Risk Assessment Using the PFDA-FMEA Integrated Method

Purpose: The paper aims to introduce risk assessment in new product development as an important activity for a successful new product launch. A practical example is presented to demonstrate the integration of tools Failure Mode and Effect Analysis (FMEA) and Pythagorean Fuzzy Dimensional Analysis (PFDA) at new product development process, which is a machined component. Methodology/Approach: Individual steps for creating a case study were carried out: create a Subject Matter Expert (SME) team, identify product failure modes, use linguistic values to assess the FMEA, compute and obtain the PFDA-FMEA and determine the product failure modes ranking. Findings: Minimized uncertainty in the final evaluation of the FMEA and improvement in the decision-making process based on the risks already identified in the new product development process. Research Limitation/Implication: The PFDA-FMEA method was based on the risk assessment of a machined part development process. Nevertheless, this method can be used for application in many other areas of industry that require high precision in risk analysis. Originality/Value of paper: The aim of this paper is to reveal a new integrated method in which FMEA, Pythagorean Fuzzy Sets (PFS) and Dimensional Analysis (DA) are coherent in one model.


INTRODUCTION
The rapid development of technologies that fit into the framework of Industry 4.0 bring new threats and new fails. Therefore, a new perspective is also needed on quality assurance in this context. It is particularly visible in demanding industries, which often require perfection in the smallest details and complex performances in difficult conditions, such as metalworking industry. Demands regarding the accuracy of details in the production of parts bring new challenges regarding risk assessment already during product design.
The goal of the research presented in the article is to choose a suitable method of risk analysis, applicable in the design of new components of an engineering product, based on a detailed literature survey, and to verify it on a specific solution.
The literature survey offers several methodologies to support risk analysis in different contexts, including industrial processes, product design or transport. In the publication Tixier et al. (2002), the authors identified and presented 62 different methodologies for the identification, assessment, and classification of risks. This set includes methodologies based on qualitative and quantitative approaches, as well as deterministic and probabilistic approaches. According to the authors, one of the most widely used methods is called FMEA (Failure Mode and Effects Analysis) and enables a qualitative risk analysis using scores represented by deterministic values. In the traditional version of this analysis, potential failure modes are assessed based on factors of severity, occurrence and detection using a numerical scale ranging from 1 to 10. The authors also state that FMEA is a risk analysis tool that is widely used in the manufacturing industry.
According to Yucesan, Gul and Celik (2021), an error is a failure. The author names it as a state of failure to fulfil the desired or intended goal. For a manufacturing environment, this term is defined as a part or component that causes damage to engineering equipment, manufactured products, or plant infrastructure, affects operations, production, and performance, as well as the plant's brand and reputation. Defective product is one of the main problems that manufacturing companies face. This problem does not only result in a financial loss, but it often also causes a loss of prestige (Boral et al., 2020). For companies to be able to continue operating in a healthy manner and achieve profits in today's strong competitive environment, it is necessary to increase the quality of production and reduce the number of defective products.
The risk identification process is the most important and time-consuming phase of risk analysis. Threats, probabilities of occurrence, impacts on the goals of the project or company or customer, severity of consequences, mutual links of risks are defined. The meaning of this is critical analysis, detailed investigation and evaluation or revealing activities or steps that are ineffective, reducing or increasing risk management requirements, proposing changes or corrective actions.

LITERARY REVIEW
Several methods can be used to evaluate potential failure modes and address their potential consequences, such as: • Event Tree Analysis (ETA) -Analytical technique used to define potential accident sequences associated with a particular initiating event or set of initiating events (Čepin, 2011); • Fault Tree Analysis (FTA) -An analytical technique that is used to evaluate the probability of failure, or the reliability of complex systems (Solc et al., 2021); • Bow Tie Analysis (BTA) -Analytical technique suitable for initial risk analysis to ensure identification of high probability and high consequence events (Ferdous et al., 2012); • 5WHY -An iterative technique used to investigate the cause-effect relationships underlying a particular problem. The primary goal of the technique is to determine the root cause of an error or problem by repeating the question "Why?". Each answer forms the basis of the next question (Nagyová et al., 2019); • FMEA; • An equally effective quantitative method for risk assessment is the What if? or Hazard and Operability Analysis (HAZOP) -Threat and operability analysis based on the assessment of the probability of threats and the risks arising from them (Cao et al., 2013); • Among the frequently used qualitative methods that help to refine procedures in detailed risk analysis are, for example, SWOT analysis (Strengths and weaknesses, opportunities, and threats analysis); • Brainstorming; • Five Forces (5F) -Industry and risk analysis. The model works with five elements and the essence of the method is forecasting the development of the competitive situation in the industry under investigation based on an estimate of the potential behaviour of subjects and objects operating on the given market (Goyal, 2020); • Delphi -Prognostic method of group search for a solution. Determination of expert estimate of future development or status using a group of experts (Cao et al., 2013).

