Testing exponentiality against renewal new better than used in Laplace transform order: applications in reliability

In this paper, a new class of life distribution is proposed, named renewal new better than used in Laplace transform order (RNBUL). The test statistic for testing exponentiality versus (RNBUL) based on U-statistic is proposed. Pitman’s asymptotic efficiencies of the test and Pitman’s asymptotic relative efficiencies (PARE) are calculated. The percentiles of this test statistic are tabulated, and the powers of this test are estimated for some famous alternatives distributions in reliability such as Weibull, linear failure rate (LFR), and Gamma distributions. The problem regarding the right-censored data is also handled. Finally, some applications to elucidate the usefulness of the proposed test in reliability analysis are discussed.

Moments Inequalities for NBRUL Distributions with Hypotheses Testing Applications

In this paper, moment inequalities for the new better than renwal used in Laplace transform order ( NBRUL ) class of ageing distributions are derived. This inequalities demonstrate that if the mean life is finite, then all higher order moments exist. A new test for exponentiality versus NBRUL can be constructed using thes inequalities. Pitman's asymptotic efficiencies and critical values of the proposed test are calculated and tabulated. The powers of this test are estimated for some famously alternatives distributions in reliability such as Linear failure rate,Weibull and gamma distributions. Finally, examples in different areas are used as a practical applications of the proposed test.