## 3 Case Study. The Applied Evaluation Processes
### Phase 4: Improvement
Table 11 shows the reliability indices of the subsystems that contributed to the failures and the reliability indices of the man-machine system for five time periods considered within the 9.5-h shift during the period from 25 to 30 January 2021. Table 11 shows that, in the 7-h period after the start of the shift, in subsystem 1 (machine), the probability that there were no failures for scrap was 5.24%, while in subsystem 2 (tool) it was 47.86% and in subsystem 3 (process/operation) it was 4.64%. The lowest reliability was obtained for subsystem 3. Regarding the reliability of the man-machine system, the analysis showed a probability of 52.89% that no scrap failures would occur in the 7-h period after the shift started. Table 12 shows the reliability indices of the subsystems present in the failure analysis and the reliability indices of the man-machine system for five time periods considered within the 9.5-h shift during the period from 17 May to 28 May 2021. Table 12 shows that in the 7-h period after the start of the shift, in subsystem 1 (machine), the probability that there were no failures for scrap was 0.57%, while in subsystem 2 (tool) it was 13.46% and in subsystem 3 (process/operation) it was 0.16%. The lowest reliability was obtained for subsystem 3. Regarding the reliability of the man-machine system, the analysis showed a probability of 14.09% that no scrap failures would occur in the 7-h period after the shift started. Once the lowest reliabilities of the subsystems (process/operation) and the components (maintenance/setup) were identified, to determine which component or components had an influence on the low reliability, the causes that generated it, the origin of these causes, and the actions to be taken, we performed a FMEA analysis. The recommended actions were documented as a work instruction. This action is described below. Failure Mode and Effect Analysis (FMEA). The analysis developed in the previous section for the case study yielded the causes that generated the low reliability of the subsystem (process/operation) and the components (maintenance/setup and institutional conditions/attitude). With this information as an input, we generated a FMEA analysis with a work team of two operators, one maintenance technician, and the production supervisor. Table 13 shows the FMEA analysis used to control and monitor the activities that affect the reliability of the man-machine system. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Periods** & **R1** & **R2** & **R3** & **R5** \\ \hline
1 h & 0.6563 & 0.9 & 0.645 & 0.9878 \\
3 h & 0.2827 & 0.7292 & 0.2683 & 0.8579 \\
5 h & 0.1218 & 0.5907 & 0.1116 & 0.6807 \\
7 h & 0.0524 & 0.4786 & 0.0464 & 0.5289 \\
9 h & 0.0226 & 0.3877 & 0.0193 & 0.4131 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Reliability of the subsystems and the man-machine system during five time periods for the period from 25 to 30 January 2021. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Periods** & **R1** & **R2** & **R3** & **R5** \\ \hline
1 h & 0.4782 & 0.7509 & 0.3990 & 0.9219 \\
3 h & 0.1094 & 0.4234 & 0.0635 & 0.5191 \\
5 h & 0.025 & 0.2387 & 0.0101 & 0.2653 \\
7 h & 0.0057 & 0.1346 & 0.0016 & 0.1409 \\
9 h & 0.0013 & 0.0759 & 0.0002 & 0.0773 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Reliability of subsystems and the man–machine system during five time periods for the period from 17 to 28 May 2021. Table 13 presents some activities identified as being of a mechanical and human-error origin. The corresponding activity for assembling, welding, and polishing, whose defect was the presentation of porous pieces due to contaminated tungsten, was the one that presented the highest NPR value. This particular action was monitored and controlled, as a work instruction, to prevent recurrence as shown in Figure 6. The work instruction presented in Figure 6 was used to reduce or eliminate failures due to this failure mode and evaluate the system's improvement.