A recent study categorized the Madden-Julian Oscillation (MJO) during boreal winter season into four types including stand, jump, slow and fast MJO. This study focuses on the stand and jump MJO. Based on whether their convection penetrates the Maritime Continent (MC), stand and jump MJO are seen as non-penetrating (NP) MJO, while the rest two are seen as eastward-penetrating (EP) MJO. Results reveal the relative roles of the westward-propagating wave (WPW), as well as the QBO and ENSO, in limiting MJO propagation. Lack of the premoistening over the southern sea surface of the MC stops NP MJO from penetrating the MC. The active convection of the WPWs hinders the descending branch of the NP MJO circulation and therefore leads to the insufficient meridional advective moistening over the southern sea surface of the MC. The independent convection over the Pacific for jump MJO is influenced by a combined effect of the QBO and ENSO. The tropopause instability induced by MJO is found to significantly decouple from its convection over the Pacific in the QBOW winters than in the QBOE winters. For jump MJO, the independent convection over the central Pacific comes from local WPWs whose amplification and further development into deep convection are correlated to jump MJO’s decoupled tropopause instability. For stand MJO, however, the seasonal-mean La Nina-like cool SST anomalies weaken the WPW activity over the central Pacific and confine WPWs within the western Pacific. Therefore, the decoupled tropopause instability of stand MJO is out phase of WPWs and fails to induce an independent convection over the central Pacific.