With the rapid development of science and technology, the structure and states of systems have become more and more complicated. Multi-state systems have widely been used in practical engineering, including aviation, aerospace, maritime, transportation and mining industries. To complete the complex required tasks, these multi systems need to keep the higher reliability, so it is important to identify the weakest link of multi-state systems. This paper proposes a weakness analysis method based on integrated importance measure (IIM) for multi-states. To better evaluate IIM, the universal generating function (UGF) method is introduced to analyze the reliability of multi-state hybrid systems. Taking the height adjustment hydraulic system of the electric traction shearer as an example, the critical states and the critical component can be determined by IIM. The performance is verified by comparing with classical multi-state importance measures, Griffith Important Measure (GIM) and Birnbaum Important Measure (BIM). The ranking accuracy is obtained by mean average precision (mAP), which shows that the ranking accuracy of IIM is 97.33%, which is 13.12% higher than that of GIM and 3.86% higher than that of BIM.