## 2 Literature Review
### FMEA and DEA Methods  
Data envelopment analysis (DEA) is a non-parametric approach that employs linear programming (LP) models to measure efficiency and determine objective weights using observed data for multiple inputs and outputs [20]. In [21], objective risk factor weights derived by DEA models varied for each failure mode; the failure modes were ranked based on the fuzzy weighted geometric means (FWGMs) of their fuzzy ratings for risk indicators (fuzzy RPN). Subjective weights for these indicators were assigned using the expert judgment method and solved through \(\alpha\)-level sets and linear programming models in addition to DEA [22]. In another study [23], the objective weights of risk factors were determined using the DEA method, and the significance of severity criteria was approached through weight restriction [23]. Furthermore, the exponential RPN (ERPN) and DEA model (CCR-AR) were integrated into the FMEA process in [24]. The authors in [25] developed and compared two models that combined FMEA and DEA: the slacks-based measure of the DEA (SBM-DEA) model and the data-driven approach (NDA). The latter was found to possess a relative advantage over the former. In [26], a DEA-FMEA methodology was presented, introducing two additional risk factors--cost and duration of treatment--as uncertain undesirable outputs. These were included alongside occurrence (O), severity (S), and detection (D), which were treated as inputs. The objective weights for these risk indicators were determined using the DEA technique. Interval values were incorporated into DEA in [27], which was then combined with grey relational analysis (GRA) to compute objective weights for risk factors and prioritize failure modes in an auto parts manufacturing process. The slacks-based data envelopment analysis (SBM-DEA) model, without outputs and using values obtained from the fuzzy inference system (FIS) and linguistic FMEA as inputs, was explained in [28]. In another fusion approach [29], AHP, fuzzy set theory, and DEA were combined, wherein experts in FMEA were assigned different weights using AHP. Moreover, the inputs for the DEA model comprised values of OSD and the reciprocal RPN, while the inverse of cost and time served as additional risk indicators set as outputs. Various types of information describing the heterogeneous features of risk factors were applied and clustered in [30], and a DEA model was utilized to rank failure modes using the values of risk factors as inputs. Additionally, in [31], fuzzy AHP, fuzzy VIKOR, and DEA (without input or output) models were integrated to determine the weights of each risk factor, where the relation of maximum to minimum weight was considered. Failure modes were obtained through the SHELL (software, hardware, environment, and liveware) model analysis in [32], where TOPSIS was used to determine the expert weights. The subjective and objective weight distribution of both experts and risk factors was computed by the DEA model using the risk factors as inputs. Meanwhile, the output was set to a constant of one; the cloud model was employed in order to cope with the fuzziness and randomness of the linguistic assessment information. Various other methods used in the literature to address the limitations of FMEA are summarized in Appendix B.