A joint-analysis by the use of (i) the multi-criteria decision-making (MCDM) technique of Typical-Analytical-Hierarchy-Process (T_AHP) and Fuzzy-Analytical-Hierarchy-Process (F_AHP) with (ii) the Hazard and Operability (HAZOP) method respectively, was conducted in a sour-crude-oil process industry (SCOPI), focusing on the deviations with economic/health/environmental impact. Consequently, the intention of this paper is dual; that means the first one is the presentation and application of the traditional HAZOP method on a SCOPI, and the second one the illustration and usage of the combined HAZOP_TAHP/FAHP framework in the previous referred industry, via the resulted hazards with economical, health and also environmental impacts, unveiling the sustainable dimension of this approach. The choice of the particular SCOPI for executing the HAZOP process is greatly powerful for the implementation of this approach, due to the plentiful hazards that the process includes, and due to its sophisticated design, as well. Originally, the conventional HAZOP study was carried out for finding out the potential destructive causes of abnormal circumstances in the SCOPI’s establishment. Subsequently, the defined (by HAZOP) hazards with particular economic, health and environmental impacts were elaborated by the T_AHP and F_AHP techniques in order to broaden the HAZOP results and prioritize the risks in the worksite of the SCOPI. It is worthwhile mentioning that this joint-analysis can afford a reliable base to enhance procedure safety and upgrade the occupational health safety’s level (OHS). Likewise, it might be a constructive means for the decision-makers to: (i) evaluate the urgent situation of the restricted resources’ investment, in measures of preventing particular deviations (like the ones with economical, health and environmental consequences), and (ii) to endorse the sustainable growth of this industry, taking into account that a significant part of literature utilized the issue of sustainability as a frame for the development of OHS RAA techniques.