On the NBU ageing notion within the competing risks model

The classical competing risks model deals with failure times of items subject to multiple causes of failure. We propose a version of the well-known 'new better than used' and 'new worse than used' ageing notions for random lifetimes within a specific cause of failure in the competing risks set up. Various properties of these new notions are studied, including the closure under time-dependent scale changes, as well as their connection to the hazard rate functions of the competing risks model. A data analytic example is finally provided.