Negative ageing properties for counting processes arising in virtual age models

• We consider negative ageing properties in virtual age models randomly stopped.
• We show the preservation of the decreasing failure rate and log convexity.
• We apply our results to Kijima type I models under quite general assumptions.
• We obtain negative ageing properties in virtual age frailty models.

This paper is focused on counting processes of interest in reliability theory. In particular, we study virtual age models. Our aim is to consider these counting models stopped at a random time T, independent of the process. We investigate the negative ageing properties for the stopped process (decreasing failure rate and log-convexity), provided that T has the analogous properties. For instance, we show that these properties hold for the so-called Kijima type I virtual age models, of interest in reliability, under quite general assumptions.