In order to reduce DPPM (defect parts per million), cell-aware (CA) methodology was proposed to cover various types of intra-cell defects. The resulting CA faults can be a 1-time-frame (1tf) or 2-time-frame (2tf) fault, and 2tf CA tests were experimentally verified to be capable of catching a significant number of defective parts not covered by other conventional tests. In this paper, we present a novel methodology for generating 2tf CA tests based on timing slack analysis. The proposed 2tf CA fault model, aware of timing slack and named TS, defines a fault (i) on a cell instance basis, and (ii) based on per-instance timing criticality (according to timing slack). More explicitly, for each cell instance with a specific defect injected, we check its output capacitive load and derive the corresponding extra delay. By comparing the extra delay against timing slack of the cell instance, a delay fault can be defined, and according to its severity, the fault can be further classified into small-delay fault or gross-delay fault. In contrast to prior 2tf CA methodology that is on a cell (rather than cell instance) basis and unaware of timing criticality/slack, our methodology can identify 'more realistic' faults which really need to be considered, and potentially the cost/effort for testing those 2tf CA faults can be reduced. Experimental results on a set of 28nm industrial designs demonstrate that, due to more realistic fault identification, the numbers of identified small-delay faults and corresponding test patterns to be applied can be reduced by 35.1% and 24.1% respectively, leading to 40.7% reduction in the runtime of ATPG.