# Failure Mode and Effect Analysis for Cyber-Physical Systems
## 2 Related Work
### RPN Estimation Improvement  
FMEA's traditional RPN has been heavily criticized for its calculation formula and its generic parameters. Over the past decade, several studies aimed at improving RPN calculation. [PERSON] et al. (2018) applied fuzzy logic to FMEA aiming to diminish the number of rules needed for the RPN. The authors used a Guided Rules Reduction System (GRRS) where the user only had to provide the most relevant rules to the fuzzy RPN model. The authors' approach was assessed through real-world scenarios, and the results state its effectiveness in reducing the number of rules while maintaining the capability of predicting failure modes. [PERSON] et al. (2018) introduced a new RPN which encompassed the fuzzy nature of the risk factor and their corresponding weights, to prioritize the failure modes. According to the authors, their approach is more realistic, practical, and flexible than the original RPN calculation. Moreover, by presenting a linguistic evaluation, the assessment is easier rather than numerical values. Finally, they combined the three parameters of FMEA aiming to provide a clear differentiation amongst them and arrange the failure modes. [PERSON] et al. (2018), addressed the representation of uncertain information, labeled D numbers, through Grey Relation Projection (GRP) to assess the RPN of failure modes. The D numbers tackle the subjective nature of FMEA. By presenting an illustrative example, the authors state that their approach surpasses any drawback of the original RPN, thus granting their framework increased value. [PERSON] et al. (2018) proposed an improvement to FMEA by adding cost, casualty, downtime, probability of occurrence, and detectability factors to the RPN calculation. Each factor value is obtained by comparing the failure mode with the worst situation in the affected area, contrary to the usual rank assignment by experts. To reduce the drawbacks of traditional RPN calculation, [PERSON] et al. (2018) suggested the use of Multi-Criteria Decision Making (MCDM) in the prioritization of failure modes. The authors aimed to accomplish fitter results in prioritizing failure modes by using an Analytic Hierarchy Process (AHP) and a Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) method. The authors prioritized the failure modes through an AHP scale and estimated the weight of each failure mode by applying the AHP to the outcome of the decision matrix. Moreover, the authors multiplied the weights of the failure modes by the RPN equivalents of the failure modes to determine AHP-RPN values which, in turn, was used to sort the failure modes. Finally, the authors concluded that compared to the other methods under scrutiny, the PROMETHEE method was more accurate to prioritize failure modes in FMEA. [PERSON] et al. (2018) adapted FMEA's RPN equivalent to the needs of health-care systems. New weights, scales, and coefficients were defined, considering patients and treatment data, for severity, occurrence, and detectability parameters. The authors concluded that FMEA's standard parameters and categorization should be adapted with technical knowledge. [PERSON] et al. (2018), merged reliability analyses, and MCDM in maintenance services optimization. The authors started with a FMECA analysis and implemented a fuzzy logic method to rank the previously obtained failure modes. To further develop the RPN calculation, the authors also used AHP to assess their weight criteria to the parameters, which was evaluated through a sensitivity analysis. Following the shortcomings of the original RPN calculation, [PERSON] et al. (2018) analyzed and compared some alternative methods within FMECA. The authors state that alternative RPN calculation formulas may be used depending on the type of application, and further provide recommendations and suggestions for such considerations. The authors used a scale reduction for the original parameters of the RPN, however,did not introduce additional factors to the formula.