Heterogeneous processors are increasingly being used in embedded systems where parallel applications with precedence-constrained tasks widely exist. Reliability is an important functional safety requirement and reliability goal should be satisfied for safety-critical parallel applications; meanwhile, resource is limited in embedded systems and it should be minimized. This study solves the problem of resource consumption cost minimization of a reliable parallel application on heterogeneous embedded systems without using fault tolerance. The problem is decomposed into two subproblems, namely, satisfying reliability goal and minimizing resource consumption cost. The first subproblem is solved by transferring the reliability goal of the application to that of each task, and the second subproblem is solved by heuristically assigning each task to the processor with the minimum resource consumption cost while satisfying its reliability goal. Experiments with real parallel applications verify that the proposed algorithm obtains minimum resource consumption costs compared with the state-of-the-art algorithms.