• Journal of Korea Water Resources Association
• /
• v.46 no.6
• /
• pp.643-653
• /
• 2013

The most important procedure in frequency analysis is to determine the appropriate probability distribution and to estimate quantiles for a given return period. To perform the frequency analysis, the goodness-of-fit tests should be carried out for judging fitness between obtained data from empirical probability distribution and assumed probability distribution. The previous goodness-of-fit could not consider enough extreme events from the recent climate change. In this study, the critical values of the modified Anderson-Darling test statistics were derived for 3-parameter Weibull distribution and power test was performed to evaluate the performance of the suggested test. Finally, this method was applied to 50 sites in South Korea. The result shows that the power of modified Anderson-Darling test has better than other existing goodness-of-fit tests. Thus, modified Anderson-Darling test will be able to act as a reference of goodness-of-fit test for 3-parameter Weibull model.

• Journal of the Korean Data and Information Science Society
• /
• v.26 no.1
• /
• pp.281-288
• /
• 2015

In this paper, the maximum likelihood estimators and confidence intervals for parameters of Weibull distribution are derived under three level constant stress accelerated life tests and the assumption that a log quadratic relationship exits between stress and the scale parameter ${\theta}$. The compound linear plan proposed by Kim (2006) is used to allocate the test units at each stress level, which performed nearly as good as the optimum quadratic plan and had the advantage of simplicity. Some simulation studies are given.

• Communications for Statistical Applications and Methods
• /
• v.30 no.4
• /
• pp.411-421
• /
• 2023

This paper provides a new estimation equation based on the concept of a minimum distance between the empirical and theoretical distribution functions under the most widely used progressive Type-II censoring scheme. For illustrative purposes, simulated and real datasets from a three-parameter Weibull distribution are analyzed. For comparison, the most popular estimation methods, the maximum likelihood and maximum product of spacings estimation methods, are developed together. In the analysis of simulated datasets, the excellence of the provided estimation method is demonstrated through the degree of the estimation failure of the likelihood-based method, and its validity is demonstrated through the mean squared errors and biases of the estimators obtained from the provided estimation equation. In the analysis of the real dataset, two types of goodness-of-fit tests are performed on whether the observed dataset has the three-parameter Weibull distribution under the progressive Type-II censoring scheme, through which the performance of the new estimation equation provided is examined.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.12 no.1
• /
• pp.11-17
• /
• 1999

Aging characteristics of the crosslinked polyethylene have been measured after applying electrical, thermal and combined stresses. ICP and FT-IR measurements confirmed diffusion of low molecular weight components such as antioxidant and presence of carbonyl group. Carbonyl group of aged crosslinked polyethylene under combined stress was detected by FT-IR. As deterioration of the crosslinked polyethylene progresses, crystallinity degree and density decrease. Also, dielectric properties have been measured by tan $\delta$ and $\varepsilon$$_{r}$ measurements. The three-parameter Weibull distribution was found to be the best suited among other probabilistic distribution representing the dielectric breakdown strength of aged crosslinked polyethylene. The scale parameter and location parameter decreases as the applied stress increases. The shape parameter increases as the stress increases.s.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.30 no.11 s.254
• /
• pp.1417-1424
• /
• 2006

In order to evaluate variation of fatigue life of mechanical components including engineering plastics, it is important to estimate probabilistic strain-life curves to accurately define the variation of fatigue characteristics. This paper intends to provide new assessment of P-$\varepsilon$-N (probabilistic strain-life curves) for considering the variation of fatigue characteristics in polyacetal. The fatigue strain controlled tests were conducted under constant 50% humidity and room temperature condition by a universal testing machine at strain ratio, R=0. A practical procedure is introduced to evaluate probabilistic strain-life curves. Three probabilistic distributions were used for generating P-$\varepsilon$-N curves such as normal, 2-parameter and 3-parameter Weibull. In this study, 3-parameter Weibull distribution was found to be most appropriate among assumed distributions when the probability distributions of the fatigue characteristic were examined using chi-square and Kolmogorov-Smirnov test. The more appropriate P-$\varepsilon$-N curves for these materials are generated by the proposed method considering 3-parameter Weibull distribution.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.66 no.3
• /
• pp.500-506
• /
• 2017

