• Journal of the Korean Data and Information Science Society
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• 제25권4호
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• pp.903-914
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• 2014

The inverse Weibull distribution has been proposed as a model in the analysis of life testing data. Also, inverse Weibull distribution has been recently derived as a suitable model to describe degradation phenomena of mechanical components such as the dynamic components (pistons, crankshaft, etc.) of diesel engines. In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the shape parameter in the inverse Weibull distribution under multiply type-II censoring. We also develop four modified empirical distribution function (EDF) type tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• 한국전기전자재료학회논문지
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• 제19권10호
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• pp.947-952
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• 2006

It has been confirmed that the inner defect of insulator and the perfect diagnosis for aging are closely related to safe electric power transmission system and that the detection of accident and diagnosis technique turn out to be very important issues. But perfect diagnosis is difficult because discharge pattern is irregular. Thus, we investigated discharge pattern using the new distribution statistical models with cross-inked polyethylene(XLPE) specimens. Voltage was applied to power frequency by step method, and calibration of discharge was set to 50 pC. After the voltage was applied, it measured the discharge occurring during 10s. We investigated discharge pattern using the K-means analysis and Weibull function. We also investigated variation of centroid and shape parameter due to variation of voltage. As a result of analyzing K-means, it was confirmed that cluster including many object numbers was formed by the presence of void. And result of Weibull distribution, it was confirmed that shape parameter of discharge varied from 1.28 to 1.62 in no void specimens, and that shape parameter of discharge number varied from 1.28 to 1.62. In the void, shape parameter of discharge varied from 5.66 to 6.43, and shape parameter of discharge number varied from 5.05 to 5.08.

• 대한전기학회논문지:전력기술부문A
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• 제55권3호
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• pp.109-115
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• 2006

The Weibull distribution is a good candidate for accurate probabilistic model with its rich shape-forming ability and relatively simple CDF(cumulative distribution function). If there are sufficient information to get convincible mean and variance for a probabilistic event, reliable parameters of the Weibull distribution can be determined uniquely. However, sufficient information is not given as usual. There needs more deliberate model building method for that case. This Paper presents an effective parameter estimation technique for Weibull distribution with limited failure data.

• Journal of the Korean Data and Information Science Society
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• 제25권6호
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• pp.1569-1579
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• 2014

This article deals with the problem of testing for the equality of the shape parameters in two inverse Weibull distributions. We propose Bayesian hypothesis testing procedures for the equality of the shape parameters under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.199-210
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• 2000

We shall propose several estimators for the shape and scale parameters I the Weibull distribution based upon the complete or truncated samples when both parameters are functions of a known exposure level and study properties for proposed several estimators

• 한국수자원학회논문집
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• 제46권6호
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• pp.643-653
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• 2013

적절한 확률분포형을 결정하고 그에 따른 확률수문량을 산정하는 것은 빈도해석에서 가장 중요한 절차이며, 이를 수행하기 위해서는 경험적 확률분포에서 얻어지는 자료와 가정한 확률분포에서 얻어지는 자료의 일치 정도를 판별하는 적합도 검정을 거쳐야 한다. 지금까지 일반적으로 적용된 적합도 검정 방법은 분포형의 전체적인 적합정도를 판별하여 최근의 기상이변으로 인한 극치 사상에 대하여는 충분히 고려하지 못하고 있다. 따라서 본 연구에서는 분포형의 극치 사상에 가중치를 주는 modified Anderson-Darling(AD) 검정 방법을 3변수 Weibull 분포형에 적용하여 검정통계량 한계값과 기각력을 살펴보았으며 이를 실제자료에 적용한 결과, modified AD 검정 방법이 다른 기존의 적합도 검정보다 더 우수한 기각력을 가지고 있음을 확인하였다. 이는 앞으로 3변수 Weibull 분포형을 이용한 극치 수문량 선정에 있어 modified AD 방법이 하나의 기준으로 작용할 수 있을 것이라 판단된다.

• Journal of the Korean Statistical Society
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• 제12권2호
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• pp.69-80
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• 1983

The purpose of this paper is to obtain representation of the mathematical special functions and the numerical values of the mean square errors for the quasi-ranges in random small smaples ($n \leq 30$) from the Weibull distribution with a shape and a scale parameters, and to estimate the scale parameter by use of unbiased estimator based on the quasi-range. It will be shown that the jackknife estimator of the range is worse than the range of random samples from the given distribution in the sense of the mean square error.

• Journal of the Korean Data and Information Science Society
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• 제15권1호
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• pp.49-57
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• 2004

In this paper, we calculate the premium rate of reliability insurance policy for wiper motors under the assumption of Weibull physics of failure. We also describe the performance factors which have an effect on failure characteristics of wiper motors. The maximum likelihood estimates of shape parameter and scale parameter are obtained by using interval censored real data of sample sizes 6 using MINITAB.

• 전기학회논문지
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• 제66권3호
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• pp.500-506
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• 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 Biosystems Engineering
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• 제11권1호
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• pp.76-85
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• 1986

This study was intended to examine the failure characteristics and breakdowns of the head-fed type combines generally used on farms. The failure distribution was assumed to follow Weibull distribution function and the Weibull parameters of the major parts, units and combine as whole were estimated by using the data collected in a survey. A computer program for the estimation of the Weibull parameter was developed. Monte Carlo method was used in predicting the time between failures. The results of study may be summarized as follows: 1. The number of failures per combine was 4.83 times per year and 0.3 times per hectare of combines of different ages. 2. According to the Kolmogorov-Smirnov test method, it was proved that the Weibull distribution function is well fitted to the characteristics of the failure and breakdowns of combines. 3. Weibull parameters of failure distribution of the combine as a whole were estimated to give the shape parameter ${\beta}$=1.3089 and the scale parameter ${\alpha}$=105.2409. The combining area with 80% reliability was 1.1 ha, and the probability of operating the combine without any failure for a year, was $2.76{\times}10^{-4}$. 4. The mean time between failures (MTBF) of the combines was predicted to be 3.2 ha of operation, which corresponds to 32 hours of operation.