Cache hit ratio (CHR) is a common metric to evaluate the performance of an edge caching system. While the CHR is efficient to measure throughput reduction gain, it fails to guarantee user quality of experience since the CHR does not capture the last-mile channel uncertainty. In this letter, we investigate a novel successful delivery probability (SDP) metric of full-duplex-enabled mobile edge caching (FD-MEC) systems, defined as a probability that the user receives the requested file before a tolerable delay. First, the average SDP is derived in a closed-form expression for arbitrary caching policy and network topology, taking into account the wireless fading distribution. Second, based on the derived SDP, a suboptimal cache placement is proposed to maximize the average SDP, which is analytically shown to surpass both the most popular and uniform caching policies. Finally, the numerical results are presented to verify the accuracy of our analysis and demonstrate the effectiveness of our proposed cache placement design.