Risk Assessment with Value Added Pythagorean Fuzzy Failure Mode and Effect Analysis for Stakeholders

The new product development process (NPDP) is crucial for maintaining business up and running in manufacturing corporations worldwide. NPDP helps firms improve their profits, where stakeholder attention is mostly focused. NPDP Risk Assessment (NPDP-RA) is a vital activity to achieve a successful new product launch. However, managing different kinds of risks over the process presents enormous challenges; thus, risk assessment over NPDP still shows gaps, even when different tools are employed to identify, mitigate, and eliminate risks throughout the process. The identified gaps are mainly produced because the uncertainty added by the individuals assessing the risks, and the currently used tools are generally focused on a single phase of the NPDP, disregarding the stakeholders’ project objectives. This paper presents the main NPDP risks for stakeholders through the NPDP phases; likewise, the integration of Pythagorean fuzzy dimensional analysis – failure mode and effect analysis and value stream mapping (PFDA-FMEA-VSM). This novel integrated method is intended to improve the manner to perform the NPDP-RA for stakeholders. A practical example is presented to demonstrate the proposed integration of PFDA-FMEA-VSM for stakeholders at NPDP of electronic devices project.

descriptions and affected functional areas, as well as involving different methodologies for RA, such as Voice of the Customer (VOC) [25], and recently the risk assessment using FMEA and dynamic weights [26]. Additionally, the international standard for risk, ISO 31000 [27] includes stakeholders as part of the affected areas in the corporate world; ISO 31000 mentions how to deal with the risk.
Thus, the current RA tools are not enough to cover the identified gaps over the NPDP-RA, in the first instance because of the uncertainty while the assessment is usually slanted by human decisions. The PFDA-FMEA proposed method [28] removes the uncertainty induced by the human factor during the RA using FMEA in NPDP. Another gap in the NPDP-RA, is the use of the tools focused on a single phase of the NPDP at a time, to cover this gap, another contribution in this paper is the integration of VSM, attaining the value added through the NPDP. The identified gaps at NPDP-RA found in the literature [29], [30], [31], [32], [33] are as follow.
• Uncertainty on NPDP-RA due to the crossfunctional team different opinions. • Ambiguity because of the right use of the current NPDP-RA tools. • Wrong ranked risks because of different NPDP phases not considered during the assessment. • Inefficient consumption of project resources while covering risks identified because of inaccurate NPDP-RA.
Moreover, most commonly in the NPDP, the stakeholders are the group usually at high levels of the organization, which dictates the portfolio objectives, impacting each project goal, usually based on the corporate general plans. There is a literature review of stakeholders at [34], and the literature indicates that there are uncertainty identifying stakeholders [35] and stakeholder assessment [36], along with stakeholder reputation presented in [37] and [38].
Additionally, value stream mapping (VSM) is currently used to determine the optimal future state of a process under analysis [39]. Finding the value added in a process is not an easy task; VSM is usually used to capture the factors that are linked to the result in a specific process, VSM applications go from improving processes in production lines, [40], [41], to improve administrative processes, including product cost improvements [42], and recently a Social-VSM was presented in [43].
Therefore, the novel proposed method PFDA-FMEA-VSM for stakeholders is presented within the integration of the PFDA-FMEA proven method [28], then adapting VSM. Likewise, PFDA-FMEA-VSM integration will help NPD project stakeholders to have an effective assessment based on their main project objectives. In addition, the novel PFDA-FMEA-VSM method aims to improve the NPDP by solving the problems regarding identified gaps, listed previously in this document.
Finally, the main contribution in this paper is present the PFDA-FMEA-VSM integration, that will support NPD project stakeholders to have an effective assessment based on their main project objectives. Consequently, our proposal method reveals contributions as following.
1. It supports stakeholders to analyze the decisionmaking process to assigning resources in effective manner. The resources play an important role during NPDP. 2. The PFDA-FMEA-VSM method adds key contraptions allowing to NPDP-RA. a. Sub-classes (explained later in Table 2 Nevertheless, NPDP-RA is generally executed considering just a specific portion of the NPDP and is typically focused on the activities that impact the product specifications and functional activities during the execution of the NPD project. Correspondingly, they usually miss the factors that affect the stakeholders' goals. Likewise, a contribution presented in this study is the novel integration of PFDA-FMEA-VSM to tackle the identified gaps mentioned previously, focusing on the main goals of the risk analysis for the NPD project stakeholders, where the potential risks are affecting, direct or indirect stakeholders' main interests over the NPDP, offering to the NPDP stakeholders, a fuzziness mode to make decisions based on informed risk assessment by the PFDA-FMEA-VSM method.
The remainder of this paper is organized as follows. Section 2 includes the basic concepts used for this research, Section 3 covers the novel proposed approach PFDA-FMEA-VSM, Section 4 contains a practical example, Section 5 presents the results and discussion, and Section 6 presents the conclusions.

