We would like to study the time dependence of the dipole width, trapping rate, and detrapping rate with Al-Mg-Si-Cu alloys in the temperature range from 260 to 300 K by zero-field muon spin relaxation method. Since the trace element Cu has the largest binding energy with vacancy among the elements and the smallest diffusivity in aluminum, we expect slow time variations of muon spin relaxaxtion rates with a larger Cu concentration sample. The temperature dependence of time variation of the trapping rate and detrapping rate will give Arrhenius plots which enable estimations of activation energies of clustering. The experimental values of the dipole width, trapping rate, detrapping rate and activation energy are quite useful to carry out the density functional calculations to figure out the early stage cluster structure of muon trapping sites in Al-Mg-Si-Cu alloys.