## 4 Case Study
### The Method Employed in this Study Is Illustrated in Figure 7
#### 4.1.2 Phases 2 and 3: Do and Check
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Process Data:** & \multicolumn{4}{c}{**Overall Capability**} \\ \hline  & **Short-Side Armature** & \begin{tabular}{c} **Long-Side** \\ **Armature** \\ \end{tabular} & \begin{tabular}{c} **Short-Side** \\ **Armature** \\ \end{tabular} & \begin{tabular}{c} **Long-Side** \\ **Armature** \\ \end{tabular} \\ \hline LSL & 58.8399 & 58.8399 & PPL & 0.37 & 1.07 \\ \hline \begin{tabular}{l} Sample \\ mean \\ \end{tabular} & 96.0496 & 134.436 & Ppk & 0.37 & 1.07 \\ \hline \begin{tabular}{l} Sample N \\ \end{tabular} & 35 & 35 & Potential (within) capability \\ \hline \begin{tabular}{l} Overall \\ StDev \\ \end{tabular} & 33.3546 & 23.6373 & CPL & 0.69 & 1.05 \\ \hline \begin{tabular}{l} StDev \\ (within) \\ \end{tabular} & 17.9247 & 23.9849 & Cpk & 0.69 & 1.05 \\ \hline \multicolumn{2}{l}{Performance:} \\ \hline  & \multicolumn{2}{c}{Observed} & \multicolumn{2}{c}{Expected Overall} & \multicolumn{2}{c}{Expected Within} \\ \hline  & \begin{tabular}{c} Short-Side \\ Armature \\ \end{tabular} & \begin{tabular}{c} Long-Side \\ Armature \\ \end{tabular} & \begin{tabular}{c} Short-Side \\ Armature \\ \end{tabular} & \begin{tabular}{c} Long-Side \\ Armature \\ \end{tabular} & \
\begin{tabular}{c} Short-Side \\ Armature \\ \end{tabular} &
\begin{tabular}{c} Long-Side \\ Armature \\ \end{tabular} \\ \hline PPM \textless{} LSL & 0 & 0 & 132,301.04 & 691.52 & 18,952.24 & 811.29 \\ \hline Total PPM & 0 & 0 & 132,301.04 & 691.52 & 18,952.24 & 811.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Process capability measures for epoxy detachment force. Figure 18: The two sides of the armature. The data considered for the statistical calculation (N in Table 6) were those obtained from the samples taken from the process before and after adjusting the voltage in the curing station. A significance level (\(\alpha\)) of 0.05 was considered for the test. Since the means and standard deviations of the populations are unknown, the t-test was chosen. As a result of the test and according to the \(p\)-value in Table 6a, it can be concluded that there is no statistical evidence to accept the null hypothesis, since the \(p\)-value is below \(\alpha\). Therefore, there was a change in the mean breaking force of the short side of the armature after the voltage change. However, based on the data shown in the mean values (mean in Table 6), the change generates a decrease in the breaking force, which contradicts the intended outcome. The \(p\)-value in Table 6b suggests that there was no change in the breaking force of the long side of the armature after the voltage change. However, a significant change in the data dispersion was observed, as shown by the values of the corresponding standard deviations (StDev in Table 6). To evaluate the effectiveness of this modification in consistently meeting the specification, the company in this case study employs the Ppk index. This index leverages extensive data collected over time to factor out external influences on the process. It relies on the standard deviation of the entire data set (\(\sigma=S\)) as an estimate for process variation, as shown in Equation (1). In this case, with only one lower specification limit and aiming for higher detachment force values, a higher Ppk indicates better process capability. \[\text{Ppk}=\left[\frac{\mu-EI}{3\sigma_{L}}\right] \tag{1}\]  
where:  
\(\mu=\) the average of the data obtained from the variable under study (the force necessary to detach the epoxy coating from the armature) in N;  
\(EI=\) the detachment specification (in N);  
\(\sigma_{L}=\) the long-run standard deviation (in N). Compliance analysis based on Figure 19 and Table 7 clearly demonstrates that the implemented curing process modification fails to meet the specification. Both the short-side Ppk of 0 and the long-side Ppk of 0.47 fall significantly short of the company's minimum acceptable value of 1.32.