# Quantitative Model for the Value of the 3D Product Model Use in Production Processes
## 3 Results
### Quicker Operator Training  
In an automotive manufacturer, the target takt time at station \(n\) on production line \(m\) (\(T_{m,n}\)) is 54 s, and a new operator takes three times as long, i.e., 162 s, to complete the new production task on their first attempt (\(\Psi_{m,n,\rho,1}\)). Prior to the implementation of 3D product model software in the shop floor training, the learning rate for this operator (\(L_{m,n,\rho}\)) is 86%. This means that each time the operator performs the task, on average, the operator will perform the same task 14% faster than the time before. This then creates a learning curve through which we can model the total time training before the operator reaches a time (\(\Psi_{m,n,\rho,\delta}\)) that is as good as or better than the target takt time for that station \(n\) on production line \(m\) (\(T_{m,n}\)). The total time training between the initial attempt and when the target takt time is reached is the total time that operator spends training (\(\Psi_{m,n,\rho}\)), which using the initial production time, learning curve percent, and target takt time above equates to three hours of training per operator. To capture the total time spent training at station \(n\) on production line \(m\) the sum of all operators who were trained on the update at station \(n\) on production line \(m\) is calculated (\(\Psi_{m,n}\)). For this manufacturer, on average there are two operators per station per shift, two shifts, 350 stations per production line, and one production line. To translate the training time to quantitative cost of training dollars for production line \(m\) (\(\Phi_{m}\)) the average cost of operators at station \(n\) on production line \(m\) (\(\overline{\zeta_{m,n}}\)), a good approximation is USD 30/h fully loaded (including burden rate) multiplied by the total time spent training at station \(n\) on production line \(m\) across all stations on line \(m\). This results in a training cost (\(\Phi_{m}\)) of close to USD 400,000 per year, under the approximation that all operators have the same learning curve rate of 86% and their first attempt at the new production process was three times longer than the target takt time. However, the implementation of the 3D product model in the production process creates an opportunity for operators to understand and visualize the production process before performing it. This knowledge enables the operator to reduce the time required in their first attempt to conduct the production process to two times the target tact time while the learning curve rate remains the same at 86% (meaning the operator still performs the task 14% better each time). This reduces the operators total training time to 0.5 h, and the operator is able to achieve the target takt time in 25 training attempts, as opposed to 155 prior to the implementation of the 3D product model in the production process. This significantly reduces the training cost for the operators to learn the new production processes as the product model changes, saving hundreds of thousands of dollars per year (\(P_{\Phi_{m}}\)) and reducing training costs by 84% while still maintaining the operators' ability to meet the target takt time.