# Selection of Production Reliability Indicators for Project Simulation Model
## 4 Results
### Experiment  
This study is about a production process which is carried out in a job shop technology. The manufacturing process confirms the use of Critical Path Method; 100 products should be manufactured, and the company wants an estimation about the total lead time of the project. As it was stated previously, all the activity should be accomplished to start the next production process. For this purpose, a CPM is the best-fit model. The network of the processes can be seen in Figure 4.  
The production process is fictional, the authors wanted to present a moderately difficult process with parallel and sequential (dependent) activities. The nodes represent the events which resulted in activities. This naming convention helps professionals conscuct the equations for the graph. The activity times and their distributions for the simulation can be seen in the next table (Table 4). Beta-distributions were used for each activity, because it is used in PERT analysis as well [4], furthermore its shape is symmetric when \(\alpha\) and \(\beta\) parameters are equal. The main information about the process can be examined in the next table (Table 4):  
The reliability problems are given in a table format (see Table 5), which includes all the necessary information regarding the process simulation, such as which activity is affected by the problem, what is the cycle number for MTBF indicator (=this represents that reliability issue takes place at every \(n\)th cycle), as well as the time in which the machine is not available (=repair + waiting for repair). A domino-effect can also be modeled by placing the same MTBF value for more problems, or common multiples can also be used for the modeling correlation among reliability issues. When all the inputs were available, a 100-iteration-simulation was loaded on the basis of the Pseudocode presented in the previous chapter. The number of iterations in the simulation was in accordance with the number of products to be manufactured. The simulation was programmed in Visual Basic Application (VBA), and the result was collected in a spreadsheet database. The reason for using this framework is the flexibility and scalability that provides a great tool for managers in decision-making [46]. The next figure (Figure 5) presents the total process times of each simulated project iterations. Most \begin{table}
\begin{tabular}{c c c c c} \hline
**Activity** & **Between Nodes** & **Minimum Value** & **Maximum Value** & **Distribution (\(\alpha\);\(\beta\))** \\ \hline A & X1–X2 & 75 & 85 & \(\beta\) (2;2) \\ B & X1–X3 & 60 & 65 & \(\beta\) (2;2) \\ C & X2–X3 & 30 & 33 & \(\beta\) (2;2) \\ D & X2–X4 & 50 & 70 & \(\beta\) (2;2) \\ E & X3–X4 & 30 & 40 & \(\beta\) (2;2) \\ F & X4–X5 & 80 & 96 & \(\beta\) (2;2) \\ G & X5–X6 & 30 & 33 & \(\beta\) (2;2) \\ \hline \end{tabular}
\end{table} 
Table 4: Activity durations. Figure 4: Process representation. of the simulated values are around the deterministic (median) value, but there are some outlier iterations. These extreme values are due to the downtime of the production which is caused by a reliability issue. At some point of iteration, more issues occurred, so downtimes are accumulated and added to the total process time. The accumulated project run time is 4688 min including reliability issues in the production. Applying a linear regression on the accumulated total process time values, the following equation can be used for describing and forecasting (\(R^{2}=0.9983\)):  
\[\hat{g}=46.777x-61.106 \tag{6}\]  
This means that the average total process time to manufacture a product is significantly more than it is described deterministically. As a great contribution, critical paths of these process runs were investigated. During the analysis, three critical paths were distinguished; let us call them A, B, C that can be seen in Table 6.  
One of the mostly found critical paths was the \"A\" path with 73 out of 100 runs.