Failure Mode and Effects Analysis -FMEA
FMEA was first used in the 1960s to solve problems in the aerospace and automotive industries (Bowles and Peláez, 1995). Since then, based on the original version, various improvements have been offered, which are developed by sector -for example, FMEA for the development process, FMEA for the service sector, FMEA for production processes.
The FMEA allows to determine the impact of failures or errors on the performance of the system so that measures can be taken to reduce the risk. Each identified risk is numerically classified in the form of a Risk Priority Number (RNP). The risk number RPN is calculated by multiplying parameters severity (S), occurrence (O), detection (D) (Qin, Xi and Pedrycz, 2020). Each parameter takes values between 1 and 10 (1 indicates the lowest value and 10 indicates the highest value). Errors that lead to a high-risk number are critical and are rated as the highest priority. In the final phase, the proposal of measures to reduce the risk number is considered.
Despite the widespread use of FMEA for more than 50 years, this method still has certain limitations, which contributes to the development of new versions by combining it with other techniques (Magalhães and Lima Junior, 2021). One of these limitations lies in the use of deterministic numerical values that do not allow the quantification of uncertain or imprecise measurements inherent in the risk assessment process. According to Yucesan, Gul and Celik (2021), the limitations of FMEA primarily include the inability to deal with indeterminate failure data, subjective risk assessment according to experts, or failure to consider conditionality between individual errors. Additional weaknesses of the FMEA are presented in Tab. 1. The value from which it is necessary to implement a corrective action is not determined by a standard or another internal company directive. Dai et al. (2011) 3 The time-consuming and financial cost of the analysis in the case of systems that are composed of many components and contain many functions, or if the analysis is used in the organization for the first time in a complex way of the system. Authors Magalhães and Lima Junior (2021) in their publication provide a proposal for the application of FMEA according to the three steps listed in Tab. 2.
In the first step (Step I), brainstorming is carried out and all available information is used on potential failure modes in the system, design or process that is the subject of the analysis. In this way, potential and known failure modes are identified, probable causes are discussed, and the existing means of detecting the causes and failures, if they occur, are discussed. For each identified failure mode, a score related to factors S, O, D is assigned. The last part of Step I is calculating the risk number RPN. In Step II, the values resulting from the RPN calculation for each mode of failure are sorted in descending order. The RPN classification determines the priority level of failure. Experts involved in the analysed process develop and implement action plans to eliminate or mitigate potential causes of priority failures. Finally, in the last step (Step III), the potential failure modes are re-evaluated to verify the effectiveness of the corrective actions taken.

Table 2 -Description of the Steps in the Application of FMEA
Step I a) Specify the investigated system, design or process. b) Create a team of experts. c) Define process requirements or individual functions of product components. d) Identify process steps. Identify potential or known failure modes. e) Analyse and describe the consequences of each type of error and assess their severity. f) Investigate and define the probable causes of each failure mode and assess the occurrence of these causes. How often can the cause occur? g) Validation of existing detection methods and assessment of the ability to detect failure modes or causes through these sources. Evaluation of the most effective of the controls in the process that can detect the error or the cause of the error. h) Calculate the risk number (RPN).
Step II a) Sort RPN values in descending order. Failure modes with the highest RPN values are considered the most important and will have a higher priority when determining corrective actions.
b) Develop a corrective or preventive action plan.
Step III a) Implement the action plan. The given sequence of steps of the FMEA method in Tab. 2 has been used for many years and has undergone a significant change in recent years. The automotive industry has a significant impact on people's daily lives worldwide and affects their safety (Mihaliková et al., 2021). Two basic approaches in the automotive industry represented by the AIAG manual (2022) and the VDA manual (2022) have united, and the result is a joint harmonized edition of the FMEA manual, the first edition of the AIAG & VDA FMEA Handbook.
AIAG is a global organization founded in 1982. The goal of the organization is to increase prosperity in the automotive industry by improving business processes and activities that are part of the supply chain (AIAG, 2022). VDA is an association of the automotive industry, which unites more than 620 German companies from this area and its main idea and goal is the research and production of modern, error-free and safe cars (VDA, 2022).
The methodology the AIAG & VDA FMEA Handbook provides a comprehensive guide. It is divided into seven steps for the creation of an FMEA analysis and contains changes in the form itself as well as in the evaluation tables for factors S, O, D. The handbook states the obligation to document the effectiveness of the implemented measures and perhaps the most significant change is the replacement of the risk number RPN with the evaluation factor Action Priority (AP). A seven-step approach to creating an FMEA -harmonized edition is presented in Tab. 3. This approach provides a comprehensive framework for documenting risks in a detailed and precise manner.

