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Abu-Youssef, S.E. The Korean Reliability Society 2003 International Journal of Reliability and Applicati Vol.4 No.4
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.
A Goodness of Fit Approach to Testing Exponential Better than Used (EBU) Life Distributions
Abu-Youssef, S.E. The Korean Reliability Society 2008 International Journal of Reliability and Applicati Vol.9 No.1
Based on the goodness of fit approach, a new test is presented for testing exponentiality versus exponential better (worse) than used (EBU (EWU)) class of life distributions. The new test is much simpler to compute, asymptotically normal, enjoys good power and performs better than previous tests in terms of power and Pitman asymptotic efficiencies for several alternatives.
Abu-Youssef, S.E.,Al-nachawati, H. The Korean Reliability Society 2006 International Journal of Reliability and Applicati Vol.7 No.2
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.
Nonparametric test for unknown age class of life distributions
Abu-Youssef, S.E.,Mohammed, B.I.,Bakr, M.E. The Korean Reliability Society 2014 International Journal of Reliability and Applicati Vol.15 No.2
Based on the kernel function, a new test is presented, testing $H_0:\bar{F}$ is exponential against $H_1:\bar{F}$ is UBACT and not exponential is given in section 2. Monte Carlos null distribution critical points for sample sizes n = 5(5)100 is investigated in section 3. The Pitman asymptotic efficiency for common alternatives is obtained in section 4. In section 5 we propose a test statistic for censored data. Finally, a numerical examples in medical science for complete and censored data using real data is presented in section 6.
Abu-Youssef, S.E. The Korean Reliability Society 2009 International Journal of Reliability and Applicati Vol.10 No.2
A non-parametric procedure is presented for testing exponentially against used better than aged in convex ordering class (UBAC) of life distributions based on u-test. Convergence of the proposed statistic to the normal distribution is proved. Selected critical values are tabulated for sample sizes 5(5)40. The Pitman asymptotic relative efficiency of my proposed test to tests of other classes is studied. An example of 40 patients suffering from blood cancer disease demonstrates practical application of the proposed test.
Testing of EBELC classes of life distributions based on TTT-transform
Abu-Youssef, S.E.,Mohie El-Din, M.M.,Hassan, M.Kh. The Korean Reliability Society 2012 International Journal of Reliability and Applicati Vol.13 No.1
Using total time on test transform (TTT), a new approach is taken for testing exponentiality versus the unknown age, exponential better than equilibrium life in convex ordering (EBELC). Selected critical values are tabulated for sample size n =2(2)50 and powers of the test are estimated for some commonly used distributions in reliability. Finally real example is presented to illustrate the theoretical results.
Abu-Youssef, S.E. The Korean Reliability Society 2004 International Journal of Reliability and Applicati Vol.5 No.4
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.
Nonparametric test for unknown age class of life distributions
S. E. Abu-Youssef,B. I. Mohammed,M. E. Bakr 한국신뢰성학회 2014 International Journal of Reliability and Applicati Vol.15 No.2
Based on the kernel function, a new test is presented, testing H?: F is exponential against H₁: F is UBACT and not exponential is given in section 2. Monte Carlos null distribution critical points for sample sizes n = 5(5)100 is investigated in section 3. The Pitman asymptotic efficiency for common alternatives is obtained in section 4. In section 5 we propose a test statistic for censored data. Finally, a numerical examples in medical science for complete and censored data using real data is presented in section 6.