• 전자공학회논문지A
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• 제32A권6호
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• pp.67-74
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• 1995

This paper proposes the step-stress type-I censoring model for analyzing the data of accelerated life test and reducing the time of accelerated life test. In order to obtain the data of accelerated life test, the step-stress accelerated life test was run with voltage stress to CMOS Hex Buffer. The Weibull distribution, the Inverse-power-law model and Maximum likelihood method were used. The iterative procedure using modified-quasi-linearization method is applied to solve the nonlinear equation. The proposed Weibull step-stress type-I censoring model exactly estimases the life time of units, while reducting the time of accelerated life test and the equipments of test.

• International Journal of Safety
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• 제1권1호
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• pp.36-42
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• 2002

This paper is aimed at predicting the life of rubber insulating gloves under normal operating stresses from relatively rapid test performed at higher stresses. Specimens of rubber insulating gloves are subject to multiple stress conditions, i.e. combined electrical and thermal stresses. Two modes of electrical stress, step voltage stress and constant voltage stress are used in specimen aging. There are two types of test for electrical stress in this experiment: the one is Breakdown Voltage (BDV) test under step voltage stress and thermal stress and the other is lifetime test under constant voltage stress and temperature stress. The ac breakdown voltage defined as the break-down point of insulation that leakage current excesses a limit value, l0mA in this experiment, is determined. Because the very high variability of aging data requires the application of statistical model, Weibull distribution is used to represent the failure times as the straight line on Weibull probability paper. Weibull parameters are deter-mined by three statistical methods i.e. maximum likelihood method, graphical method and least squares method, which employ SAS package, Weibull probability paper and FORTRAN, respectively. Two chosen models for predicting the life under simultaneous electrical and thermal stresses are inverse power model and exponential model. And the constants of life equation for multistress aging are calculated using numerical method, such as Gauss Jordan method etc.. The completion of life equation enables to estimate the life at normal stress based on the data collected from accelerated aging test. Also the comparison of the calculated lifetimes between the inverse power model and the exponential model is carried out. And the lifetimes calculated by three statistical methods with lower voltage than test voltage are compared. The results obtained from the suggested experimental method are presented and discussed.

• 전기학회논문지
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• 제68권1호
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• pp.52-60
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• 2019

In this paper, four types of insulation coils were fabricated by adding various kinds of glycols to improve the flexibility and adhesion of insulating coils in varnish dispersed with PAI / Nano Silica_15wt%. The applied voltage and frequency were 1.5 kV / 20 kHz for accelerated life evaluation. Through the 6th temperature stress level, the cause of the insulation breakdown of the coil was ignored and only the breakdown time was measured. The Arrhenius model was chosen based on the theoretical relationship between chemical reaction rate and temperature for estimating the insulation life of the coil due to accelerated thermal stress. Three types of distributions (Weibull, Lognormal, Exponential) were selected as the relationship between thermal stress model and distribution. The average insulation lifetime was estimated under the temperature stress of four types of insulation coils through the relationship between one kind of model and three kinds of distributions.

• Journal of the Korean Statistical Society
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• 제28권4호
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• pp.415-433
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• 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.

• Communications for Statistical Applications and Methods
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• 제30권2호
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• pp.191-213
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• 2023

Unit distributions are frequently used in probability theory and statistics to depict meaningful variables having values between zero and one. Using convenient transformation, the unit inverse exponentiated weibull (UIEW) distribution, which is equally useful for modelling data on the unit interval, is proposed in this study. Quantile function, moments, incomplete moments, uncertainty measures, stochastic ordering, and stress-strength reliability are among the statistical properties provided for this distribution. To estimate the parameters associated to the recommended distribution, well-known estimation techniques including maximum likelihood, maximum product of spacings, least squares, weighted least squares, Cramer von Mises, Anderson-Darling, and Bayesian are utilised. Using simulated data, we compare how well the various estimators perform. According to the simulated outputs, the maximum product of spacing estimates has lower values of accuracy measures than alternative estimates in majority of situations. For two real datasets, the proposed model outperforms the beta, Kumaraswamy, unit Gompartz, unit Lomax and complementary unit weibull distributions based on various comparative indicators.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1275-1301
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• 2023

This paper introduced the Weibull Marshall-Olkin Power Lomax (WMOPL) distribution. The statistical aspects of the proposed model are presented, such as the quantiles function, moments, mean residual life and mean deviations, variance, skewness, kurtosis, and reliability measures like the residual life function, and stress-strength reliability. The parameters of the new model are estimated using six different methods, and simulation research is illustrated to compare the six estimation methods. In the end, two real data sets show that the Weibull Marshall-Olkin Power Lomax distribution is flexible and suitable for modeling data.

