Abstract
A new class of life distributions, namely new better than used in the total time on test transform ordering (NBUT), is introduced. The relationship of this class to other classes of life distributions, and closure properties under some reliability operations, are discussed. We provide a simple argument based on stochastic orders that the family of the NBUT distribution class is closed under the formation of series systems in case of independent identically distributed components. Behavior of this class is developed in terms of the monotonicity of the residual life of k-out-of-n systems given the time at which the (n-k)-th failure has occurred. Finally, we discuss testing exponentially against the NBUT aging property.