• 응용통계연구
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• 제21권2호
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• pp.265-273
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• 2008

본 논문에서는 Kim (2001a)에서 제안한 지수분포에서의 수정된 Shapiro와 Wilk (1972) $W_E$-통계량을 중도절단자료에 적용하였다. 검정통계량은 Samanta와 Schwarz (1988)에서 $W_E$-통계량을 중도절단자료에 대해 수정한 것과 같은 방법으로 정규화 등간격(normalized spacings)을 이용하여 수정하였다. 그 결과 제안된 통계량은 귀무가설에서 중도절단이 없는 경 우와 같은 분포를 갖고 표본크기만 변하게 된다. 제안된 통계량의 검정력을 Samanta와 Schwarz (1988)의 통계량과 비교한 결과, 중도절단이 없는 경우와 마찬가지로 중도절단이 있는 경우에도 변동계수가 1보다 크거나 같은 대립가설에서 제안된 통계량은 더 좋은 검정력을 나타내었다.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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• pp.235-240
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• 2000

In this paper a test of fit for exponentiality and we propose the estimator of Kullback-Leibler Information functions using the data from accelerated life tests. This acceleration model is assumed to be a tampered random variable model. The procedure is applicable when the exponential parameter based on the data from accelerated life tests is or is not specified under null hypothesis. Using Simulations, the power of the proposed test based on use condition of accelerated life test under alternatives is compared with that of other standard tests in the small sample.

• International Journal of Reliability and Applications
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• 제8권1호
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• pp.27-39
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• 2007

Based on goodness of fit new testing procedures are derived for testing exponentiality against harmonic new renewal better than used in expectation (HNRBUE). For this aging properties, a nonparametric procedure (U-statistic) is proposed. The percentiles of this test statistic are tabulated for sample sizes n=5(1)30(10)50. The Pitman asymptotic efficiency (PAE) of the test is calculated and compared with, the (PAE) of the test for new renewal better than used (NRBU) class of life distribution [see Mahmoud et al (2003)]. The power of this test is also calculated for some commonly used life distributions in reliability. The right censored data case is also studied. Finally, real examples are given to elucidate the use of the proposed test statistic in the reliability analysis.

• International Journal of Reliability and Applications
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• 제7권2호
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• pp.89-99
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• 2006

A new classes of life distribution, namely harmonic used better than aged in expectation in upper tail (HUBAEUT) is introduced. Testing exponentiality against this class is investigated using kernel method. The limiting null and nonnull distribution of the test statistics is normal and the null variance is calculated exactly. Selected critical values are tabulated for sample sizes of 5(1)40. Power of the test are estimated by simulation. the efficacies of the test statistics used for testing against HUBAEUT are calculated for som common alternatives and are compared to some other procedures. It is shown that proposed test is simple, has high relative efficiency and power for some commonly used alternatives. The set of real data are used as an examples to elucidate the use of the proposed test statistics for practical reliability.

• International Journal of Reliability and Applications
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• 제4권4호
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• pp.171-181
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• 2003

This paper proposes a U-test statistic for the problem of testing that a life distribution is exponential against the alternative that it is harmonic new better (worse) than used in expectation upper tail HNBUET (HNWUET), but not exponential on complete data. Selected critical values are tabulated for sample sizes n =5(1)60. The asymptotic normality of the statistic is proved and a comparison is made of the asymptotic efficiency between the statistic and other statistics. The power of the test is studied by simulation. A test for HNBUET in the case of randomly right-censored data is also considered. An application of the proposed test statistic in medical sciences is given.

• 품질경영학회지
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• 제31권4호
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• pp.194-202
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• 2003

In this paper, we propose goodness of fit test statistics for exponentiality in accelerated life tests data based on Kullback­Leibler information functions. This acceleration model is assumed to be a tampered random variable model. The procedure is applicable when the exponential parameter using the data from accelerated life tests is or is not specified under null hypothesis. And we compare the power of the proposed test statistics with Kolmogorov­Smirnov, Cramer von Mises and Anderson­Darling statistics in the small sample.

• International Journal of Reliability and Applications
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• 제4권2호
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• pp.57-69
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• 2003

A non-parametric test based on U-statistic for testing exponentiality against the new better than used renewal failure rate (NBURFR) alternatives is introduced and the percentiles of this test statistic are tabulated for sample size 5(1)50. Its properties are also discussed including the Pitman asymptotic efficiency relative to the tests of the new better than used and new better than used failure rate (Ahmed (1994) and Hendi (2000)). The powers of this test are also calculated for some used life distributions. An example from blood cancer patients demonstrates a practical application of our test in the medical sciences is presented. Finally the problem when right-censored data is available is handled.

• International Journal of Reliability and Applications
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• 제5권4호
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• pp.105-113
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• 2004

The exponential better (worse) than used EBU (EWU) class of life distributions is considered. A moment inequality is derived for EBU (EWU) distributions which demonstrate that if the mean life is finite, then all moments exist. Based on this inequality, a new test statistic for testing exponentiality against EBU (EWU) is introduced. It is shown that the proposed test is simple, enjoys good power and has high relative efficiency for some commonly used alternatives. Critical values are tabulated for sample sizes n = 5(1)40. A set of real data is used as a practical application of the proposed test in the medical science.

• International Journal of Reliability and Applications
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• 제4권4호
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• pp.191-199
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• 2003

In the present work, a moment inequality is derived for new renewal better (worse) than used in expectation(NRBUE) (NRWUE) distributions. This inequality demonstrates that if the mean life is finite then all higher order moments exist. A new test statistics for testing exponentiality against NRBUE (NRWUE) is introduced based on this inequality. It is shown that the proposed test is simple and has high relative efficiency for some commonly used alternatives. Critical values are tabulated for sample sizes n = 5(1)30. A set of real data is used as an example to elucidate the use of the proposed test statistics for practical reliability analysis.

• 응용통계연구
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• 제6권2호
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• pp.289-302
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• 1993

본 연구에서는 지수분포성 적합도검정 문제를 다루는데, 모수가 미지인 상황에서 제1종단일 우측중도절단 표본과 제2종우측중도절단 표본인 경우에 각각 적용될 수 있는 새로운 검정통 계량을 제안하였다. 미지의 모수 문제를 해결하기 위해서 K-변환을 고려하였으며 중도절단 균일표본을 완결 균일표본으로 전환시키기 위해서 Rosenblatt 변환을 적용하였다. 전환된 완결 균일표본의 적합도검정을 위한 통계량은 분포함수와 경험분포함수의 편차의 $L_1-norm$ 으로 정의되었다. 검정 통계량의 임계치는 Monte Carlo simulation에 의해 구 했으며, 잘 알려진 Pettit 검정법과 검정력을 비교하였는데, 새로 제안된 검정통계량의 검정 력이 대체로 우수한 것으로 평가되었다.