The muSR experiments on a diluted Ising antiferromagnet HoxY1-xRu2Si2 are proposed for aiming verification of the Griffiths singularity. In preceding neutron scattering and muSR experiments, we found signatures of the Griffiths singularity at TN(1.0) = TG in the diluted antiferromagnet; the gradual development of magnetic diffuse scatterings and the divergent behavior of the muon relaxation rate. On a basis of these preceding experimental results, we propose the longitudinal-field (LF) muSR experiment up to 5 T using the HiFi spectrometer at ISIS to investigate the critical spin dynamics of the Griffiths singularity by extracting the relaxation time of the Ho-spins correlations via the decoupling study of the muon relaxations.