• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.4
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• pp.790-805
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• 1988

Static strength and fatigue life scattering of glass fiber reinforced epoxy composite materials has been studied. Normal, lognormal, two-parameter and three-parameter Weibull distribution functions are used for strength and one-stress fatigue life distribution. The value of mean fatigue life is analysed using mean fatigue life, mean log fatigue life and expected value of 2 and 3-parameter Weibull distribution functions. Modification on non-statistical cumulative damage models is made in order to interpret the result of two-stress level fatigue life scattering. The comparison results show that 3-parameter Weibull distribution has better predictions in static strength and one-stress level fatigue life distributions. However, no advantage of 3-parameter Weibll distribution is found over 2-parameter Weibull distribution in two-stress level fatigue life predictions. It is found that two-stress level fatigue life prediction by the expanded equal rank assumption is close to the experimental data.

• The Korean Journal of Applied Statistics
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• v.16 no.2
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• pp.273-282
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• 2003

The problem of estimating the parameters of k-population Weibull distributions is discussed under the prior of ordered scale parameters. Parameters are estimated by the Gibbs sampling method. Since the conditional posterior distribution of the shape parameter in the Gibbs sampler is not log-concave, the shape parameter is generated by the adaptive rejection sampling. Finally, we applied this estimation methodology to the data discussed in Nelson (1970).

• Journal of the Korea Institute of Military Science and Technology
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• v.24 no.4
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• pp.401-407
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• 2021

To confirm the change of muzzle velocity and the most suitable probability distribution model of the 155 mm K9 howitzer barrel with chrome plating and changed rifling. Using a statistical program, the muzzle velocity were plotted on a normal distribution, a 2-parameter and 3-parameter Weibull distribution on a probability paper. Also, statistical parameters were estimated and muzzle velocity fitness test and probability of K676 charge were plotted. In both the chrome-plated with standard rifling and changed rifling for K9 barrel, the 2-parameter and 3-parameter Weibull distribution were skewed to the left compared to the normal distribution. It was confirmed that the muzzle velocity of the K9 barrel with chromium-plated is suitable for the normal distribution and 3-parameter Weibull distribution model.

• Proceedings of the KSME Conference
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• 2001.11a
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• pp.272-277
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• 2001

In order to evaluate variation of fatigue data of the LP steam turbine blade steel, it is important to estimate P - S - N curves to accurately define the probability distributions. In this study, new procedure is introduced to determine the expression of P - S - N curves. For this purpose, 3-parameter Weibull distribution was found to be most appropriate among assumed distributions when the probability distributions of the fatigue life were examined by the proposed analysis. Furthermore, parameter estimation for P - S - N curves was performed using various optimization to maximize the correlation coefficient. As a result of this, sequential linear programing method is used for estimation of P - S - N curves.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.36 no.1
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• pp.20-36
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• 2024

In this study, probabilistic models for the wave- and lifting forces were derived directly from long-term in-situ wave data embedding the Korean marine environment characteristics varying from sea to sea based on the Three-Parameter Weibull distribution. Korean marine environment characteristics varying from sea to sea carved out their presence on the probability coefficients of probabilistic models for wave- and lifting forces. Energetic wave conditions along the southern coast of Korea distinguish themselves from the others with a relatively large scale coefficient, small location coefficient, and shape coefficient around 1.3. On the other hand, mild marine environment along the western coast has a small variability, leading to small scale-coefficient, large location coefficient and shape coefficient around 2.0. In the sea off Mokpo, near the boundary between the South- and West Seas, marine environment was characterized by small scale-coefficient, large location coefficient, and shape coefficient around 1.2, implying that marine environments characteristics of the South-and West Sea coexist in the sea off Mokpo.

• Journal of Korean Society of Forest Science
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• v.90 no.2
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• pp.176-183
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• 2001

Loblolly pine (Pinus taeda L.) is the most economically important timber producing species in the southern United States. Much attention has been given to predicting diameter distributions for the solution of multiple-product yield estimates. The three-parameter Weibull diameter distribution yield prediction systems were developed for loblolly pine plantations. A parameter recovery procedure for the Weibull distribution function based on four percentile equations was applied to develop diameter distribution yield prediction models. Four percentiles (0th, 25th, 50th, 95th) of the cumulative diameter distribution were predicted as a function of quadratic mean diameter. Individual tree height prediction equations were developed for the calculation of yields by diameter class. By using individual tree content prediction equations, expected yield by diameter class can be computed. To reduce rounding-off errors, the Weibull cumulative upper bound limit difference procedure applied in this study shows slightly better results compared with upper and lower bound procedure applied in the past studies. To evaluate this system, the predicted diameter distributions were tested against the observed diameter distributions using the Kolmogorov-Smirnov two sample test at the ${\alpha}$=0.05 level to check if any significant differences existed. Statistically, no significant differences were detected based on the data from 516 evaluation data sets. This diameter distribution yield prediction system will be useful in loblolly pine stand structure modeling, in updating forest inventories, and in evaluating investment opportunities.

• Journal of Ocean Engineering and Technology
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• v.18 no.2
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• pp.64-69
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• 2004

The characteristics of the probability distribution for mechanical properties, e.g. tensile strength, reduction of area, and elongation, for STS304 stainless steel in elevated temperature are investigated. Tensile test is performed by constant crosshead speed controls with 1mm/min. The probability distribution function of measured mechanical properties seems to follow $\alpha$ 3-parameter Weibull, and shows a slight dependence on the temperature. When the temperature is raised, the shape parameter a is increased, but both the scale parameter $\beta$ and location parameter v are decreased.

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

• Journal of Ocean Engineering and Technology
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• v.10 no.2
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• pp.61-68
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• 1996

Weibull distribution function is applied very successfully to the strength of brittle materials such as ceramics and the weakest link model is applied to explain the ovents. This paper deals with the effect of specimen size on the strength of ceramics. The values of tensile strength were calculated by the Monte-Calro simuation. The tensile strength obtained was plotted on Weibull probabillity papers and represented by the 3-parameter Weibull distribution. The strength distribution function was compared with the theoretical weibull distribution. As a result, it was found that the Weibull shape parameter was changed due to the size and there was a possibility of a false indication as if the weakest link model holds good. We should be very careful when we apply the Weibull statistics to estimate the strength of products.

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