We propose a synthesis-centric model-based systems engineering framework for discrete-event systems with general distributions. Supervisory control theory studies supervisory controllers' automated synthesis. Thus, it ensures the safe coordination among various distributed system components in terms of their discrete-event behavior. General distributions provide for (convenient) modeling of important real-world phenomena that cannot be consistently modeled only by means of timed or Markovian delays. Our approach relies on a behavioral preorder termed partial bisimulation to define existence of supervisory controllers, and on an appropriate abstraction from stochastic time, which enables usage of standard synthesis tools. In the special cases when the distributions degrade to standard timed delays or Markovian processes, we provide for appropriate reductions of the models suitable for timed and stochastic model checking.