Abstract
In this paper, a general characterization property considering two new dynamic relative reliability measures is obtained. The new dynamic relative reliability measures are expressed as the ratio of hazard rates and as the ratio of reversed hazard rates. The measures are evaluated partially at some sequential random times following a specific distribution. We show that several particular statistics, as random times, fulfill that specific distribution, and thus, the result is applicable in the context of the specified random times. The results are applied to some examples to characterize the Weibull distribution and the inverse Weibull distribution.