• 전산구조공학
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• 제1권1호
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• pp.113-122
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• 1988

본 연구에서는 강도로교의 피로파손의 위험을 예측할 수 있는 실용적 모형을 개발하였다. 제안된 피로해석 모형은 피로신뢰성 이론과 교량의 피로수명에 영향을 미치는 여러가지 요인들을 고려하여 유도되었다. 피로신뢰성 함수는 Weibull분포로 가정하였고, Weibull의 수치계산형태는 강재의 피로수명과 변진폭재하로 인한 응력범위 등의 통계적 불확실량을 모두 포함하는 Ang-Munse의 식을 사용하였다. 피로해석모형에는 교량이용 기간중에 발생할 수 있는 일평균교통량(ADTT)의 변화, 재하이력의 변화, 진추조사의 효과 등을 고려하였다. 응력범위 주상도는 개설 교량에 대한 현장실측결과로부터 구한 랜던 응력파로부터 작도하고, 그 결과 구해지는 응력범위분포는 Beta분포로 모형화 하였다. 본 연구에서 제안한 피로해석 방법을 실제 개설 교량에 대해 적용한 결과, 제안된 피로해석모형과 수치계산을 위하여 개발된 전산프로그램은 기설 노후 강교의 피로 내하력 판정이나 잔존수명의 예측 등을 위한 실용적인 방법으로 사용될 수 있다고 생각된다.

• 품질경영학회지
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• 제9권1호
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• pp.3-11
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• 1981

동일한 부품 K개를 갖고 있으며, 그 중에서 S개 이상의 스트렝스(strength)가 스트레스(stress) 보다 크게 될 경우 신뢰성이 유지되는 시스템에서 스트레스와 스트렝스가 모두 와이블(weibull) 분포를 하고 있을 때의 시스템 신뢰성을 고찰하였다. 2 절에서는 시스템 신뢰성의 최소분산불편추정량(MVU estimator)을 구하였고, 3 절에서는 최소분산불편추정량의 점근분포(asymototic distribution)를 구하고 표본크기가 클때 시스템 신뢰성의 최소분산불편추정량과 최우추정량(MLE)과의 관계를 구하였으며, 4 절에서는 시스템 신뢰성의 일양최적불편신뢰구간(uniformly most accurate unbiased confidence interval) 을 구하였고, 5 절에서는 몬데 카를로 씨뮤레이션(Monte Carlo Simulation)을 사용하여 작은 표본에서의 최우추정량과 최소분산불편추정량의 편기(bias)와 평균자승오차(MSE)를 비교하였고 6 절에서는 결과를 간단히 요약하고 본 논문을 더 확장할 경우에 문제점을 제시하였다.

• 한국신뢰성학회지:신뢰성응용연구
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• 제14권1호
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• pp.45-51
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• 2014

Thermal shock tests at two stress levels were performed to see the life (cycles) of LPF ASSY (low pass filter assembly) at normal stress level. In this case Coffin-Manson relationship is generally used to describe the relationship between the temperature difference and the life, together with the Weibull distribution describing the life at each stress level. So for given data Coffin-Manson is fitted to predict the life at normal stress level. However, different types of models are appropriate for this type of test. Hence, a more appropriate model such as General log-linear model which can also incorporate the duration at the highest and lowest temperatures and acceleration time will be introduced.

• Structural Engineering and Mechanics
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• 제61권4호
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• pp.463-473
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• 2017

Reinforced concrete is a complex material to be modeled in finite element domain. A proper material model is necessary to represent the nonlinear behaviour accurately. Though the nonlinear analysis of RC structures evolved long back, still an accurate and reliable model to predict the realistic behaviour of components are limited. It is observed from literature that there are three well-known models to represent the nonlinear behaviour of concrete. These models include Chu model (1985), Hsu model (1994) and Saenz model (1964).A new stress-strain model based on Weibull distribution has been proposed in the present study. The objective of the present study is to analyze a reinforced concrete beam under flexural loading by employing all the models. Nonlinear behaviour of concrete is considered in terms of stress vs. strain, damage parameter, tension stiffening behaviour etc. The ductility of the RC beams is computed by using deflection based and energy based concepts. Both deflection ductility and energy based ductility is compared and energy based concept is found to be in good correlation with the experiments conducted. The behavior of RC beam predicted using ABAQUS has been compared with the corresponding experimental observations. Comparison between numerical and experimental results confirms that these four constitutive models are reliable in predicting the behaviour of RC structures and any of the models can be employed for analysis.