## 4 Logistic Cyber-Physical Systems: A Prototypal Case Study  
In the following, we present a case study implementation on a prototypal system. The innovative context of the proposed approach, the substantial lack of algorithms, and the subsequent unavailability of test data (necessary to compare different design solutions), represented a great difficulty of this research. This case study comes from a project experience where a prototypal logistic CPS was built. The objective of this prototype was to demonstrate the potential of Industry 4.0 concerning the material handling problem of a typical job-shop production system. The considered prototype consists of four processing stations, each connected to an automatic conveyor belt by means of a system designed to withdraw/release baskets that are conceived to handle loads of various magnitude. When the scheduled basket is approaching the designed processing station, the system automatically activates the withdraw/release system. From a technical point of view, we used NXT Bricks as actuators groups for the motors of the withdraw/release systems and STM32F4 NUCLEO by ST Microelectronics for the data collection from the various sensors. The behaviour of our prototype showed failures and malfunctioning due to several different causes, including wear of mechanical parts, insufficient motor thrust, insufficient power supplied by the battery pack of the NXT Brick, and system movements that were out of nominal tolerances. In particular, the power level delivered from the Li-ion accumulator of the brick and the insufficient thrust of the motor (due to the high temperature of its windings) turned out to be the leading causes of the withdraw/release system failure. With reference to these failure causes, the project team identified the physical variables to monitor for an accurate estimation of the failure probability: (i) battery temperature (gauged by a thermocouple); (ii) battery voltage (measured with ADC voltmeter); (iii) motor windings temperature (gauged by a thermocouple); and (iv) rest position and speed of the withdraw/release system (controlled by an encoder). We collected all this data from sensors by means of the above mentioned STM32F4 NUCLEO, which allowed us to transfer in real-time all the data to a PC through a virtual serial connection through USB. Thus, for the degradation assessment model phase, we took advantage of the assistance of technical experts in electric motors, who specified the parameters to be monitored and included in the logistic regression model previously described. Having defined the parameters to be monitored, nine experimental cycles at the fixed operating parameters were performed until component failure was observed. Thus, the combined data aided the inferential process (based on the maximum likelihood estimation in Section 3) of parameter estimation for the proposed logistic regression model. The considered model is shown in Equation (7):  
\[Prob(failure)=Prob(\vec{x})=\alpha+\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{3}x_{3} +\beta_{4}x_{4}+\beta_{5}x_{5} \tag{7}\]  
where \(x_{1}\) is the battery temperature, \(x_{2}\) is the battery voltage, \(x_{3}\) is the motor winding temperature, and \(x_{4}\) and \(x_{5}\) are, respectively, the rest position and the speed of the withdraw/release system (Figure 3). As expected, the estimated regression coefficients showed that the battery voltage (\(\beta_{2}\)) and the motor winding temperature (\(\beta_{3}\)) coefficients have the highest values (meaning that these parameters are the most important causes of failure). After the validation of the degradation model, the experiments continued with six other runs, in which the information about each workload being allocated by the production scheduler to the processing station at every time period was available. It should be noted that, in the considered prototype, the workload was represented by the weight of the handled material.