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Testing unknown age classes of life distributions based on TTT-transform
El-Din, M.M. Mohie,Abu-Youssef, S.E.,Ali, Nahed S.A. The Korean Reliability Society 2013 International Journal of Reliability and Applicati Vol.14 No.1
A nonparametric procedure for testing exponentially against used better than aged in expectation (UBAE) class of life distributions is presented. We construct a test statistics based on scaled total time on test (TTT)-transformation, to test exponentiality against UBAE class of life distributions. The distribution of the statistic is investigated via simulation. Practical applications of the proposed test are presented.
Testing unknown age classes of life distributions based on TTT-transform
M. M. Mohie El-Din,S. E. Abu-Youssef,Nahed S. A. Ali 한국신뢰성학회 2013 International Journal of Reliability and Applicati Vol.14 No.1
A nonparametric procedure for testing exponentially against used better than aged in expectation (UBAE) class of life distributions is presented. We construct a test statistics based on scaled total time on test (TTT)-transformation, to test exponentiality against UBAE class of life distributions. The distribution of the statistic is investigated via simulation. Practical applications of the proposed test are presented.
On testing NBUL aging class of life distribution
Hassan, M.Kh.,El-Din, M.M. Mohie,Abu-Youssef, S.E. The Korean Reliability Society 2014 International Journal of Reliability and Applicati Vol.15 No.1
Let X and $X_t$ denote the lifetime and the residual life at age t, respectively. X is said to be a NBUL (new better than used in Laplace transform order) random variable if $X_t$ is smaller than X in Laplace order, i.e., $X_t{\leq}_{LT}X$. We propose a new test statistics for testing exponentiality versus NBUL class of life distribution. The tests by Hollender and Proschan (1975) and the generalized Hollender and Proschan test by Ains and Mitra (2011) are considered as special cases of the our of test statistics. Our proposed test statistics is simple, consistent and asymptotically normal. Efficiency and powers of the test statistics for some commonly used distributions in reliability are discussed. Finally, real examples are presented to illustrate the theoretical results.
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.
On testing NBUL aging class of life distribution
M. KH. Hassan,M. M. Mohie El-Din,S. E. Abu-Youssef 한국신뢰성학회 2014 International Journal of Reliability and Applicati Vol.15 No.1
Let X and Xt denote the lifetime and the residual life at age t , respectively. X is said to be a NBUL (new better than used in Laplace transform order) random variable if Xt is smaller than X in Laplace order, i.e., Xt≤LT X. We propose a new test statistics for testing exponentiality versus NBUL class of life distribution. The tests by Hollender and Proschan (1975) and the generalized Hollender and Proschan test by Ains and Mitra (2011) are considered as special cases of the our of test statistics. Our proposed test statistics is simple, consistent and asymptotically normal. Efficiency and powers of the test statistics for some commonly used distributions in reliability are discussed. Finally, real examples are presented to illustrate the theoretical results.