Cloud service providers (CSPs) promise to reliably store repositories outsourced by clients. Unfortunately, once files have left the client's control, he has no means to verify their redundant storage. In this article, we develop Proof of Physical Reliability (PoPR) auditing mechanisms that prove that a CSP stores an outsourced repository across multiple physical storage nodes. A PoPR complements the existing proof-of-retrievability (PoR) and proof-of-data possession (PDP) methods that are concerned with file retrievability, but without any verification of the fault-tolerance to physical storage nodes failures. A PoPR goes beyond retrievability by verifying that a file is redundantly stored across multiple physical storage nodes according to a pre-agreed layout and can, therefore, survive node failures. The verification mechanism relies on a combination of storage integrity and timing tests on the simultaneous retrieval of a collection of file symbols from multiple storage nodes. Compared to the state-of-the-art, our approach accommodates CSPs with heterogeneous storage devices (hard disks, SSDs, etc.) and does not assume constant data processing nor network delays. Instead, it can operate under any delayvariance, because it relies only on (loose) delay bounds. We analytically prove the security of our construction and experimentally validate its success in heterogeneous storage settings.