# Failure Mode and Effect Analysis for Cyber-Physical Systems
## 3 Failure Mode and Effect Analysis  
FMEA is an engineering method designed to identify potential failure modes and its failure causes, assessing the effects these have within a given system. A failure mode is usually defined as a fluctuation inside the performance criteria for the component (inability to perform the design functions). The FMEA method identifies the decisions necessary to prevent individual system failures [4]. Nevertheless, FMEA has some associated problems, which [PERSON] et al. [16] expose comprehensively, from which we gathered, among others, subjectivity, time consumption, staff level, too expensive, and late application. The authors also classified the FMEA's problems into four main classes (Applicability, Cause and effects representation, Risk analysis, and Problem-solving) and 18 different subproblems. Additionally, regarding FMEA's solutions/improvements they used the same four categories and 19 types of solutions. FMEA's risk assessment procedure can be divided into five fundamental steps: System subdivision, failure modes identification, RPN calculation, prevention actions recording, and analysis reporting. The first step consists of system subdivision, in which the system is broken down into subsystems, with a complete list of components. In the second step, it is necessary to identify failure modes, its causes for each component, and determining the consequences for each. Subsequently, the third step is to assess the risk, considering Severity, Occurrence, and Detection of each failure mode. Where Severity is the reckoning of the severity of the potential failure, Occurrence is a numerical subjective assessment of the probability for each cause of failure, and Detection is the performance of detecting the failure before failure occurrence [8]. This assessment is usually represented as a cost caused by failures represented as probabilities [17]. Each one of these parameters is recorded and estimated in predefined categories. Then, calculating the RPN to prioritize the identified vulnerabilities, through the product of Severity, Occurrence, and Detection values. The fourth step consists of recording actions to prevent serious consequences, correct failures, and to restore system functions. Finally, the fifth, and last, step is to report the analysis, summarizing the FMEA process, and its results. The FMEA method is universally used and easy to understand the method, mainly because it applies to complex systems, and efficient for identifying all technical failure modes. Table 1 represents the FMEA risk factors, evaluated through a 10-point scale [12]. [PERSON] et al. [5] provided the crisp ratings for each parameter with a thorough description, thus we refer to this paper for a more in-depth analysis of the scale of each parameter. However, the FMEA's result outcome heavily depends on the study team experience, given the fact that the RPN parameters and its values are categorized by them. Moreover, FMEA only considers vulnerabilities that emerged from single failures, failing to identify vulnerabilities originated by combinations of failures. From a structural point of view, FMEA's classical RPN formula for risk index calculation has several drawbacks, such as the existence of gaps in the range of admissible values, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Occurrence** & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \cline{2-8}
**(O)** & \multicolumn{4}{c}{Nearly Impossible} & \multicolumn{4}{c}{Failure Almost Inevitable} \\ \hline
**Severity** & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \cline{2-8}
**(S)** & \multicolumn{4}{c}{No Effect} & \multicolumn{4}{c}{Hazardous Effect} \\ \hline
**Detectability** & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \cline{2-8}
**(D)** & \multicolumn{4}{c}{Almost Certain} & \multicolumn{4}{c}{Absolute Uncertainty} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Failure Mode and Effect Analysis (FMEA) parameters for the Risk Priority Number (RPN) calculation Variables.