Cough is an important symptom of chronic respiratory diseases, necessitating quantitative assessment of its frequency in order to ascertain clinical relevance. This study proposes a cough detection system that uses multi-sensor smart clothing with embedded accelerometers and bending angle sensors based on double-layer capacitance technology. These sensors were strategically positioned on the rib cage and abdomen. Key indicators for cough detection were extracted using the Mahalanobis-Taguchi system (MTS). This study evaluated the impact of posture on cough detection performance in 20 healthy male subjects. The areas under the receiver operating characteristic curves (AUC) for the supine position and lateral positions were both 0.97, demonstrating a sensitivity of 0.82 and a specificity of 0.93 for the supine position, and a sensitivity of 0.83 and a specificity of 0.92 for the lateral position. Performance evaluation by five-fold cross-validation revealed an AUC of 0.97, with a sensitivity of 0.81 and a specificity of 0.95. Using only the top three attributes ranked according to gain identified based on MTS yielded a sensitivity of 0.78 and a specificity of 0.94. These top three attributes, comprising measurements from the acceleration sensors along the Y- and Z-axes as well as that from the bending angle sensor positioned in at the rib cage, highlighted the need to place the sensors on the rib cage. This study demonstrates that the proposed cough detection system, which incorporates multi-sensor smart clothing with specified sensors, effectively detects coughs in both the supine and lateral positions.