## 2 Optimization Problem  
In this work, a new method was developed to optimize CBM activities of a simplified multi-equipment hub cap production system. The work is based on the multi-component but single equipment model presented in [9]; as added value, this research extends it using DES so that in this case it is possible to perform a multi-equipment optimization. In previous studies [10; 11], a PM optimization [10] and a CBM optimization based on a different deterioration model [11] were presented. In the case of [PERSON] etal. [11], they applied it for the same system but using a different ageing model, whereas [PERSON], [PERSON] and [PERSON] [10] optimized preventive maintenance instead of CBM. This system is set up in a company of the Mondragon Corporation. As shown in Figure 1, the production system is made up of three identical plastic injection machines and a painting station and it generates plastic made hub caps for car-maker companies.  
In the studied production system, the manufacturing process starts by injecting and compressing the plastic contemporaneously in the injection machine. Then, once it is cooled, the mold is opened, and the injected product is extracted. Later, the final product is located along the side of the injection machine buffer which consists of two pallets of 100 hubcaps each.  
When a pallet is filled with hub caps, it is transported from the injection machine buffer to the painting station buffer. Then, the products are loaded onto a conveyor that leads to the painting station. At the painting station, the products are painted. Finally, they are sent to a warehouse.  
Each machine belonging to the model is formed of three subsystems, which are designed as components and constructed in serial configuration.  
One maintenance activity is implemented on each subsystem to control its aging: M1, M2 and M3 are, respectively, executed over sub-systems S1, S2 and S3 of the injection machines, whereas M4, M5 and M6 are sequentially applied on sub-systems S4, S5 and S6 of the painting station. Table 1 represents the influence of each subsystem on the performance of each machine: regarding the injection machine, S1's deterioration has an effect only on unavailability, S2's deterioration has an influence on unavailability and productive speed loss, and S3's deterioration affects quality and unavailability. In the case of the painting station, S4's deterioration affects only unavailability, S5's deterioration has an effect on productive speed loss and unavailability, and S6's deterioration has an influence on quality and unavailability.  
Regarding the equipment failure process, a two-parameter (\(\lambda_{1}\) and \(\gamma_{1}\)) Weibull failure rate is used for the modeling. The Weibull distribution was chosen for developing this model because it is the most common distribution to model reliability data. In addition, during the modeling, a process deterioration which shifts the system from an under-control state to an out-of-control state is taken into account. This process of deterioration acts in accordance with a Weibull distribution of parameters \(\lambda_{2}\) and \(\gamma_{2}\). The Weibull reliability data for the studied problem are demonstrated in Table 2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Equipment** & **Subsystem** & **PM Activities Performed** & **Influences on** \\ \hline Injection machines & M1 & S1 & Unavailability \\  & M2 & S2 & Unavailability and Productive speed loss \\  & M3 & S3 & Unavailability and Quality \\ \hline Painting station & M4 & S4 & Unavailability \\  & M5 & S5 & Unavailability and Productive speed loss \\  & M6 & S6 & Unavailability and Quality \\ \hline \hline \end{tabular}
\end{table}
Table 1: Components, PM activities and their influences.  
Figure 1: A representation of the simplified plastic injection system.