• 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.

• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.325-337
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• 2017

In this paper, we proposed a new long-term lifetime distribution with four parameters inserted in a risk competitive scenario with decreasing, increasing and unimodal hazard rate functions, namely the Weibull-Poisson long-term distribution. This new distribution arises from a scenario of competitive latent risk, in which the lifetime associated to the particular risk is not observable, and where only the minimum lifetime value among all risks is noticed in a long-term context. However, it can also be used in any other situation as long as it fits the data well. The Weibull-Poisson long-term distribution is presented as a particular case for the new exponential-Poisson long-term distribution and Weibull long-term distribution. The properties of the proposed distribution were discussed, including its probability density, survival and hazard functions and explicit algebraic formulas for its order statistics. Assuming censored data, we considered the maximum likelihood approach for parameter estimation. For different parameter settings, sample sizes, and censoring percentages various simulation studies were performed to study the mean square error of the maximum likelihood estimative, and compare the performance of the model proposed with the particular cases. The selection criteria Akaike information criterion, Bayesian information criterion, and likelihood ratio test were used for the model selection. The relevance of the approach was illustrated on two real datasets of where the new model was compared with its particular cases observing its potential and competitiveness.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2002.05a
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• pp.104-109
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• 2002

In this paper, a statistical analysis of fatigue crack growth behavior under constant amplitude loads has been carried out. Fatigue crack growth tests were conducted on sixteen pre-cracked compact tension (CT) specimens of the pressure vessel (SPV50) steel in controlled identical load and environmental conditions. The assessment of the statistical distribution of fatigue crack growth experimental data obtained from SPV50 steel was studied and also the correlation of the parameter C and m in the Paris-Erdogan law was discussed. The probability distribution function of fatigue crack growth life seems to follow the 3-parameter Weibull. The fatigue crack growth rate seems to follow the 3-parameter Weibull and the log-normal distribution. The coefficient of variation (COV) of fatigue crack growth life was observed to decrease as the crack grows. A strong negative linear correlation exists between the coefficient C and the exponent m in Paris model. Fatigue crack growth rate data shows a normal distribution for both m and logC.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.9
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• pp.767-773
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• 2016

A Weibull statistical analysis of the mechanical properties of SiC ceramics was carried out by immersion in acidic and alkaline solutions. The heat treatment was carried out at 1373 K. The corrosion of SiC was carried out in acidic and alkaline solutions under KSL1607. The bending strength of corroded crack-healed specimens decreased 47% and 70% compared to those of uncorroded specimens in acidic and alkaline solutions, respectively. The corrosion of SiC ceramics is faster in alkaline solution than in acid solution. The scale and shape parameters were evaluated for the as-received and corroded materials, respectively. The shape parameter of the as-received material corroded in acidic and alkaline solutions was significantly more apparent in the acidic solution. Further, the heat-treated material was large in acidic solution but small in alkaline solution. The shape parameters of the as-received and heat-treated materials were smaller in both acidic and alkaline solutions.

• Proceedings of the KIEE Conference
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• 1997.07e
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• pp.1702-1704
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• 1997

본 논문은 HDPE 필름의 절연성능을 평가하기 위하여 절연파괴강도의 결과를 Weibull분에 적용하였다. 각 절연파괴강도의 Weibull분포로부터 형의 모수를 구하였다. 또한 Weibull분포의 활용은 2개 및 3개의 모수법을 각각 적용시켜 절연파괴강도의 평가를 하였다. HDPE 필름을 열화시켜, 형의 모수변화를 비교하였다. 이와같은 Weibull분포의 활용은 절연성능과 수명의 평가를 통계적으로 평가코져 한다.

