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Diagnosis tools can be used to speed up the process for finding the root causes of functional or performance problems in a VLSI circuit. In this paper, we propose a method to locate possible segments that cause extra delays on circuit paths. We use the delay bounds of the tested paths to build linear constraints. By guiding the solutions of the linear constraints solved by a linear programming solver, we can identify segments with extra delays. Also, with the ranks of segment delays, we can prioritize the search for possible locations of failed segments. Besides, we also propose to reduce the search space by identifying indistinguishable segments. Essentially, we cannot separate segments in the same category no matter which segments have faults. This approach greatly increases the efficiency of the diagnosis process. Three main features of the proposed method are that: 1) it does not assume any delay fault model; 2) it derives diagnosis results directly from test data; and 3) it is able to diagnose failures caused by multiple delay defects. These features make our proposed method more realistic on solving the real problems occurring in the manufacturing process. In the experimental results, for most cases of injecting 5% of the longest path delay, the probabilities are over 90% for locating faulty segments within the list of top-ten suspects, and the average rankings, that is often referred to as first hit rank (FHR), which is defined as the rank of the first hit of the defect in the ranking list, are among the top five suspect locations for single fault injection. In the experimental results of multiple faults injection, the average FHRs are also lower than 5 for all cases of injecting 1% of the longest path delay.