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Multi‐access edge computing (MEC) enables users to exploit the resources of cloud computing at a base station (BS) in proximity to the users where an MEC server is hosted. While we have advantage of being able to communicate with low latency and small network load in MEC networks, the resources in BSs are limited. One challenge is where to provide users with services from to make efficient use of resources. Furthermore, to enhance the reliability of MEC system, the case that a BS fails needs to be considered. This paper proposes a service placement and user assignment model with preventive start‐time optimization against a single BS failure in MEC networks. The proposed model preventively determines the service placement and user assignment in each BS failure pattern to minimize the worst‐case penalty which is the largest penalty among all failure patterns. We formulate the proposed model as an integer linear programming problem. We prove that the considered problem is NP‐hard. When the problem size becomes large, it may not be solved in a practical computation time. To solve larger size problems, we introduce two algorithms: one is the greedy algorithm with allocation upgrade and the other is with allocation upgrade and preemption. The results show that the introduced algorithms obtain solutions with smaller worst‐case penalty than the benchmark in a practical time.