# Case Study of Expected Loss Failure Mode and Effect Analysis Model Based on Maintenance Data
## 2 Research Methodology  
### Data Definition and Modeling Procedure  
This section explains in detail variables and calculation processes that can quantitatively perform risk evaluation based on the EL-FMEA model. The indicators used in the EL-FMEA model are expected loss due to failure and the best alternative decision coefficient. The alternative meaning here is installing a detection system (e.g., a sensor) to prevent the recurrence of a failure. The procedures for the EL-FMEA model are shown in Table 1. Prerequisite data for the EL-FMEA model is defined as shown in Part (a) of Table 1 to calculate various indicators for risk assessment. The prerequisite data is defined as a variable necessary for calculating the expected loss based on the maintenance record data that can be easily collected in the industrial field. Based on the prerequisite data, we present the process of formulating intermediate variables step by step, as shown in Part (b) of Table 1. Based on the variables in this part, the expected loss and coefficient of determination for the best alternative can be calculated as shown in Part (c) of Table 1. \begin{table}
\begin{tabular}{c l} \hline \hline  & **(a)** Prerequisite data \\ \hline
**Variable** & **Description** \\ \hline \(T\) & Total time \\ \(\tau\) & Regular maintenance period \\ \(\tau_{i,1}\) & \(i^{th}\) system failure time \\ \(\tau_{i,2}\) & Re-operating time of the \(i^{th}\) system failure \\ \(n_{C}\) & Number of parts to repair a cause failure \\ \(n_{\text{pepo}}\) & Number of repairing people at each system failure \\ \(n_{\text{prod}}\) & Number of productions per unit time \\ \(\tau_{C}\) & Price of a part required to be repaired at each cause failure \\ \(\tau_{\text{pepo}}\) & Laboring cost per unit person per unit time \\ \(\pi_{\text{prod}}\) & Price of a unit product \\ \(\pi_{\text{sens}}\) & Price of a detection sensor \\ \(\lambda_{\text{sens}}\)* & Sensor failure rate \\ \hline \hline \end{tabular}  
* If \(\lambda_{\text{sens}}=1/MTB_{\text{sens}}\) is unknown and \(MTB_{\text{sens}}\) is expected to be longer than \(T\), it can be set \(1/T\) conservatively.  
\end{table} 
Table 1: Procedure for the EL-FMEA model. First of all, the primary data required for FMEA performance has failure modes, causes, and failure effects, which can be organized as shown in Table 2. Based on FMEA's primary data, the prerequisite data is organized as shown in Part (a) of Table 1.  
The total time (\(T\)) is calculated by multiplying the working days by 24 h a day as the system operating time. In the regular maintenance period (\(\tau\)), it generally means an inspection cycle performed for preventive maintenance in the industrial field. System failure time (\(\tau_{i,1}\)) and re-operating time (\(\tau_{i,2}\)) of the system failure are defined for system down and uptime calculation. Moreover, the number of parts to repair a cause failure (\(n_{C}\)), number of repairing people at each system failure (\(n_{\text{people}}\)), number of productions per unit time (\(n_{\text{prod}}\)), price of parts required to be repaired at each cause failure (\(\tau_{C}\)), laboring cost per unit person per unit time (\(\pi_{\text{people}}\)), price of a unit product (\(\pi_{\text{prod}}\)), price of a detection sensor (\(\pi_{\text{sens}}\)), sensor failure rate are defined (\(\lambda_{\text{sens}}\)). Here, the price of the detection sensor means an installation price of a sensor for detecting a cause failure. Second, based on the prerequisite data defined in Part (a) of Table 1, intermediate variables for the EL-FMEA model are calculated according to the procedure in Part (b) of