The possibility of singlet-triplet pairing in noncentrosymmetric (NCS) superconductors makes them prime candidates to exhibit time-reversal symmetry breaking (TRSB). However, there are only a handful of superconductors that exhibit TRSB. More importantly, the role played by the relative strength of spin-orbit coupling and electron correlation in parity mixing and TRSB is still unresolved. To this end, we propose to measure a new family of NCS superconductors ZrMo2Ru3 and HfW2Os3. Interestingly, ZrMo2Ru3 contain only 4d elements whereas HfW2Os3 contain 5d elements. Hence, the nature of the interplay between spin-orbit coupling and electron correlation can be efficiently studied. In this proposal, we want to investigate the superconducting ground state of ZrMo2Ru3 and HfW2Os3 using transverse field (TF) and zero field measurements on the MuSR spectrometer