Three-Dimensional Stacked Integrated Circuit (3D-SICs) based on Through-Silicon Vias (TSVs) provide a highdensity integration technology. However, integrating pre-tested dies requires post-bond interconnect testing, which is complex and costly. An imperfect TSV-based interconnect indicates a defective chip that should be rejected. Thus, it increases the yield loss and test cost. On the other hand, approximate computing (AC) is a promising design paradigm suitable for errorresilient applications, e.g., processing sensory-generated data, by judiciously sacrificing output accuracy. AC perform inexact operations and accepts inexact data. Thus, introducing AC into 3D-SICs will significantly ameliorate the efficiency of design approximation. Therefore, this work aims to increase the yield and reduce the test cost by accepting 3D-SICs with defected interconnects as approximate 3D-SICs. This work considers 3D-SICs, where the sensor is stacked on logic (CPU) which is stacked on memory (DRAM). Then, use the memory-based interconnect testing (MBIT) approach to detect and diagnose the faulty interconnect. Based on the detected fault location and type, and for a maximum allowed error, some sensory 3D-SICs with defected LSBs interconnects are accepted and used in errorresilient and data-intensive applications. Targeting data lines only, 50% of the defected interconnects, i.e., least significant bits (LSBs), were accepted as approximate. Thus, the proposed work was able to significantly increase the yield. Two applications, i.e., ECG signal compression and detecting of their R peaks, demonstrated the effectiveness of using a sensory device with a faulty data line in its least significant 8-bits. The approximate ECG signals have a compression rate higher than the exact with negligible (around 0.1%) reduced accuracy.