• International Journal of Reliability and Applications
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• v.4 no.3
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• pp.113-129
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• 2003

Based on moments inequalities new testing procedures are derived for testing exponentiality against new renewal better than used (NRBU) and renewal new better than used (RNBU). These classes play an important role in formulating repair or replacement policies. The asymptotic Pitman efficiency of (NRBU) and (RNBU) testes are studied. Selected critical values are tabulated for sample sizes n=5(1) 50. The power estimates for some commonly used life distributions in reliability are also calculated. Some set of real data is used as an example to elucidate the use of the proposed test statistic for practical reliability analysis. The problem in case of right-censored data is also handled.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.141-153
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• 2006

In this paper, we present the U-Statistic test for testing exponentiality against new renewal better than used (NRBU) based on a goodness of fit approach. Selected critical values are tabulated for sample sizes n=5(1)30(10)50. The asymptotic Pitman relative efficiency relative to (NRBU) test given in the work of Mahmoud et all (2003) is studied. The power estimates of this test for some commonly used life distributions in reliability are also calculated. Some of real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. The problem in case of right censored data is also handled.

• 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.