# A Guideline for Implementing a Robust Optimization of a Complex Multi-Stage Manufacturing Process
## 2 Materials
### The Manufacturing Process  
The growing demand for geometrical precision and the guarantee of high process capability by limiting material damage is a continuous task that engineers must chase. The manufacturing process of ultrasound probes for medical imaging is composed of 23 stages (Figure 2a) and it requires homogeneous layers with specific thicknesses (from some microns up to 500 \(\upmu\)m) by the bonding operation between materials with different thermal expansion coefficients and densities. The bonding stages of the layers requires homogeneous bonding lines with specific thickness (up to 1 \(\upmu\)m) [34]. The bonding process is realized in a controlled environment, 24 \(\pm\) 1 \({}^{\circ}\)C with relative humidity less than 50%. Factors such as roughness of the components, curing time and temperature, deposition technique, and viscosity of the epoxy resin are very important for guaranteeing not only the adhesion between layers, but also a bonding line less than 1 \(\upmu\)m and the homogeneity of the deposition. Other essential operations, having a high impact on the final quality of the US probe, are the micro-soldering of the electrical interconnections and the mechanical dicing operation, that create the element of the piezoelectric array. The operations are completely manufactured at the site of Esaote S.p.A. located in Florence (Italy). The production line for this type of US probe is organized in batches, in which different components are assembled through step by step processes. The manufacturing process based on a batch size of 4 pieces had been principally chosen due to the blade wear (dicing saw--DAD3350--DSCO--Tokyo, Japan) devoted to mechanical dicing for this specific product. This stage is critical for the manufacturing process, and the fundamental requirement consisting in strong and homogeneous adhesion between materials must be satisfied. The major additional variability source for the generation of micro-cracks, chipping, or delamination [35; 36] is provided by mechanical dicing stress (Figure 2b), considered a very critical operation for the manufacturing of the US probe. The factors of feed rate (mm/s), spindle revolution (rpm), diamond grains size and the density of grains in the blade, and the quality of the blade cooling water avoiding the impurities [37] are important for obtaining an US transducer without cracks or delamination. The left (Figure 2b) allows for the electrical separation (electrical insulation) of the piezoelectric material for the generation of the piezoelectric elements array. The separation is provided by the blade of mechanical dicing: for C1-8 probe the kerf is 40 \(\pm\) 2 \(\upmu\)m.  
The high number of process stages (#23), as reported in Figure 2a, needs to predict, in advance, the detection of failures in order to decrease the costs of the waste material, and the manufacturing labor costs. Moreover, it should be underlined that: (i) the analysis here carried out allows to reveal the faults in advance at stage #5 (mechanical dicing), instead of through the electrical measurements performed at stage #15 (capacitance test); and (ii) the causes of the cracks, as shown in the non-destructive technique applied at stage #3  
Figure 2: The manufacturing of an US probe: (**a**) the stages of the process; (**b**) the mechanical dicing of the US array. (bonding piezoelectric element on backing), are further stressed during the mechanical pricing. However, these causes can be related to the bonding operations (performed in the early manufacturing stages), but they require a deep investigation by means of the fault detection analyses (Section 3.1) and SAM (Sections 3.3 and 4). The quality of the US transducer is important to maintain the same limited variability in terms of acoustic output and image quality. The workers must perform specific and critical operation linked to the experience and the knowledge about the assembly of components with different type of characteristics.