treated by 2-parameter Weibull distribution and the fracture surface was observed by scanning electron microscope.

• Journal of Korean Society for Quality Management
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• v.11 no.1
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• pp.10-17
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• 1983

This paper studies item-life test plans with the specified item mean life $T_1$ (MTBF) - Producer's risk ${\alpha}$ and item mean life $T_2$ (MTBF, $T_2$ < $T_1$) - Consumer's risk ${\beta}$ when the probability of item survival follows the Weibull distribution (known shape parameter) as a expansion of [1]. And Operating Characteristic Curves and Average Life-testing Times of item-life test plans are computed for this paper and [1]. Cost analysis procedures are same as [1]. These results are computed by using computer program written in Level II Basic for Apple II Plus Micro-computer. Both this paper and [6] reduce the life-testing time for Weibull distribution in comparision with Exponential distribution, but results of [6] were computed for different criterions from this paper.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.5
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• pp.1829-1831
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• 2012

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates. Methods: We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010. Results: In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg" are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time. Conclusions: The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.

• Journal of Korean Society of Water and Wastewater
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• v.34 no.4
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• pp.251-258
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• 2020

Sewer deterioration models are needed to forecast the remaining life expectancy of sewer networks by assessing their conditions. In this study, the serious defect (or condition state 3) occurrence probability, at which sewer rehabilitation program should be implemented, was evaluated using four probability distribution functions such as normal, lognormal, exponential, and Weibull distribution. A sample of 252 km of CCTV-inspected sewer pipe data in city Z was collected in the first place. Then the effective data (284 sewer sections of 8.15 km) with reliable information were extracted and classified into 3 groups considering the sub-catchment area, sewer material, and sewer pipe size. Anderson-Darling test was conducted to select the most fitted probability distribution of sewer defect occurrence as Weibull distribution. The shape parameters (β) and scale parameters (η) of Weibull distribution were estimated from the data set of 3 classified groups, including standard errors, 95% confidence intervals, and log-likelihood values. The plot of probability density function and cumulative distribution function were obtained using the estimated parameter values, which could be used to indicate the quantitative level of risk on occurrence of CS3. It was estimated that sewer data group 1, group 2, and group 3 has CS3 occurrence probability exceeding 50% at 13th-year, 11th-year, and 16th-year after the installation, respectively. For every data groups, the time exceeding the CS3 occurrence probability of 90% was also predicted to be 27th- to 30th-year after the installation.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.9 no.2
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• pp.141-147
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• 2016

NHPP software reliability models for failure analysis can have, in the literature, exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, infinite failures NHPP models that repairing software failure point in time reflects the situation, was presented for comparing property. Commonly used in the field of software reliability based on Flexible Weibull extension distribution software reliability of infinite failures was presented for comparison problem. The result is that a relatively small shaping parameter was effectively. The parameters estimation using maximum likelihood estimation was conducted and model selection was performed using the mean square error and the coefficient of determination.. In this research, software developers to identify software failure property follows shape parameter, some extent be able to help is considered.

• Journal of Biomedical Engineering Research
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• v.37 no.1
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• pp.21-30
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• 2016

Weibull distribution with two parameters, shape (k) and scale (s) parameters are used to model the fatigue failure analysis due to periodic vortex shedding of the synovial fluid in knee joints. In order to determine the later parameter, a suitable statistical model is required for velocity distribution of synovial fluid flow. Hence, wide applicability of Weibull distribution in life testing and reliability analysis can be applied to describe the probability distribution of synovial fluid flow velocity. In this work, comparisons of three most widely used methods for estimating Weibull parameters are carried out; i.e. the least square estimation method (LSEM), maximum likelihood estimator (MLE) and the method of moment (MOM), to study fatigue failure of bone joint due to periodic vortex shedding of synovial fluid. The performances of these methods are compared through the analysis of computer generated synovial fluidflow velocity distribution in the physiological range. Significant values for the (k) and (s) parameters are obtained by comparing these methods. The criterions such as root mean square error (RMSE), coefficient of determination ($R^2$), maximum error between the cumulative distribution functions (CDFs) or Kolmogorov-Smirnov (K-S) and the chi square tests are used for the comparison of the suitability of these methods. The results show that maximum likelihood method performs well for most of the cases studied and hence recommended.