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This book is devoted to define two new classes of life distributions named overall decreasing life in Laplace transform order (ODL lt) and new better than renewal used in Laplace transform order (NBRUL). Testing exponentiality versus these classes based on complete and censored samples is discussed. The powers of this test are estimated for some famously alternatives distributions in reliability such as Linear failure rate, Weibull and gamma distributions. Finally, the proposed tests are applied to many sets of real data.