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This paper considers a low signal-to-noise ratio (SNR) target detection problem for phased array radar, where classical constant false alarm rate (CFAR) detection framework would cause missed detection. To overcome this problem, we propose a variable false alarm rate (VFAR) detection framework for phased array radar to ensure the detection performance for low-SNR targets in multi-stage target detection. First, exploiting the previous detected results, the searching area of interest is divided into multiple sub-areas, while automatically reducing the false alarm probability of each range section of each frame. Then, a joint allocation strategy of beam and time resources accounting for maximizing the weighted sum of SNRs of spatial sectors in the whole surveillance area of the phased array radar along with some practical coupled constraints, is proposed. Next, the fuzzy analytic hierarchy process and convex optimization methods are, respectively, developed to obtain beam and time resource allocation scheme. Finally, the effectiveness and superiority of the proposed framework are highlighted and evaluated by numerical simulations.