II. BASIC CONCEPTS
This section presents the basic concepts used in this study.
Then, ⍵ represents the Pythagorean sets, denotes the Membership values assigned, and the Values of nonmembership. Next, Tj symbolizes the weights assigned to each expert, for j= 1, 2, … , , = 1,2, … , , and " " is the universe of elements measured, where Tj ∈ [0, 1], index is defined by the PFS.
Definition. Simplifying the NPDP phases, the SME team will refer only to "Phase 1," "Phase 2," and "Phase 3." Figure  1 depicts the definition of NPDP phases.  Additionally, as for reference, original stage-gate NPDP process diagram is shown in Figure 2.

III. PFDA-FMEA-VSM FOR STAKEHOLDER APPROACH
PFDA-FMEA-VSM integration aids NPDP risk analysis based on the PFDA-FMEA approach, integrating VSM to collect the value-added risks during the NPDP, allowing the stakeholders to optimize the available resources administrating the NPDP risks. Figure 3 shows a flow diagram of the PFDA-FMEA-VSM method. Step 1. The first step in this process is to create the subject matter expert (SME) team, which is usually a group of experts in the area to be assessed, and it is recommended to use different levels of expertise and experience and at least select tree experts.
Step 2. Next, the weights are equation 1 to each selected expert that will participate in the PFDA-FMEA-VSM method. The weights can be applied based on the expertise level of each expert; the higher the value, the more important the expert decision.
Step 3. Later, the SME team needs to capture the main potential risks for stakeholders (PRS) that affect stakeholders' project key objectives. To summarize, each PRS should have a unique identification, RID, adding a consecutive number. For this step, it is recommended to have a meeting between the SME group and stakeholders prior to this exercise.
Step 4. Later, the SME team performs the risk VSM diagram (rVSM) current scenario at the NPDP, considering the risks identified.
Step 5. Next, the SME team will define and document the NPDP phase where the identified risk is commonly presented. The SME can duplicate the risk description if it applies to a different NPDP phase. Here, Figure 1 is used, and it is recommended to have a meeting between the SME team and the stakeholders to complete this exercise.
Step 6. Subsequently, the SME team must assign a functional sub-class to each identified risk. Table 1 shows the subclasses and descriptions proposed for this method. This addition is an important part of the method, and it is necessary to successfully execute the proposed methodology, as well as helps the stakeholders to easily identify at what functional area are located the value-added risks. Step 7. Consequently, the PFDA-FMEA should be assessed using the linguistic values listed in Table 3. Step 8. In this step, Equation 1 is used to compute the collected data and obtain the PFDA-FMEA index.
Step 9. Next, ranking can be calculated based on the PFDA-FMEA index hierarchy; at the maximum index, the minimum ranking is. The ranking facilitates risk priority over the assessment. Additionally, in this step, the RID should be modified by adding a dash to the ranking number, that is, RID rank = RID10-1.
Step 10. Later, the rVSM future scenario can be performed by the SME team. The sub-class, NPDP phase, and RID rank should be considered in future VSM scenarios.
Step 11. This step refers to the PFDA-FMEA-VSM interpretation. Once the rVSM is completed, the SME team highlights the top RIDs considered as the main offensive for the NPDP. It is also recommended to meet again the stakeholders to agree on what will be the RID rank level considered to suggest preventive actions.
Step 12. During this step, the SME team will suggest preventing actions for each of the chosen top RIDs.

