First-passage times of increasing Markov processes and classes of life distributions

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.