## 4 Discussions  
The findings can be depicted as one measurement system design for parameter design in the Taguchi method. The literature review explained that most Taguchi method applications only informed about application of the tool without discussing the concept of variation measurement in the early implementation [29; 30; 31; 32; 33]. The parameter design in a robust engineering tool is further analyzed to ensure the measurement covers total variability in data. There are four stages in measurement systems for this flexible film. The first measurement system is the function system measurement (F). Secondly, noise strategy measurement (N) is done followed by control factor selection (C) and optimization (O). Figure 11 showed the measurement system in parameter design.  
Figure 11: F-N-C-O ladder for measurement system in robust design engineering.  
Figure 10: Ideal function plot for optimum (**a**) and worst condition (**b**).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type A** & **Condition** & **Estimated SNR (dB)** & **Confirmation SNR (dB)** \\ \hline Optimum & A1 B1 C3 D1 E2 F2 G3 & 14.91 & 14.82 \\ \hline Worst & A2 B2 C1 D3 E1 F3 G2 & 4.3 & 7.07 \\ \hline SNR dB Gain & 10.61 & 7.75 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Optimum and worst condition with confirmation run.  
The system is a close-loop measurement system called an F-N-C-O ladder. The problem statement is the system ignition followed by the four sub-systems; F for Function system, N for Noise system, C for Control system, and O for Optimization system. The application of the optimum condition is the output of the F-N-C-O ladder. The elements F-N-C-O are connected to each other by the Plan-Do-Study-Act so-called P-D-S-A cycle. In each element, the P-D-S-A cycle is used for continuous improvement from one sub-system to another. Each sub-system starts with P: Plan stage and ends up with A: Act stage. The Act stage in Function system (F) moves the Plan stage in Noise system (N).  
Act stage in N moves the Plan stage in Control system (C) and so on. In optimization system (O), S: Study stage analyzes the normality of the data spread. If the spread of data is not good (NG), the flow is back to Function system (F) under D: Do stage of selecting the quality characteristic. If the reproducibility is low detected in O system, the experiment is a failure. The failure is often related to basic function setting, quality characteristics, and other components of measurement. Thus, the flow is back to F. This P-D-S-A cycle ensures the mobility of the system and dependency to each sub-system. Details on each element are elaborated in further sections.  
[PERSON] and [PERSON] [34] explained that a robust design is considered as improvement stage of the product development process. A simple mathematic description is illustrated with an output variable denoted as y with a target value \(y_{\rm o}\). Three design parameters \(X_{1}\), \(X_{2}\), \(X_{3}\) and a noise factor \(Z\) as an uncontrollable variation is shown in Equation (5):  
\[Y=f(X_{1},\,X_{2},\,X_{3},\,\ldots\,\,Z_{1},\,Z_{2},\,Z_{3},\ldots\,\,\varepsilon \,)=b_{o}+b_{1}X_{1}+b_{2}X_{2}+b_{3}X_{3}+b_{Z}Z+b_{2Z}\,X_{2}Z+\varepsilon \tag{5}\]  
\(\varepsilon\) is an unknown, small residual term which is independent on the design parameter.  
With \(X_{2}=-bZ\,/\,b_{2}Z\), the influence of noise factor \(Z\) is completely disappearing. The equation is said to be robust because the influence of noise factor is minimized and disappeared. Therefore, the equation is placed at the bottom as the F-N-C-O foundation. The noise factors in an experiment can be varied, assumed that it is controllable during the experiment and uncontrollable in real life. There is some case whereby noise is not detected and its appearance is not even known. These variations are caused by extraneous factors. Extraneous factor could deviate the output result unintentionally.