Algorithms based on the 'signed directed graph(SDG)' and its modifications, the 'SDG with delay' and the 'Multi-stage Signed Directed Graph (MSDG), were developed for the diagnosis of the system failure in the chemical process. A feasibility study on the automated fault diagnosis system based on the 'SDG' was performed making use of a practical pilot plant. The fault diagnosis based on the 'SDG with delay' can give the candidates in order of possibilities of being the origin of failure if it can utilize the information about delays of immediate influences among the variables. The advantage of this method was demonstrated by applying to the same data obtained from the pilot plant. In order to utilize the time varying information, the concept of the 'MSDG' is introduced. The MSDG enables ones to diagnose impulse-type failures and the failures in the back-up systems. The capability of the method based on the MSDG was with the example of the TMI accident.