Table 3 -Seven-steps Approach to Creating an FMEA -Harmonized Edition
Step Description Step 1.

Planning and preparation
What project?
Team, tasks Identify source FMEA

Lessons learned
What project?

Structure analysis
Visualize the scope of the analysis

Process Flow Diagram
Identification of process steps and substeps Step 3. Function analysis

Visualization of functions
Function tree

Binding requirements to features
Customer functions (both internal and external) Step 4. Failure analysis

Creation of the chain Error -Cause and Error -Consequence
Potential consequences of failures, failures, causes for each function of the process

Identifying the causes of process failures
Customer -supplier cooperation Step 5.

Risk analysis
Assigning preventive measures to the causes of failures Assigning detection measures to the causes of failures

Monitoring measures
Step Description

Safety and legal requirements
Assessment of importance, frequency and monitoring Step 6. Optimization Identification of measures necessary for risk reduction Determination of responsibility and deadlines for the introduction of actions Implementation, including confirmation of the effectiveness of measures and risk assignment after their implementation Step 7. Documenting the results

Complete documentation
The new approach in the harmonized Edition of FMEA guides the user to reconcile information between individual steps to ensure accuracy and completeness of the analysis. It helps identify and assign priorities to actions designed to prevent risk. It considers factors S, O, D individually, but also in combination with risk-reducing factors. The benefit of the new approach is a more intensive cooperation between the FMEA team, production plant management, customers, and suppliers.

Advanced Methods of Risk Analysis and Risk Management (MCDM methods)
To add new functions to FMEA, some studies propose a combination of decision models with existing multi-criteria decision-making methods (MCDM). According to Sarkar (2011), multicriteria decision-making is a branch of Operations Research (OR). Decision-making often involves imprecision and vagueness, which can be effectively handled using fuzzy sets and fuzzy decisionmaking techniques. In recent years, a considerable amount of research has been carried out on the theoretical and application aspects of MCDM and fuzzy MCDM.
According to Karunathilake et al. (2020), multi-criteria decision-making generally follows six steps, which include: (1) problem formulation, (2) requirements identification, (3) goal setting, (4) identification of various alternatives, (5) criteria development and (6) identification and application of decision-making techniques. Various mathematical techniques can be applied to this process, the choice of techniques being made based on the nature of the problem and the level of complexity assigned to the decision-making process. All methods have their pros and cons.
FMEA is considered a robust tool and is one of the most widespread techniques used to identify and assess risks (Kumar et al., 2021). It considers three risk factors at the same time, and in the industrial production sector, where the term "risk" appears frequently, it occupies an important position, which is why the discussion of risk management in the context of FMEA is also important.
Determining and classifying potential failure modes in FMEA is a multifaceted challenge that requires decision-making based on multiple criteria -MCDM (Karunathilake et al., 2020). For this reason, FMEA can be considered a question of multi-criteria decision-making. The reason is the involvement of multiple risk factors, which includes setting priorities and evaluating potential failure modes based on the mentioned three factors S, O, D. Several studies have provided an overview of the application of multi-criteria decision-making techniques in various areas, including, but not limited to energy industry, environment and sustainability, quality management, construction and project management, safety and risk management, etc. OR achieved a relatively higher application (Sarkar, 2011;Karunathilake et al., 2020;Liu et al., 2019).
The MCDM considers the importance of risk factors, breaks down the risk assessment process into different phases and prioritizes potential failure modes through mathematical models. According to a recent literature review by Liu et al. (2019), more than 150 research papers have been published over the past two decades that report the application of multiple-criteria decision-making in the context of FMEA in different scenarios. At a broader level, common MCDM used in FMEA include, but are not limited to, winner-take-all techniques, outranking techniques, pairwise comparison techniques. In addition, various hybrid and multi-factor techniques have been developed to solve FMEA analysis.
In the issue of multi-criteria decision-making the basic components are criteria and alternatives. The various alternatives are evaluated according to established criteria to formulate a comparison of the alternatives. The results can be further improved by assigning weights to different criteria, as the importance can vary greatly between raters. Thus, there may be different levels of importance for the selected criteria from the perspective of different decision makers (Karunathilake et al., 2020). To ensure the reliability of the results, it is important to evaluate the weights assigned to each criterion by different decision makers.
The choice of a multiple-criteria decision-making technique to solve a particular problem may vary depending on the context, thus emphasizing the need to understand decision-making classifications. Multi-criteria decision-making techniques are categorized into: (1) compensatory and non-compensatory, (2) discrete and continuous, and (3) individual and group decision-making. The classification of MCDM based on discrete and continuous data is most often used. (Sabaei, Erkoyuncu and Roy, 2015) From the point of view of discrete and continuous data, the techniques of MCDM are divided into multi-attribute decision-making (MADM) and multi-objective decision-making (MODM). MADM considers problems in an inherently discrete decision space, and MODM is based on mathematical theory and deals with problems in a continuous decision space. (Tzeng and Huang, 2014)

