Comparing the renewal random variable with its parent in terms of convex ordering gives the new better (or worse) than renewal used aging property. Closures under reliability operations of classes of life distributions having this property are explored. Tests statistics for these aging property are established. Percentiles of the statistics are simulated and their power estimates are determined. The mean and the estimated risks of the statistics are calculated and their approach to normality is checked empirically

In this paper, the new or worse better than renewal used classes of life distributions are considered. Relations of these classes with other existing ageing criteria are presented. Closure properties under some reliability operations is studied. Test statistics of exponentiality for these classes are established under random censoring. Percentiles and the power estimates are simulated. The asymptotic normality of these tests is also tested.