Dual stochastic orderings describing ageing properties of devices of unknown age

Dual usual stochastic ordering and dual increasing linear ordering are introduced as the dual of two well-known stochastic orderings in order to provide characterization of various ageing notions useful to describe ageing properties of devices with unknown age. The ‘harmonic used better than aged in expectation’ ageing notion is then given, and various of its properties as well as an application to Poisson shock models are discussed.