# Safety-Oriented System Hardware Architecture Exploration in Compliance with ISO 26262
## 4 Safety-Oriented System Hardware Architecture Exploration Framework
### System Hardware Architecture Exploration with Safety and Hardware Overhead Consideration
#### 4.3.2. ASIL-Oriented Hardware Architecture Exploration Algorithm
Thus, to reduce the failure rates of these two hardware elements more efficiently, we apply the hardware duplication with diversity \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Hardware Elements** & **Failure Rate \(\lambda\) (h)** & **\% Non-Safe Fault** & \(SM\_LibC(i))** \\ \hline Brake ECU & \(3.3\times 10^{-7}\) & 100\% & Not Necessary \\ EBM & \(4.2\times 10^{-7}\) & 100\% & \\ CAN bus & \(2.4\times 10^{-7}\) & 100\% & \\ AEB microcontroller & \(3.8\times 10^{-7}\) & 100\% & \\ Brake pedal sensor & \(2.6\times 10^{-8}\) & 100\% & \\ Brake pedal ECU & \(1.05\times 10^{-8}\) & 100\% & \\ Radar & \(1.3\times 10^{-7}\) & 100\% & \\ Radar ECU & \(1.05\times 10^{-8}\) & 100\% & \\ Speed sensor & \(2.6\times 10^{-8}\) & 100\% & \\ Speed Meter ECU & \(1.05\times 10^{-8}\) & 100\% & \\ Power supply & \(2\times 10^{-8}\) & 100\% & \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Hardware element’s failure rates of the AEB system. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**MCS** & \(FP_{MCS_{k}}(t)\) & \(Gap_{PMHF}\) (\(MCS_{k}\)) & \(Gap_{SPTM}\) (\(MCS_{k}\)) & \(Gap_{LFM}\) (\(MCS_{k}\)) & _Max_Gap_ \\ \hline \(\{\)CAN bus\(\}\) & \(1.19928\times 10^{-3}\) & \(2.3986\times 10^{1}\) & \(6.3856\times 10^{0}\) & N/A & \(2.3986\times 10^{1}\) \\ \(\{\)AEB microcontroller\(\}\) & \(1.89820\times 10^{-3}\) & \(3.7965\times 10^{1}\) & \(1.0107\times 10^{1}\) & N/A & \(3.7965\times 10^{1}\) \\ \(\{\)Brake pedal sensor\(\}\) & \(5.24986\times 10^{-5}\) & \(2.5999\times 10^{0}\) & \(6.9178\times 10^{-1}\) & N/A & \(2.5999\times 10^{0}\) \\ \(\{\)Brake pedal ECU\(\}\) & \(1.29992\times 10^{-4}\) & \(1.0500\times 10^{0}\) & \(2.7953\times 10^{-1}\) & N/A & \(1.0500\times 10^{0}\) \\ \(\{\)Radar\(\}\) & \(2.64965\times 10^{-4}\) & \(5.2994\times 10^{0}\) & \(1.4108\times 10^{0}\) & N/A & \(5.2994\times 10^{0}\) \\ \(\{\)Radar ECU\(\}\) & \(5.24986\times 10^{-5}\) & \(1.0500\times 10^{0}\) & \(2.7953\times 10^{-1}\) & N/A & \(1.0500\times 10^{0}\) \\ \(\{\)Speed sensor\(\}\) & \(1.29992\times 10^{-4}\) & \(2.5999\times 10^{0}\) & \(6.9178\times 10^{-1}\) & N/A & \(2.5999\times 10^{0}\) \\ \(\{\)Speed Meter ECU\(\}\) & \(5.24986\times 10^{-5}\) & \(1.0500\times 10^{0}\) & \(2.7953\times 10^{-1}\) & N/A & \(1.0500\times 10^{0}\) \\ \(\{\)Power supply\(\}\) & \(9.99995\times 10^{-6}\) & \(2.0000\times 10^{-1}\) & \(5.3245\times 10^{-2}\) & N/A & \(2.0000\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: List of MCSs and their failure probabilities for the AEB system. design to the CAN bus and AEB_MCU to let their faults become safe faults. Table 13 exhibits the results of the safety mechanism deployment in this design iteration. After safety mechanism deployment, the hardware architecture metrics are calculated as shown below:

\[SPFM_{\textit{lite\_d}}=1-\frac{\sum_{\textit{Softy-Related HW elements}}\left(\lambda_{SPF}+\lambda_{RF}\right)}{\sum_{\textit{Softy-Related HW elements}}\lambda}=1-\frac{2.51\times 10^{-8}}{3.76\times 10^{-6}}=99.33\%\]

\[LFM_{\textit{lite\_d}}=1-\frac{\sum_{\textit{Softy-Related HW elements}}\left(\lambda_{DFF,L}\right)}{\sum_{\textit{Softy-Related HW elements}}\left(\lambda-\lambda_{SPF}-\lambda_{RF}\right)}=1-\frac{7.05\times 10^{-9}}{3.73 \times 10^{-6}}=99.81\%\]

\[PMHF_{\textit{lite\_d}}=\lambda_{SPF}+\lambda_{RF}+\lambda_{DPF,L}=3.215\times 1 0^{-8}\]

Consequently, only the \(PMHF_{\textit{lite\_d}}\) still exceeds \(PMHF_{\textit{tar}}\) and therefore a subsequent design iteration is required. The process of the FTA-based weak-point analysis and ASIL-oriented hardware architecture exploration at subsequent design iterations is very similar to the previous iteration and omitted here.