# A Reliability Engineering Approach for Managing Risks in CubeSats
## 3 Materials and Methods
### Step 3. Perform the Criticality Analysis
#### 3.3.1 Defining the Occurrence Index  
Starting from the outcomes of Step 2, each identified failure mode has to be analyzed in terms of its possibility to happen, following the scale presented in Table 1, which adapts ESA guidelines (ECSS-Q-ST-30-02C) in the range 1-5. Even if for CubeSats it is nowadays possible to retrieve some publicly available data about mission status, type, orbit status, builder type, spacecraft class, and specific failure rate data remain \begin{table}
\begin{tabular}{c c} \hline \hline
**Score** & **OCCURRENCE: Potential Failure Rate** \\ \hline
1 & Extremely remote (P \(\leq\) 1E\(-\)7) \\
2 & Remote (1E\(-\)7 \(<\) P \(\leq\) 1E\(-\)5) \\
3 & Occasional (1E\(-\)5 \(<\) P \(\leq\) 1E\(-\)3) \\
4 & Probable (1E\(-\)3 \(<\) P \(\leq\) 1E\(-\)1) \\
5 & Extremely probable (P \(>\) 1E\(-\)1) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Occurrence index. generally unavailable for university CubeSat components [32; 33]. With the purpose of increasing a systematic assessment of the occurrence index, failure mode probabilities of occurrence can be grouped in qualitative levels, based on engineering judgments or other reliability analysis performed for similar missions (see Table 2). Since these data usually refer to generic failure modes, following the functional breakdown of the system (developed in Step 2), the probability of failure mode at system level has been further explored, considering the failure propagation, i.e., the occurrence of mode of failures in other sub-systems, hypothesizing the principal failure mode already verified. This top-down perspective is implemented through the adoption of a variable represented by the conditioned probability coefficient, in order to integrate data of a generic failure mode, both at sub-system level (occurrence of a sub-system failure mode) and part level (occurrence of a specific fail at a part level). Table 3 presents the conditioned probability coefficients (in the range 1-5). At this step, specific inference rules have to be adopted for combining the three coefficients (system failure mode, sub-system failure mode, part failure mode), using specific IF-THEN criterion, created by the support of a fuzzy-based expert system [34]. In particular, the inference rule block adopted in the analysis follows the principle of Fuzzy Associative Map inference (FAM) able to guarantee different degrees of support for the relative importance of probabilities in the rule development. The rule-block aggregation overcomes the limitations of a simple mathematical product, supporting an in-depth analysis of failure propagation, still following a systematic perspective. The obtained index, i.e., Occurrence (O), represents one of the three coefficients of the FMECA (see Figure 1), and follows the qualitative scale already presented in \begin{table}
\begin{tabular}{c p{284.5 pt}} \hline \hline
**Score** & **FAILURE PROBABILITY: Likelihood of a System Failure Mode** \\ \hline \multirow{2}{*}{1} & The likelihood of the failure mode is estimated as extremely low, or it has never been experienced in similar missions. \\ \hline \multirow{2}{*}{2} & The likelihood of the failure mode is estimated as low, or it has been experienced once in similar missions. \\ \hline \multirow{2}{*}{3} & The likelihood of the failure mode is estimated as moderate, or the failure mode has been experienced twice in similar missions. \\ \hline \multirow{2}{*}{4} & The likelihood of the failure mode is estimated as high, or the failure mode has been experienced several times in similar missions. \\ \hline \multirow{2}{*}{5} & The likelihood of the failure mode is estimated as extremely high, or the failure mode has been experienced in almost every similar mission. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Failure probability coefficients.