  The generalized Crewther relation relates the cross section ratio
$R=\sigma(e^+e^- \to {\rm hadrons})/\sigma(e^+e^- \to {\mu}^+ {\mu}^-)$ in
$e^+e^-$ annihilation with the Bjorken sum rule or the Gross-Llewellyn Smith
sum rule in deep inelastic scattering and provides a fundamental connection for
observables in Quantum Chromodynamics (QCD) without scale or scheme
ambiguities. The ratio $R$ can be measured at the upgrated Bejing Electron
Positron Collider or the $\tau$-Charm factory with higher precision and thus
can be served for a high precision test of QCD in the Standard Model.
