© 2022, Indian Academy of Sciences.We have used mean-field theory based on the Bogoliubov inequality for the free energy to study the effects of random transverse single-ion anisotropies and magnetic field on the mixed spin-1 and spin-1/2 Blume–Capel quantum model with the coordination number z= 3. The interactions of the transverse crystal fields Dx and Dy act only on the spin-1 sites and are randomly active with probability p and q and inactive with probability 1−p and 1−q respectively. The thermal behaviours of the order parameters are studied to determine the nature of phase transitions and to calculate the phase diagrams on the (φx= Dx/ Jz, kBT/ J) , (p, kBT/ J) and (q, kBT/ J) planes. It is found that the model exhibits only second-order phase transitions. The compensation temperatures are also observed and their lines, Tcomp-lines, are depicted on the (φx, kBT/ J) planes. The hysteresis loops are obtained by introducing an external magnetic field on the system which reveals that the coercive field decreases with temperature and with positive values of φx and φy. It is also found that remanent magnetisation increases with negative values of φx and φy.