IV. PRACTICAL EXAMPLE
This section presents a practical example of an NPD project at an electronic device manufacturing company. An NPD electronic device project was used to validate the PFDA-FMEA-VSM approach.
Step 1. Beginning the process, the project manager (PM) leading the NPD project, chose a group of three experts, including a senior program manager, a senior engineering leader, and a senior finance leader. Immediately after the SME team was created, the PM led a meeting between the experts and the identified stakeholders, the Research and Development Director, supply chain director, program management officer, and general manager. During the meeting, the SME team captured the main concerns about the project results, as well as the most important objectives for each stakeholder, which will help the SME team to gain a better understanding of the potential risks information required for the next steps.
Step 2. Next, the project manager assigns weights considering equation 1 to each expert in the team. For this example, the assigned weights are the same for each expert because SME team members have the same level of expertise.
Step 3. Later, the SME Team defines the PRS.
Step 4. Next, the SME team evaluates the PRS, and based on the NPDP, creates the NPDP process rVSM current scenario. Figure 4 depicts the current scenario results of this practical example. Step 5. Then, for each identified risk, an NPDP phase was identified. The NPDP phase was chosen based on the location of risk. Figure 1 is considered for this step to identify the NPDP phases: "Phase 1," "Phase 2," and "Phase 3." Step 6. Next, the subclass should be completed for each PRS using Table 1. Table 4 presents the charts created until this step. Step 7. Consequently, the PFDA-FMEA should be assessed using the linguistic values listed in Table 3.
Step 8. Using Equation 1, the PFDA-FMEA is performed, and the PFDA-FMEA index is shown in Table 5. Step 9. Likewise, the ranking is obtained by sorting the index in a descending manner, then considering the maximum index value as the number one ranked, followed by ascending numbers to obtain the full list. Additionally, to obtain the RID Rank, the RID is concatenated with the rank, as shown in Table 6. Step 10. Later, the rVSM future scenario can be performed by the SME team, considering the highest risks identified, the sub-class, and the NPDP phase. The results are shown in Figure 5.  Step 11. This step refers to the interpretation of the PFDA-FMEA-VSM. Figure 6 shows the VAD highlighting the main risks, where it is easy to identify by the stakeholders in what functional area and project stage, the risk impact can occur.  Step 12. The SME team considered the top nine RIDs to generate major problems during the NPDP, following a list of preventing actions being deployed. Table 7 shows the suggested actions for the NPDP.

V. RESULTS AND DISCUSSION
This section reveals the PFDA-FMEA-VSM integration results, as well as a discussion comparing the current and future state scenarios analyzed in the practical example presented in Section 4 of this document. Table 8 and 9 illustrate the PFDA-FMEA-VSM results, including the sub-class, RPS, NPDP phase, PFDA-FMEA results, and RID Rank. Furthermore, Table 8 and 9 (continuation), depict proposed method additions in columns: Sub-class and NPD Phase, that are the key elements allowing to integrate VSM to PFDA-FMEA method. Likewise, this contribution facilitates to visualize later in the VSM, where to assign just the required resources to mitigate the value-added risks identified. Sub-class is an added subject to classify the main interest stakeholder area, goal, or objective to achieve. Likewise, this integration gives a visual picture about the specific areas because of the VAD. Following, RID in Table 8, represents the PRS identification, acting as an abbreviation, required to reflects the value-added risks at VSM diagram.  In addition, to prove the consistency of the PFDA-FMEA-VSM, an experiment was performed by changing the weights assigned to the experts. Even when changing the weights, the method yields the same trend, which means that the method is trustworthy. Figure 8 illustrates the experiment results.

VII. CONCLUSION
There is still room to improve the NPDP, according to the literature examination. However, PFDA-FMEA-VSM for stakeholders, is a novel integrated method beating the main gaps identified, giving an advanced resolution for risk assessment methods, adding value, and avoiding jeopardizing the stakeholders' project objectives.
Following, the main conclusive findings and benefits to use the PFDA-FMEA-VSM for stakeholders method.
1. PFDA-FMEA-VSM for stakeholders integration, avoids jeopardizing the NPDP main objectives for stakeholders, removing the fuzziness of human intervention at the risk assessment, and providing an accurate and visual way to identify the focal area and the specific NPDP phase where the risk can occur. 2. Value-added risks highlighted, allowing us to focus the resources, at the right time, at the right area that it is required, allowing the optimization of the resources available. 3. High visibility for stakeholders on where is required to apply more resources, depending on the NPDP phase, and the possible impact of the identified risks.
The precise risk ranking in PFDA-FMEA-VSM for stakeholders makes possible to focus on the available resources in the right place where is required, for individual stakeholder objectives, and for specific NPDP phases.
The PFDA-FMEA-VSM for the stakeholder method is capturing in a systematic way, the value-added risks because of the VSM integration, and applying PDFA-FMEA-VSM for stakeholder methods, the project available resources can be used wisely, depending on the appropriate required phase, which is possible because of the integration of the proposed method.
Subsequently, the ambiguity for NPDP-RA is removed using PFDA-FMEA-VSM for stakeholders, allowing to clearly and accurate pinpointing the area and project phase where the resources are required.
Furthermore, future work is considered to create a PFDA-FMEA-VSM automated template, making it easier to use this method in any industry by any stakeholder group to optimize the NPDP resources.