Multi-criteria scheduling problems, involving optimization of more than one criterion, are subject to a growing interest. In this paper, we present a new bi-criteria scheduling heuristic for scheduling data-flow graphs of operations onto parallel heterogeneous architectures according to two criteria: first the minimization of the schedule length, and second the maximization of the system reliability. Reliability is defined as the probability that none of the system components will fail while processing. The proposed algorithm is a list scheduling heuristics, based on a bi-criteria compromise function that introduces priority between the operations to be scheduled, and that chooses on what subset of processors they should be scheduled. It uses the active replication of operations to improve the reliability. If the system reliability or the schedule length requirements are not met, then a parameter of the compromise function can be changed and the algorithm re-executed. This process is iterated until both requirements are met.