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With the growth of memory capacity and density, test cost and yield improvement are becoming more important. In the case of embedded memories for systems-on-a-chip (SOC), built-in redundancy analysis (BIRA) is widely used as a solution to solve quality and yield issues by replacing faulty cells with extra good cells. However, previous BIRA approaches focused mainly on embedded memories rather than commodity memories. Many BIRA approaches require extra hardware overhead to achieve the optimal repair rate, which means that 100% of solution detection is guaranteed for intrinsically repairable dies, or they suffer a loss of repair rate to minimize the hardware overhead. In order to achieve both low area overhead and optimal repair rate, a novel BIRA approach is proposed and it builds a line-based searching tree. The proposed BIRA minimizes the storage capacity requirements to store faulty address information by dropping all unnecessary faulty addresses for inherently repairable die. The proposed BIRA analyzes redundancies quickly and efficiently with optimal repair rate by using a selected fail count comparison algorithm. Experimental results show that the proposed BIRA achieves optimal repair rate, fast analysis speed, and nearly optimal repair solutions with a relatively small area overhead.