  Recent experimental progress in prolonging the coherence time of a quantum
system prompts us to explore the behavior of quantum entanglement at the
beginning of the decoherence process. The response of the entanglement under an
infinitesimal noise can serve as a signature of the robustness of entangled
states. A crucial problem of this topic in multipartite systems is to compute
the degree of entanglement in a mixed state. We find a family of global noise
in three-qubit systems, which is composed of four W states. Under its
influence, the linear response of the tripartite entanglement of a symmetrical
three-qubit pure state is studied. A lower bound of the linear response is
found to depend completely on the initial tripartite and bipartite
entanglement. This result shows that the decay of tripartite entanglement is
hastened by the bipartite one.
