On The New Better Than Used Renewal Failure Rate at Specified Time

In this paper we introduce a new class of life distribution called the new better (worse) than used renewal failure rate at specified time t 0 NBURFR-t 0 (NWURFR-t 0). Some closure properties, such as closure under convolution, arbitrary and general mixture, and Shock model are discussed. Furthermore, a nonparametric test is proposed to test exponentiality against the NBURFR-t 0 class. The critical values, the powers and Pitman efficiencies are calculated for t 0 = 0:25.