To determine the critical component in an industry is one of the most important tasks performed by maintenance personnel to choose the best maintenance policy. Therefore, the purpose of the current paper is to develop a methodology based on integrated cloud model and extended preference ranking organization method for enrichment evaluation (PROMETHEE) method for finding the most critical component of the framework by ranking the failure causes of the system from multiple decision maker perspective. For this purpose, ranking of failure causes is performed by taking into account five factors namely chances of occurrence of failure (F0), non-detection probability (Nd), downtime duration (Dd), spare part criticality (Spc) and safety risk (Sr). In this paper, first the primary and secondary weight of decision makers are calculated based on the uncertainty degree and divergence degree, respectively, to determine overall weight using cloud model theory by converting the uncertain linguistic evaluation matrix into interval cloud matrix, and then ranking of the steam handling subunit of paper making unit in a paper mill using extended PROMETHEE. The effectiveness of the proposed methodology is explained by considering steam handling subunit of paper making unit to find the critical component.