In 2014, ISO 55000s has been enacted and the power plant asset management is becoming a hot issue for all over the world. The asset management system is being developed as a combination of CBM(Condition Based Maintenance) and RCM(Reliability Centered Maintenance). Therefore, the research on the calculation of the failure rate which is the most basic index of RCM is actively carried out. The failure rate calculation has been going on for a long time, and the most widely used probability distribution is the Weibull distribution. In the Weibull distribution, the failure rate function is determined in three types according to the value of the shape parameter. However, the Weibull distribution has a limitation that it is difficult to apply it when the trend of failure rate changes-such as bathtub curves. In this paper, the failure rate is calculated using the mixture Weibull distribution which can appropriately express the change of the shape of the failure rate. Based on these results, we propose the necessity and validity of applying mixture Weibull distribution.

• Journal of Power System Engineering
• /
• v.21 no.5
• /
• pp.79-85
• /
• 2017

Vickers hardness is an important material in the design and reliability is required. Therefore, these values are very important as the basic data for design, manufacture and development, and the identification of quantitative probability distribution characteristics such as mean and dispersion is a very important parameter in design. In this study, Vickers hardness was measured after artificially heat-treated in the temperature range 753K, where chrome depletion near the grain boundary occurred for three kinds of stainless steels, and the Vickers hardness were evaluated. From the results, Vickers hardness increased with increasing heat treatment temperature. In Weibull distribution for Vickers hardness, the dispersion of STS310S at 813K and 873K was small, and the dispersion of STS316L at 753K, 933K and 993K was small. Also, STS347H exhibited the lowest dispersion at 753K in three kinds of stainless steels. The scale parameter increased with increasing heat treatment temperature in three kinds of stainless steels.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.35 no.10
• /
• pp.1281-1289
• /
• 2011

This paper deals with several statistical distribution functions for the analysis of fatigue life data of composite laminates for small wind-turbine blades. A series of tensile tests was performed on triaxial glass/epoxy laminates for loading directions of $0^{\circ}$, $45^{\circ}$, and $90^{\circ}$. Then, fatigue tests were carried out to determine the fatigue life at the aforementioned loading directions and the fatigue stresses at four levels. Two-parameter Weibull, three-parameter Weibull, normal, and log-normal distributions were used to fit the fatigue life data of the triaxial composite laminates. The three-parameter Weibull distribution most accurately described the fatigue life data measured experimentally for all the cases considered. Furthermore, the variation of fatigue life was simultaneously affected by the loading direction and fatigue stress level.

• Journal of the Korean Statistical Society
• /
• v.28 no.4
• /
• pp.415-433
• /
• 1999

This paper considers the design of step-stress accelerated life tests for the Weibull distribution with a nonconstant shape parameter under Type I censoring. It is assumed that scale and shape parameters are log-linear functions of (possibly transformed) stress and that a cumulative exposure model holds for the effect of changing stress. The asymptotic variance of the maximum likelihood estimator of a stated quantile at design stress is used as an optimality criterion. The optimum three step-stress plans are presented for selected values of design parameters and the effects of errors in pre- estimates of the design parameters are investigated.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.35 no.4
• /
• pp.375-381
• /
• 2011

The primary aim of this study is to investigate the probabilistic characteristics of the fatigue parameters that describe the fatigue crack growth behavior in magnesium alloy. Statistical fatigue crack propagation experiments have been performed on rolled AZ31 magnesium alloy CT specimens with different specimen thickness, load ratio, and maximum load at ambient temperature in a laboratory. Using the statistical fatigue data obtained from these experiments, the goodness-of-fit of the probability distribution of the fatigue behavior parameters is evaluated in this study by performing statistical analyses. The crack growth rate coefficient is a fatigue parameter having a very large COV(Coefficient of Variation), but the variation of a crack growth rate exponent is not substantial. It is considered that a crack growth rate exponent can be a material constant. It is also found that the best fit probability distribution of the parameters such as the crack growth rate coefficient and crack growth rate exponent for a magnesium alloy is a three-parameter Weibull distribution, and two-parameter Weibull distribution is a good distribution only for the crack growth rate coefficient.