Abstract While modelling deterioration or ageing of devices, first-passage times of Markov processes play a significant role, especially when the devices are subject to shocks and wear during their operation. In view of this, obtaining sufficient conditions for first-passage times to belong to specific ageing families constitutes an important problem. There exists a rich literature dealing with this class of problems; see for example 11, 18, 35, 67. We address the same problem in the context of some new ageing classes such as DMTTF (IMTTF), IMIT, and DRHR. In this connection, some issues in 11 have also been investigated. We wind up by including certain examples to highlight the practical relevance of the results.
Parveen et al. (Mon,) studied this question.