1. A method of compound hold-time fault diagnosis, comprising: receiving scan pattern test information and faulty scan chain information, the scan pattern test information comprising test response data for scan patterns, the faulty scan chain information comprising information of a scan chain having one or more hold-time faults; performing a profiling-based scan chain diagnosis on the scan chain to determine observed scan cell failing probability information and one or more faulty segments based on the scan pattern test information; deriving calculated scan cell failing probability information for the one or more faulty segments; and verifying existence of one or more compound hold-time faults associated with one or more validated faulty segments based on the calculated scan cell failing probability information and the observed scan cell failing probability information.