New families of life distributions Based on the Exponential Better than Used Concept are introduced. Definitions and Basic Results are stated. Several properties of these classes are presented, including the preservation under convolution and mixing. Testing exponentially against exponential better (worse) than used in convex order (2),EBUC(2), is proposed by using moment inequalities. The Pitman asymptotic efficiency (PAE) is discussed. Selected critical values are tabulated for selected sample sizes. Application with real data is given to illustrate the theoretical results.