Mobile edge computing (MEC), as an emerging technology, allows application vendors to deploy application instances on edge servers to deliver low-latency services to nearby end-users. However, due to hardware faults, software exceptions, or cyberattacks, edge servers are prone to failures in the highly distributed and dynamic MEC environment. Hence service reliability must be ensured when failures occur. This raises a critical and open problem - improving service reliability when deploying application instances in the MEC environment. In this article, we jointly consider both user coverage and service reliability when deploying application instances on edge servers with a given application deployment budget <inline-formula><tex-math notation="LaTeX">$\mathcal {K}$</tex-math></inline-formula> . We formally define this joint <u>C</u> overage- <u>R</u> eliability for <inline-formula><tex-math notation="LaTeX">$\mathcal {K}$</tex-math></inline-formula> - <u>B</u> udgeted <u>E</u> dge <u>A</u> pplication <u>D</u> eployment ( <i>CR-BEAD</i> ) problem and model it as a constrained optimization problem. Next, we propose an optimal approach (named <i>BEAD-O</i> ) based on integer programming to find optimal solutions to small-scale CR-BEAD problems. We also propose a greedy approach named <i>BEAD-G</i> with a constant approximation ratio of <inline-formula><tex-math notation="LaTeX">$1 - 1/e$</tex-math></inline-formula> to solve large-scale CR-BEAD problems efficiently. Extensive experimental evaluation against three representative approaches illustrates the effectiveness and efficiency of our approaches.