In processor and high-end chip designs, path delay difference between pre-silicon and post-silicon have become an important issue. Identifying the factors for the difference with speed limiting paths is required to achieve target performance. A statistical diagnosis framework, called speed-path analysis, identifies them. Speed-path analysis uses fail data from at-speed delay test with silicon samples. Since at-speed delay test activates multiple paths simultaneously, it makes many failed latches with multiple sensitized paths. We will refer to these failed latches as multi-path failed latches. Previous works have not discussed how to handle multi-path failed latches because they are discussions under the assumption that path delay differences are obtained correctly. Generating additional test patterns to activate a single path for each latch is a very time-consuming task. Without using multi-path failed latches from at-speed delay test, the fatal factors for path delay differences with speed limiting paths can be missed because the number of non multi-path failed latches is small. This paper proposes methods for handling multi-path failed latches. By experiments based on a test processor design, we can deal with 12% of the timing-critical latches adopted as failed latches while 1% using only non multi-path failed latches.