Information reliability and uncertainty are two important characteristics that need to be taken care of in any kind of decision‐making process. The hesitancy of the human mind is one of the major factors that introduce uncertainty in decision‐making. To include the reliability and to resolve the issue of hesitancy in a single framework, in this study, two novel concepts, namely, dual hesitant Z‐number (DHZN) and correlated distance measure between two DHZNs (CD‐DHZN) are proposed. DHZN = (Ah, Bh ), is a judicious integration of hesitant fuzzy sets and Z‐number. Here, Ah is the expert's opinion and Bh is the reliability of the expert's opinion. Further, the randomness of the information brings uncertainty to the decision‐making process. To circumvent this issue, DHZN is quantified with Cloud model theory and fuzzy envelope. To enhance the information utilization and to reduce the information loss problem while quantifying CD‐DHZN, the correlation and the underlying hidden probabilistic relationship between the two parts of a DHZN are captured using the Pearson correlation coefficient, the maximum entropy principle, and Hellinger distance. Then, the extended failure mode and effect analysis (E‐FMEA) is proposed with the help of DHZN, CD‐DHZN, and VlseKriterijuska Optimizacija IKomoromisno Resenje technique for prioritization of risks. Similarly, extended bow‐tie (E‐BT) is also proposed for the quantification of basic events (BEs), top event, and accident scenarios. Two case studies with systematic experimental investigations are presented and results are compared with other existing techniques. The results show that the proposed models are able to effectively prioritize the failure modes in E‐FMEA and quantify the BEs in E‐BT. The results confirm the feasibility and applicability of the proposed models. Sensitivity analysis is also performed to ensure the plausibility and robustness of the proposed model. [ABSTRACT FROM AUTHOR]