# A Guideline for Implementing a Robust Optimization of a Complex Multi-Stage Manufacturing Process
## 3 The Methodology for Continuous Improvement: Robust Process Optimization
### The PDCA Cycle Implementation  
The PDCA cycle approach helps the company to identify the major root causes that limit the quality of the manufacturing process and to improve the know-how of the manufacturing process. Following [PERSON]'s philosophy [15; 17; 38], an inter-disciplinary team composed of engineers and physicists of R&D (research and development) of the US probes, mechanical designers together with the production and the people in charge of data collection on MES (manufacturing execution system) platform was assembled. For improving the production of an existing process, the initial step consisted of the identification of the weak points, assessing a classification of the risk level-based critical phases with the aim to obtain benefits through corrective actions in a short time. For complex manufacturing such as US probes, it becomes obvious that the improvement of process efficiency needs a medium-long term analysis, due to critical phases of the process manufacturing, in which different materials and components are involved. Furthermore, some stages are worker-dependent. SIPOC (suppliers, inputs, process, outputs, customers) [39; 40], Pareto chart [41], COPQ (Cost of poor quality) [42], brainstorming [43], FMECA (Failure mode, effects and criticality analysis) [24; 44], CTQ (Critical to quality) matrix [45], control charts [46], design of experiments [4; 47], cause and effect diagram [48], and process capability [49] are well-known tools and techniques in the engineering field. The latter have been used during the PDCA cycle implementation aiming to bring an effective solution of a problem and to provide benefits for the industrial scenario. Nevertheless, when dealing with many technical issues, it is not trivial to obtain valid and efficient results, also considering the issues due to the collection of data, and the identification of causes and related effects. Therefore, the manufacturing process (Figure 3) was analyzed not only through the process map (Figure 2a), but also using fault tree analysis (FTA) and the process failure modes and effects analysis (PFMEA), top-down and bottom-up techniques, respectively (Figure 3a). These latter are methods applied for root cause analysis and for potential failure modes, whose combination was used for the validation and for the assessment of electric/electrical devices in the railway and aircraft systems [50] and for the risk analysis of safety-critical engineering systems [51]. The implementation of FTA and PFMEA was developed according to [52] and [53], respectively. In the context of the manufacturing process of ultrasound (US) probes for medical imaging, the implementation of the fault tree (logical diagram) started from the two main top events (undesired events), that are \"capacitance test--FAIL\" (stage #15) and \"mean sensitivity test--FAIL\" (stage #23) with the aim to search for the possible causes of such events. More specifically, the capacitance test is the measurement of the capacitance of each piezoelectric element. The mean capacitance of the 192 piezoelectric elements must be in the range (350-400) pF. The mean sensitivity for the US probe, that is the average for all array elements, named _Sensitivity\({}_{j}\)_, and defined as follows:  
\[Sensitivity_{j}=\frac{V_{RX_{j}}}{V_{TX_{j}}} \tag{1}\]  
In Formula (1), the index \(j\) relates to the number of piezoelectric elements, \(V_{RX}\) is the peak amplitude of the received echo, and \(V_{TX}\) is the peak amplitude of the transmitted ultrasound pulses. \(V_{TX}\) and \(V_{RX}\) are automatically measured through the measurement system for the electroacoustic (pulse echo) characterization [54]. The deductive analysis through FTA investigates the combination of failures of the process stage reaching the FAIL. In fact, the detailed analysis of the logical and temporal relationships leads to more details about the description of the possible failures of each sub-process and process stage starting from the undesired top event.