# Life-Cycle Oriented Risk Assessment Using a Monte Carlo Simulation
## 4 Results
### Application on the Use-Case  
The Monte Carlo simulation-based risk assessment tool is used within the presented use-case. The general results from the risk assessment are shown in Table 2. In the use-cases' configuration, an immediate switch will generate savings in the order of EUR 450,000 during the investigated timespan in more than half of the simulated scenarios. This is more than the other two switching scenarios can possibly generate. However, the mean of all the simulated change in costs is about EUR \(-4.2\) M; i.e., a substantial loss. The reasons for this unevenness in the distribution are a few costly incidents: if a switch is performed immediately and the new lifetime falls just a little short, the first incident will require a recall of a lot of products. This observation is in line with the experience made during the use case. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Immediate Switch** & **Test and Switch** & **Test, then Switch** \\ \hline \(\Delta t_{t}\) & \(=0\) & \(=t_{0}/g\) & \(=t_{0}/g\) \\ \(\Delta t_{r}\) & \(=\left\{\begin{array}{ll}0&\text{if }t_{i}\geq t_{0}\\ t_{i}&\text{else}\end{array}\right.\) & \(=\left\{\begin{array}{ll}0&\text{if }t_{i}\geq t_{0}\\ t_{i}/g&\text{else}\end{array}\right.\) & \(=0\) \\ \(\Delta t_{s}\) & \(=\min(t_{i},\ t_{0})\) & \(=\left\{\begin{array}{ll}t_{0}&t_{i}\geq t_{0}\\ t_{i}/g&\text{else}\end{array}\right.\) & \(=\left\{\begin{array}{ll}t_{0}-\Delta t_{t}&t_{i}\geq t_{0}\\ 0&\text{else}\end{array}\right.\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dependencies of the timespans and switching scenarios. Looking at the expected savings over time (Figure 6), these effects can be studied in more detail. If an immediate switch is performed, the saving becomes effective immediately. During the first days after the change, the expected savings are positive and grow continuously. However, these savings are just \"borrowed\". This can be a very dangerous situation in real applications: seeing the savings being effective, might be a premature sign of good performance of this switch. The opposite situation could occur in the case of the third switching strategy (Figure 6c), where even if the strategy shows the best average performance, the savings do not become effective immediately. Moreover, during the testing phase in the beginning of this change, only losses are seen. By performing a sensitivity analysis of the expected savings on the testing time and the certainty of the specification-performance-match, additional improvements can be identified. The results of this analysis are shown in Figure 7. The sensitivity analysis shows that matching the specification and the performance--i.e., reducing \(\Delta\)y in (1)-provides the biggest savings. If the specifications match the requirements and the product fully fulfills the specification an immediate switch with the risk of costly recalls is enabled. In any other case, testing is recommended. For short testing times, the test should be performed before the switch. For relatively long testing times, one might consider performing the test in parallel to the switch. This decision is affected by the assessed risk of an immediate switch before the test results are in. Hence, the sensitivity analysis is an important tool to identify \begin{table}
\begin{tabular}{l r r r} \hline \hline
**k\(\mathbf{\xi}\)** & **Immediate Switch** & **Test and Switch** & **Test, then Switch** \\ \hline MEAN & \(-4232\) & \(179\) & \(299\) \\ MEDIAN & \(450\) & \(442\) & \(442\) \\ STV & \(6859\) & \(377\) & \(209\) \\ Q1 & \(-11\),\(585\) & \(-308\) & \(-5\) \\ Q3 & \(450\) & \(442\) & \(442\) \\ MIN & \(-17\),\(512\) & \(-457\) & \(-8\) \\ MAX & \(450\) & \(442\) & \(442\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of the risk-assessment tool application on the use-case. Figure 5: Implemented risk assessment tool for the three switching strategies. the approach, and thus the department, offering the biggest leverage towards increasing saving and reducing risk.