# A New Hybrid Dynamic FMECA with Decision-Making Methodology: A Case Study in an Agri-Food Company
## 3 Case Study
### Criticality Analysis (CA)  
Our case study carried out the criticality analysis using Vensim PLE x64, a widely used software in System Dynamics models' simulation. Before moving on to the construction of a CLD and then to the simulation, it is necessary to identify the critical events using the Pareto principle. This famous principle has often been used in criticality analysis [34]. The critical events found with the analysis carried out are those that the experts indicated a priori as critical events in the machine operation's deployment. Furthermore, in this study, the model proposed leads to actual results. For ease of representation and analysis, it has been decided to exclude the causes CF55/CF57/CF58/CF70/CF71/CF72/CF73/CF80 from the analysis. The choice was taken into consideration since the causes are the same. Furthermore, all the actions and analyses that were carried out on the causes related to the tunnel chain and the chicken release station can be proposed again strictly for the causes CF55/CF57/CF58/CF70/CF71/CF72/CF72/CF73/CF80 related to the calibration chain and the chicken release station. Besides, the causes related to the chicken release station and the calibration chain are the most serious for the reasons mentioned above:  
* The tunnel chain is considerably longer than the sizing chain; if it breaks, it causes more damage at the economic level;
* The release guide, on the other hand, unlike the hooking guide, is subject to more significant stress and, therefore, more prone to failure. As already mentioned in this work, a dynamic simulation program is used to simultaneously study the causes of failure and not take them individually as in the traditional FMEA [34]. The first step is to represent the causal relationships between the variables present graphically. This diagram is called the Causal Loop Diagram (CLD). Thanks to CLD, it is possible to identify possible strengthening or balancing cycles [35]. These cycles are significant as they tell us if two or more failures increase each other over time or eliminate each other. In Figure 5, an illustration of our Causal Loop Diagram is presented. To better understand the proposed CLD, a list is provided that explains the representation:  
* The causes of failure have been entered without a box;
* The failure modes have been entered in the circles;
* Effects have been placed in rectangles;
* Maintenance actions have been placed in hexes. In the diagram, thanks to the presence of these maintenance interventions, four balancing loops can be seen:  
1. FM10-E10-STOP PRODUCTION-Guide Maintenance-FM10;
2. FM9-E10-STOP PRODUCTION-Guide Regulation-FM9;
3. FM1-STOP PRODUCTION-Tunnel chain maintenance-FM1;
4. FM26-STOP PRODUCTION-Transfer chain maintenance-FM26. Since each cause has its stochastic properties, the probability distribution that best suits the different causes of failure must be identified:  
* Due to the causes CF11/CF86/CF91 (Blackout), CF2 (Incorrect feed speed), CF3 (Incorrect product life forecast), and CF20 (Inadequate tolerances) being purely random events, the model that best interprets the behaviour is the exponential one; \[F(t)=1-exp^{-\lambda st}\] (23) \[\text{f(t)}=\lambda*exp^{-\lambda st}\] (24) \[\text{h(t)}=\frac{f(t)}{1-F(t)}=\lambda\] (25) where \(\lambda\) is the event occurrence frequency. * For the causes CF18/CF21 (Wrong adjustment), CF19 (Excessive vibrations), CF38 (Over-stressing), CF1 (Insufficient lubrication), and CF4 (Over-stressing), being causes of failure of mechanical components, the model that best represents their behavior is [PERSON]'s model: \[\text{F(t)}=1-exp^{-(\frac{t}{\delta})^{\beta}}\] (26) \[\text{f(t)}=\frac{\beta}{\alpha^{\beta}}*t^{\beta-1}*exp^{-(\frac{t}{ \delta})^{\beta}}\] (27) \[\text{h(t)}=\frac{f(t)}{1-F(t)}=\frac{\beta}{\alpha^{\beta}}*t^{\beta-1}\] (28) The model under analysis with the relationships is shown in Figure 6.  
Figure 5: Causal Loop Diagram.