# Quantitative Model for the Value of the 3D Product Model Use in Production Processes
## 3 Results  
Accuracy of Assignment of the Right Parts, Tools, Work Allocation, and Work Instructions Value Model  
An aggregation of data collected from interviews with industry experts in industrial and systems engineering leadership roles will be used to demonstrate the application of the model developed in the Materials and Methods section of this paper. One large automotive manufacture makes vehicles on a production line with a production line takt time of 60 s (\(T_{m}\)). Although each station along a production line will have its own inherent variability, in this aggregate analysis all production stations have the same target station takt time of 54 s (\(T_{m,n}\)) with a standard deviation of 3 s (\(\sigma_{T_{m,n}}\)). This results in a probability that each station will be able to keep up with the production line takt time of 60 s 97.7% of the time. Now, if that automotive manufacturer introduces the 3D product model into the production process, the company can reduce the variability of the time to complete an operation at a station given all of the right parts, tools, work allocation, and work instructions have been implemented. By reducing the standard deviation from 3 to 2 s as a result, reducing the standard deviation by 1 s while retaining the 54 s average takt time and retaining the 97.7% probability of completing the task within the production line task time, the takt time can be reduced by 2 s to approximately 58 s. This is a 3.3% reduction in production line takt time, allowing the company to produce approximately 3.3% more products per year (if production is the bottleneck in the overall manufacturing facility). In this aggregate example, prior to the 3D product model use in the production process, the average takt time of the line (\(T_{m}\)) is 60 s, the production line operates 24 h per day (\(\overline{H}_{m}\)), so the assemblies produced on the line per day (\(\alpha_{m}\)) is 1440. The automotive manufacturer makes an average profit (\(\overline{P}_{A_{M}}\)) on cars of approximately USD 5000 per vehicle (note that profit on trucks and sports utility vehicles [SUVs] is significantly more at closer to USD 20,000-25,000 per vehicle, and thus the value demonstrated throughout this paper would be much greater in dollar volume if applied to an SUV or truck production line). This results in an average daily profit (\(\overline{P}_{D_{m}}\)) of USD 7.2 million. This automotive plant runs their production lines 5 days a week (\(\overline{\delta}_{m}\)) for 50 weeks per year (\(\Omega_{m}\)). The production line is down for maintenance work on weekends and over the fourth of July and Christmas holidays for a week each, resulting in 250 days of operation per year (\(D_{m}\)). This generates a yearly profitability for that production line (\(P_{Y_{m}}\)) of USD 1.8 billion. Now when the 3D product model is introduced in the production process and reduces the standard deviation of the takt time at the stations, the products produced on the line per day (\(\alpha_{m}\)) increase to 1490 based on the 58 s takt time, or 50 more assembled units per day. This increase in production generates a daily profit (\(\overline{P}_{D_{m}}\)) of USD 7.45 million, or an increase of USD 0.25 million per day. The yearly profit (\(P_{Y_{m}}\)) increases as a result, to USD 1.86 billion, or an increase of approximately USD 62 million per year for that production line (\(P_{T_{m}}\)). Note that if multiple production lines were improved via reduced variation from the implementation of the 3D product model in the production process, the value could be summed across these multiple production lines to capture the profitability benefit per year for a given plant. The profitability increases across all plants could then be summed to capture the total value for the increase in value generated by the implementation of the 3D product model in the production process.