Summary: The concept of reciprocal coordinate subtangent (RCST) has been used as a useful tool to study the monotone behaviour of a continuous density function and for characterizing probability distributions through its functional forms (see [S. P. Mukherjee and D. Roy, Bull., Calcutta Stat. Assoc. 38, No. 151–152, 169–180 (1989; Zbl 0715.62024)]). In this paper, we prove that the monotone failure properties of probability models are invariant under non-singular transformation. We obtain characterizations to mixtures of exponential, Lomax and beta distributions based on RCST. Finally, characterizations based on RCST of record values are proved for important probability models.