In the chemical process industry, product quality and plant safety are maintained by controlling process variables. A massive number of state variables are involved in decision making the characteristics of propagating failures in the chemical system. The Signed Directed Graph (SDG) is a qualitative graphical model that has been widely applied in chemical process industries for fault diagnosis. It describes and represents the causal relations between the process variables and their effect relations in systems. The conventional SDG fault diagnosis algorithm is a single-scale fault representation origin, and it cannot effectively solve multiple fault representation origins. Due to the qualitative nature of SDG, it produces spurious and erroneous interpretations when the process variable is going through a non-single transition. The wavelet-based SDG (MSSDG) method is a successful methodology because it effectively separates determinist and stochastic characteristics. The MSSDG fault diagnosis modelling is applied to a continuous stirred tank reactor system (CSTR) to discuss thoroughly. In short, new model studies on processes from the petrochemical industries and research on implementing the multilevel modelling approach of signed directed graphs are intended. © 2022 Author(s).