In this paper, stochastic scheduling problems are considered when processing times and due dates follow arbitrary distributions and due dates are either common or exchangeable. For maximizing the expected number of early jobs, two policies, one, based on pairwise comparisons of the processing times, and the other, based on survivabilities, are introduced. In addition, it is shown that the former guarantees optimal solutions when the processing times and due dates are deterministic and that the latter guarantees optimal solutions when the due dates follow exponential distributions. Then a new approach, exploiting the two policies, is proposed and analyzed which turns out to give better job sequences in many situations. In fact, the new approach guarantees optimal solutions both when the processing times and due dates are deterministic and when the due dates follow exponential distributions.