# PFDA-FMEA, an Integrated Method Improving FMEA Assessment in Product Design
## 4 Numerical Case  
The industry currently identifies challenges to risk assessment during the PD process. The proposed integrated method PFDA-FMEA will bridges the identified gaps and help have a clear view to take decisions based on risks during the process. A practical real case is presented in this document, to exemplify and validate the PFDA-FMEA methodology. The example is based on an electronic device new product design scenario, and the group of SMEs is engineering, closed connected with the electronic design product process. A risk assessment is required for Product Design to avoid failures in the product and to complete the design on time within customer specifications. This numerical case shows the PFDA-FMEA assessment at the very beginning of the first stage of the project. PFDA-FMEA helps in obtaining a clear view of the impact of the risks associated with the electronic device product design process and helps to take the right decisions on where to apply more resources to avoid the impact of the risks identified. The proposed PFDA-FMEA method uses FMEA as a base for this methodology; FMEA helps to collect and organize the main PFMs in the PD process by the SMEs group for the practical example. Then, PFDA is applied with the intention to minimize the uncertainty in human decision taken on the ranking of S, O, and D. PFDA is as per Equation (1) by [8; 9; 64]. **Step 1. ** Creation of the SMEs group. A group of three experts in electronic devices' Product Design is created; they are numbered in a sequence as SME 1, SME 2, and SME 3. **Step 2. ** Assign weights to SMEs. Weights are assigned to each SME member depending on their experience. In this practical example, the values of the weights are assigned equally to each SME, giving 1/3 in accordance with the total value between 0 to 1, as per (3). **Step 3. ** The SME group identifies PFMs. The SMEs group on the electronic devices' PD process suggests PFMs that directly or indirectly impact the performance of the PD in the first stages of the process. For this example, the SME group agree to use the 19 PFMs listed in Table 2.  
**Step 4. ** Assess FMEA using Linguistic Values. The Linguistic Values in Table 1 were used to assess the FMEA. The SMEs group performs the FMEA assessment using Linguistic Values instead of the regular FMEA scale to assess the S, O, and D for each PFM. This step pretends to manipulate the uncertainty in the evaluation process with human judgment. Table 3 collects linguistic values used to assess the PFDA-FMEA. To be practical, we used the acronym of the linguistic values to represent Table 3, i.e., \"Low affectcation to quality\" = LQ, using \"LQ\" instead of the full sentence. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Linguistic Values**} & **Membership Function** & **Non-Membership** \\  & **(\(\mu\)**k)** & **Function (\(\
u\)**k)** \\ \hline Low affectation to quality (LQ) & 0.15 & 0.95 \\ Regular affectation to quality (RQ) & 0.55 & 0.55 \\ High affectation to quality (HQ) & 0.80 & 0.20 \\ Low affectation on time (LT) & 0.35 & 0.85 \\ Regular affectation to time (RT) & 0.45 & 0.55 \\ High affectation to time (HT) & 0.95 & 0.10 \\ Low affectation to budget (LB) & 0.20 & 0.75 \\ Regular affectation to budget (RB) & 0.45 & 0.45 \\ High affectation to budget (HB) & 0.75 & 0.25 \\ Low affectation to market (LM) & 0.25 & 0.95 \\ Regular affectation to market (RM) & 0.50 & 0.50 \\ High affectation to market (HM) & 0.85 & 0.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Linguistic Values for PFDA, Membership and Non-Membership Functions. **Step 5. ** Compute and obtain PFDA-FMEA. PFDA is applied to the assessment results by using Equation (3); later, Equation (2) is used to de-fuzzify the fuzzy numbers and obtain crisp values. The computation results are presented in Table 4, obtaining values for S, O, and D using the PFDA-FMEA.