Mapping a pipelined application onto a distributed and parallel platform is a challenging problem. The problem becomes even more difficult when multiple optimization criteria are involved, and when the target resources are heterogeneous (processors and communication links) and subject to failures. This report investigates the problem of mapping pipelined applications, consisting of a linear chain of stages executed in a pipeline way, onto such platforms. The objective is to optimize the reliability under a performance constraint, i.e., while guaranteeing a threshold throughput. In order to increase reliability, we replicate the execution of stages on multiple processors. We present complexity results, proving that this bi-criteria optimization problem is NP-hard. We then propose some heuristics, and present extensive experiments evaluating their performance.