• Advances in Energy Research
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• v.8 no.2
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• pp.95-110
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• 2022

Wind energy can be utilized for the generation of electricity, due to significant wind potential at different parts of the world, some countries have already been generating of electricity through wind. Pakistan is still well behind and has not yet made any appreciable effort for the same. The objective of this work was to add some new strategies to calculate Weibull parameters and assess wind energy potential. A new approach calculates Weibull parameters; we also developed an alternate formula to calculate shape parameters instead of the gamma function. We obtained k (shape parameter) and c (scale parameter) for two-parameter Weibull distribution using five statistical methods for five different cities in Pakistan. Maximum likelihood method, Modified Maximum likelihood Method, Method of Moment, Energy Pattern Method, Empirical Method, and have been to calculate and differentiate the values of (shape parameter) k and (scale parameter) c. The performance of these five methods is estimated using the Goodness-of-Fit Test, including root mean square error, mean absolute bias error, mean absolute percentage error, and chi-square error. The daily 10-minute average values of wind speed data (obtained from energydata.info) of different cities of Pakistan for the year 2016 are used to estimate the Weibull parameters. The study finds that Hyderabad city has the largest wind potential than Karachi, Quetta, Lahore, and Peshawar. Hyderabad and Karachi are two possible sites where wind turbines can produce reasonable electricity.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.2
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• pp.308-313
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• 2009

This paper presents a reliability analysis of S-bonds for AF track circuits, which detect train movement and transmit a speed control signal to the train. Field survey shows that S-bonds are exposed to very large vibrations transferred from rail, and suffer from frequent failures when they were installed on ballasted track. We collected the time-to-failure data of S-bonds from the maintenance field of Seoul metro line 2, and made a parametric approach to estimate the statistical distribution that fits the time-to-failure data. The analysis shows that S-bonds have time-to-failure characteristics described by Weibull distribution. The estimated shape parameter of Weibull distribution is 1.1, which means the distribution has constant failure rate characteristics like exponential distribution. The reliability function, hazard function, percentiles and mean lifetime are derived for maintenance support.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.3
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• pp.365-372
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• 2013

In this study, a statistical method for evaluating the fatigue life of a vehicle muffler was used to obtain reliable fatigue data using a limited number of specimens. Cyclic bending tests were conducted using specimens manufactured to be exactly the same as the mufflers installed in cars that are currently in use. To estimate the fatigue life by comparing the data obtained during the fatigue tests, the most suitable probability density function for the normal, lognormal, and Weibull distributions was selected. A goodness-of-fit test was performed on the probability distributions, and then a Weibull distribution using the least square method was selected. By using the selected Weibull distribution, the probability-moment-life curves (P-M-N curve) reflecting the fatigue characteristics were suggested as the data for the reliable design of a muffler.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.19
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• pp.8371-8376
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• 2014

Background: The use of statistical methods has become an imperative tool in breast cancer survival data analysis. The purpose of this study was to develop the best statistical probability model using the Bayesian method to predict future survival times for the black non-Hispanic female breast cancer patients diagnosed during 1973-2009 in the U.S. Materials and Methods: We used a stratified random sample of black non-Hispanic female breast cancer patient data from the Surveillance Epidemiology and End Results (SEER) database. Survival analysis was performed using Kaplan-Meier and Cox proportional regression methods. Four advanced types of statistical models, Exponentiated Exponential (EE), Beta Generalized Exponential (BGE), Exponentiated Weibull (EW), and Beta Inverse Weibull (BIW) were utilized for data analysis. The statistical model building criteria, Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Deviance Information Criteria (DIC) were used to measure the goodness of fit tests. Furthermore, we used the Bayesian approach to obtain the predictive survival inferences from the best-fit data based on the exponentiated Weibull model. Results: We identified the highest number of black non-Hispanic female breast cancer patients in Michigan and the lowest in Hawaii. The mean (SD), of age at diagnosis (years) was 58.3 (14.43). The mean (SD), of survival time (months) for black non-Hispanic females was 66.8 (30.20). Non-Hispanic blacks had a significantly increased risk of death compared to Black Hispanics (Hazard ratio: 1.96, 95%CI: 1.51-2.54). Compared to other statistical probability models, we found that the exponentiated Weibull model better fits for the survival times. By making use of the Bayesian method predictive inferences for future survival times were obtained. Conclusions: These findings will be of great significance in determining appropriate treatment plans and health-care cost allocation. Furthermore, the same approach should contribute to build future predictive models for any health related diseases.