  Generalized quantum discord $(D_q)$, Einstein-Podolsky-Rosen steering $(S)$,
entanglement $(E)$, and Bell nonlocality ($N$), are logically distinct
quantifiers of quantum correlations. All these measures capture nonclassical
aspects of quantum states and play some role as resources in quantum
information processing. In this work, we look for the hierarchy satisfied by
these quantum correlation witnesses for a class of two-qubit states. We show
that $N \triangleright S\triangleright E\triangleright D_q$, meaning that
nonlocality implies steering, which in turn implies entanglement, which then
implies $q$-discord. For the quantum states under concern, we show that the
invariance of this hierarchy under noisy quantum channels directly implies a
death chronology. Additionally, we have found that sudden death of all quantum
resources except discord is absent only for a subset of states of measure zero.
At last, we provide an illustration of another consequence of the
aforementioned hierarchy, namely, the existence of a sudden birth chronology
under non-Markovian channels.
