Time interval-based pattern mining is proposed to improve the lack of the information of time intervals by sequential pattern mining. Previous works of time interval-based pattern mining focused on the relations between events without considering the duration of each event. However, the same event with different time durations will cause definitely different results. For example, if some people cough for one week, they may get a cold for a while. In contrast, if some patients cough for one year, they may get pneumonia in the future. In this work, we propose two algorithms, SARA and SARS, to extract the frequent Time Interval-based Event with Duration, TIED, patterns. TIED patterns not only keep the relations between two events but also reveal the time periods when each event happens and ends. In the experiments, we propose a naive algorithm and modify a previous algorithm to compare the performances with SARA and SARS. The experimental results show that SARA and SARS are more efficient in execution time and memory usage than other two algorithms.