The main objective of this work is to accelerate the maximum likelihood (ML) estimation procedure in radio interferometric calibration. We introduce the ordered-subsets-least-squares (OS-LS) and the ordered-subsets-space alternating generalized expectation (OS-SAGE) radio interferometric calibration methods, as a combination of the OS method with the LS and SAGE maximization calibration techniques, respectively. The OS algorithm speeds up theML estimation and achieves nearly the same level of accuracy of solutions as the one obtained by the non-OS methods. We apply the OS-LS and OS-SAGE calibration methods to simulated observations and show that these methods have a much higher convergence rate relative to the conventional LS andSAGEtechniques. Moreover, the obtained results showthat theOS-SAGE calibration technique has a superior performance compared to the OS-LS calibration method in the sense of achieving more accurate results while having significantly less computational cost.