Almost all functional safety standards that regulate safety-critical domains impose to periodically test hardware platforms at run-time. RAM memories are among the fundamental components of computing platforms and are notably subject to faults. Hence, they are also primary components to be tested. Unfortunately, RAM tests are destructive, require to be atomically executed, and are not cheap from a computational perspective. As such, if not properly managed, they can jeopardize the timing performance of a real-time system, especially when running upon a multicore platform.This paper proposes a software architecture to integrate online memory tests on multicore real-time systems. Furthermore, by jointly considering a task model and a safety model based on the EN50129 safety standard, it presents an approach to compute the optimal configuration of memory tests that preserves the system schedulability and guarantees a given tolerable functional failure rate (TFFR). Experimental results show that the proposed approach allows achieving a marginal impact on schedulability while preserving a TFFR that is compatible with the highest safety integrity level specified by the EN50129.