• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.487-495
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• 2010

This paper develops a goodness of fit test statistic to test if the progressively Type II censored sample comes from an exponential distribution with origin known. The test is based on normalizing spacings and Stephens (1978)' modified Shapiro and Wilk (1972) test for exponentiality. The modification is for the case where the origin is known. We applied the same modification to Kim (2001a)'s statistic, which is based on the ratio of two asymptotically efficient estimates of scale. The simulation results show that Kim (2001a)'s statistic has higher power than Stephens' modified Shapiro and Wilk statistic for almost all cases.

• Journal of Korean Society for Quality Management
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• v.31 no.4
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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.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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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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• v.6 no.1
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• pp.1-12
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• 2005

A new test for 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 is presented based on the highly popular 'Kernel methods' of curve fitting. This new procedure is competitive with old one in the sense of Pitman's asymptotic relative efficiency, easy to compute and does not depend on the choice of either the band width or kernel. It also enjoys good power.

• International Journal of Reliability and Applications
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• v.8 no.1
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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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• v.4 no.2
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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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• v.5 no.4
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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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• v.7 no.2
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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.

• Journal of Korea Society of Industrial Information Systems
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• v.5 no.2
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• pp.39-46
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• 2000

Recent]y van Es (1992) and Correa (1995) proposed an estimator of entropy. In this paper, we proposed the goodness of fit test statistics for exponentiality based on Vasicek's estimator and Correa's estimator of Kullback-Leibier Information. And we compare the power of the proposed test statistics with Kolmogorov-Sminov, Kuiper, Cramer von Mises, Watson, Andersen-Darling and Finkelstein and Schefer statistics.

• International Journal of Reliability and Applications
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• v.4 no.4
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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.