Previous works of subsequence search in time interval-based events sequences have focused on the relations among events without considering the duration of each event. However, the same event with different time duration may lead to different results. In this work, we propose an index structure referred to as Endpoint Index based on the concept of inverted index to efficiently extract the Time Interval-based Event with Duration, TIED, subsequence. TIED subsequence search considers duration of event intervals in conjunction with relation among events. This makes the results of TIED subsequence search more accurate than those obtained using traditional search methods. In addition, we propose an algorithm SSD, Subsequence Search with Duration, incorporating a pruning strategy to search TIED subsequences efficiently. For the performance evaluation, we modify previous algorithms to compare with our proposed methods SSD_Endpoint and SSD_ER. The experimental results demonstrate that SSD_Endpoint and SSD_ER are more efficient than state-of-the-art algorithms.