## 3 Product Service System Case Study
### Cost Optimization Model  
For the next step of the process, the PSS availability regression model created from the previous step is embedded into the field repair kit cost optimization model. The IPO diagram for the optimization model is shown in Figure 3.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values Ranges** \\ \hline Spare part failure rate (1/spare part life) & 0.001–0.5 failures per million prints \\ Onsite spare part quantity & 0–10 \\ PSS usage per unit period & 5.7–10.2 million prints \\ \hline \hline \end{tabular}
\end{table}
Table 1: Key parameters and their value ranges for simulation and optimization.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Runs** & \begin{tabular}{c} **Spare Part Failure** \\ **Rate (per Million** \\ **Prints)** \\ \end{tabular} & \
\begin{tabular}{c} **Quantity in** \\ **the Field** \\ **Repair Kit** \\ \end{tabular} &
\begin{tabular}{c} **PSS Availability** \\ **based on Monthly PSS Usage** \\ \end{tabular} \\ \hline
1 & 0.032 & 2 & 100\% & 100\% & 78\% \\
2 & 0.100 & 1 & 50\% & 50\% & 15\% \\
3 & 0.100 & 5 & 100\% & 100\% & 56\% \\
4 & 0.500 & 2 & 100\% & 100\% & 80\% \\
5 & 0.500 & 10 & 100\% & 100\% & 88\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Partial results of deterministic PSS simulation.  
Figure 2: Input-Process-Output (IPO) diagram of the simulation model.  
For the field repair kit cost optimization, several input parameters are required. The first parameter is the required PSS availability target. This is typically dictated by the customer who utilizes the PSS when the maintenance contract is signed. The second parameter is the unit cost for each spare part in the field repair kit. The third parameter is the quantity of each spare part in the field repair kit, and the last parameter is the failure rate of each spare part. Table 3 shows a partial list of the actual spare parts included in the field repair kit, with actual parameter values. It should be noted that the unit cost of each spare part is added, since the objective of the optimization is to minimize the total cost of the field repair kit. For the monthly PSS usage, it was set at 8.0 million, based on field data for similar systems. Optimization was performed using spreadsheet-based commercial software (QuantumXL(tm)), which uses a heuristic algorithm.  
For the optimization, three different scenarios were formulated after discussion with the design team. Table 4 lists proposed scenarios. The first scenario serves as the base scenario, where the PSS operates with the original field repair kit composition shown in Table 3. In the second scenario, the PSS availability requirement parameter is set to 95%, and the field repair kit is optimized for total cost. For the third scenario, the PSS availability requirement parameter is relaxed to 90%.  
Figure 3: IPO diagram of the field repair kit cost optimization model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Spare Part** & **Unit Cost (Normalized)** & \
\begin{tabular}{c} **Original Part Quantity** \\ **in the Field Repair Kit** \\ \end{tabular} &
\begin{tabular}{c} **Failure Rate** \\ **(per Million Prints)** \\ \end{tabular} \\ \hline A & 100.00 & 2 & 0.033 \\ B & 2.89 & 1 & 0.040 \\ C & 1.23 & 1 & 0.035 \\ D & 0.78 & 6 & 0.500 \\ E & 0.77 & 1 & 0.035 \\ F & 0.29 & 2 & 0.033 \\ G & 0.19 & 1 & 0.050 \\ H & 0.17 & 4 & 0.056 \\ I & 0.05 & 4 & 0.040 \\ J & 0.03 & 4 & 0.056 \\ K & 0.01 & 2 & 0.500 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Partial list of spare parts and quantities in the PSS field repair kit originally proposed by the design team.