This paper presents some practical applications of signed directed graphs (SDGs) to computer-aided hazard and operability study (HAZOP) and fault diagnosis, based on an analysis of the SDG theory. The SDG is modeled for the inversion of synthetic ammonia, which is highly dangerous in process industry, and HAZOP and fault diagnosis based on the SDG model are presented. A new reasoning method, whereby inverse inference is combined with forward inference, is presented to implement SDG fault diagnosis based on a breadth-first algorithm with consistency rules. Compared with conventional inference engines, this new method can better avoid qualitative spuriousness and combination explosion, and can deal with unobservable nodes in SDGs more effectively. Experimental results show the validity and advantages of the new SDG method.