International Journal of Reliability and Applications
- Volume 8 Issue 1
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- Pages.27-39
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- 2007
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- 1598-0073(pISSN)
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- 2283-8914(eISSN)
On Testing Exponentiality Against HNRBUE Based on Goodness of Fit
- Mahmoud, M.A.W. (Math. Department, Faculty of Science, AL-Azhar University) ;
- Diab, L.S. (Math. Department, Faculty of Science, AL-Azhar University)
- Published : 2007.06.30
Abstract
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.
Keywords
- harmonic new renewal better than used in expectation (HNRBUE);
- U-statistic;
- goodness of fit testing;
- efficiency;
- relative efficiency;
- Monte Carlo methods;
- power and censored data