This paper investigates theresilientmulti-robot efficient search problem (R-MuRES), which aims at coordinating multiple robots to detect a ‘non-adversarial’ moving target with the minimal expected time. One unique characteristic of R-MuRES among others is the possibility of individual robot's malfunction and withdrawal from the team during task execution, which results in avariablenumber of searchers in the deployment phase and entails that the possibility of team member failures must be considered during the planning stage, particularly in the training phase. We propose a resilient value function factorization (R-FAC) paradigm, which constructs the central value function from individual ones in a resilient manner, taking into account individual robots' failures, and ensures that the constructed central value function has the minimal mean squared temporal difference error across various team compositions. R-FAC stipulates that the individual global maximum (IGM) principle is satisfied for whichever team configuration and thus any functioning robot contributes positively to the remaining team, as long as it executes the greedy policy with respect to the factorized individual value function. Subsequently, we introduce thevariationalvalue decomposition network (V2DN) as one of the instantiated R-FAC algorithms. V2DN employs the$\log$-sum-$\exp$mechanism to construct the central value function from individual ones, enabling it to take a varying number of robots' individual value functions as inputs. Then, we explain why, specifically for the multi-robot search task, the$\log$-sum-$\exp$mechanism is superior to the brute-force summation operation used in the canonical value decomposition network (VDN), and compare V2DN with state-of-the-art MuRES solutions as well as the vanilla VDN algorithm in two canonical MuRES testing environments and show that it achieves the best resiliency score when one or several individual robots quit the team during task execution. Furthermore, we validate V2DN with a real multi-robot system in a self-constructed indoor environment as the proof of concept.