# A Guideline for Implementing a Robust Optimization of a Complex Multi-Stage Manufacturing Process
## 5 Discussion  
The collaboration between statisticians and engineers led to implementing the general PDCA cycle (Figure 8). The identification of main failures and the weak points of the manufacturing process, the implementation of regression models and the detection of latent failure at the early stage of the process allowed for optimizing the overall production cycle.  
The successful efforts of collaboration among the engineers and statisticians became fundamental in providing clear and specific advantages articulated through the following steps:  
1. The re-examination of each ultrasound probe manufacturing phase under strong critical point of view;
2. Need to add electrical and mechanical in-process measurements (several factors, several responses);
3. The identification and the analysis of factors, never evaluated by engineering, that can influence the variability of the production process;
4. The management and the analysis by considering 36 difference factors and 38 response variables (both qualitative and quantitative); and  
Figure 8: Plan-do-check-act (PDCA) cycle for the continuous improvement in US probes manufacturing process.  
Figure 7: Latent defect detected in the workpieces at stage #3: crack in the US probe bulk (red rectangular). The detection is provided by SAM.  
The distinction between systematic, noise, and block effects for defining and planning the design of experiment [70].  
Through this rigorous approach, the engineers, in agreement with the statisticians, were able to manage and to organize the analysis by considering more than 36 different factors, and 38 response variables, both quantitative and qualitative.  
The two different statistical models led to the identification, by successive refinements, of the final set of factors considered most significant within the process variability. As a contribution to reduce the failure occurrences, the two selected (and applied) statistical models were used for implementing the actions necessary to improve of the production process.  
The statistical results revealed:  
Significant effects of the process factors;  
The operators involved in the manufacturing play a key role in the variability of the production process;  
The need to implement a DoE (design of experiments) in the early stages of the production process for a better screening of the principal critical factors.  
The continuous discussion between the engineering and the statisticians together the gradual development of know-how during this study suggested to analyze the early stages of the manufacturing process. Therefore, the NDT technique as SAM allowed for mitigating the risk level of the US probes manufacturing by intercepting latent defects during the process (Figure 9).  
The robust process optimization led to a lower risk level for some stages of the process, i.e., the mechanical dicing (stage #5), but highlighting that stage #3 is also affected by latent failure detected by the SAM analysis and not recognized at priori. The damage consisting in a crack opened a tangible framework for the engineers that need to solve the problem. In a multi-stage complex manufacturing process such as US probes, the risk level is medium and this allows engineers to follow the continuous improvement approach for guaranteeing the products quality. The corrective actions applied to the multi-stage production process thanks to the continuous PDCA application have been verified and validated according to the regulations for medical products [72].  
The knowledge acquired during this project allowed for transferring the methodology and the effectiveness of the process quality improvement to other products. Furthermore, the continuous improvement strategy helped the workers to take ownership for their work by reinforcing the team working and their motivations.  
Figure 9: The risk level mitigation during the robust process optimization.