METHODOLOGY
As the machining processes market grows globally, global consumers are demanding new manufacturing technologies and product innovations. As a result, new complex processes and challenges are presented in manufacturing companies during the very development of a new product, making it necessary to overcome new and greater engineering and scientific challenges. Subsequently, however, the risk of not introducing new products to the market increases. For this reason, a risk analysis is needed in the development of a new product so that stakeholders make the right decisions and achieve the expected goals. Current risk analysis tools are not sufficient to cover identified deficiencies in the development of a new product, primarily due to the uncertainty that is present in human decisions. The proposed Pythagorean Fuzzy Dimensional Analysis -Failure Mode and Effects Analysis (PFDA-FMEA) method removes the uncertainty caused by the human factor during the risk analysis using FMEA in the new product development process.
Dimensional analysis (DA) is a technique used in the decision-making process, especially when choosing alternatives of the multi-criteria type. It is an MCDM technique that assumes that there is an optimal solution, better than others. When evaluating, DA compares each alternative with the ideal alternative to create an Index of Similarity, therefore the highest similarity index is selected as the best alternative to the MCDM multi-criteria decision-making problem. (Villa Silva et al., 2019) Pythagorean Fuzzy Dimensional Analysis (PFDA) is applied in practice even before the FMEA is started. Its important part is the verbal assessment, based on which the results of the analysis are sorted. The advantage of PFDA is that it allows using input data both quantitatively and qualitatively, so that the information is comparable, even if the types of input data are mixed.
According to García-Aguirre et al. (2021a), the risk evaluation in PFDA compared to the conventional FMEA method is at a more advanced level, while the ambiguity of subjective human judgment is eliminated by applying Pythagorean Fuzzy Sets (PFS).
The basic concept of PFS, which are also used in the case study, is presented through the following definitions (Yager, 2013;Cao et al., 2013; García-Aguirre et al., 2021b).
Definition 1: if represents the macroworld of considered elements, then the Pythagorean Fuzzy set in is given by the eq. 1: where : → 0, 1 defines the degree of membership. Consequently, : → 0, 1 defines the degree of non-membership of element , where ∈ in .
According to García-Aguirre et al. (2021b), the goal of the PFDA-FMEA method is to minimize uncertainty in the final evaluation of the FMEA and thus improve the decision-making process based on the risks already identified in the product design process. The method uses FMEA as a basis for collecting potential failure modes through Subject Matter Experts (SME) on the given issue, and only then is the PFDA method applied. The proposed PFDA-FMEA method is generalized in seven steps, presented in Fig. 1.

Figure 1 -Methodology of the PFDA-FMEA Approach
Step 1: Create SME team of experts on the given issue. Depending on the product/process being assessed, a group of n experts is created for the given issue.
Step 2: Assignment of weights to experts in the SME team. After the creation of the SME team, each of the experts is assigned a weight; generally: the higher the assigned value, the more important the expert's decision is for the analysis.
Step 3: The SME team of experts identifies potential failure modes and jointly determines the main internal and external characteristics that directly or indirectly affect the analysed product/ process.
Step 4: Assessment through linguistic values. Potential failure modes are evaluated by each expert independently and based on their own experience in the given field. The SME team of experts collects and defines the main areas of impact on the product/process and assigns member and non-member functions based on experience in each area of the analysed product/process.
Step 5: Calculate and perform PFDA-FMEA analysis. The results obtained in the previous step (Step 4) are used for the application of PFDA analysis according to eq. 3, subsequently using eq. 2 the values are defuzzified and the values of PFDA-FMEA analysis are obtained.
Step 6: The value of the PFDA-FMEA index is given by the mathematical calculation of the values S, O, D.
Step 7: Determining the order of potential failure modes. The results are ranked to identify the risks of potential failure modes and to support the decision to be made.

CASE STUDY
The company registers questions regarding the identification of risks in the design of a new component, the visualization of risks in specific areas and phases of the project, and indecision in the number and composition of interested parties who are responsible for effective risk assessment.
The proposed PFDA-FMEA method in the case study, which is based on the design of a machine part, uses FMEA analysis as the first step. FMEA helps collect and organize the main potential failure modes in the design phase of the part through the SME team of experts. The SME team of experts consists of a product designer, process engineer and quality engineer who deal with the design and development of parts for the engineering industry, managing the production preparation process and ensuring and improving the quality of production within the plant.
During the design phase of a machine part, risk analysis and assessment is required to avoid product failures and to complete the part design on time and within customer requirements. PFDA-FMEA helps to get a clear overview of the impact of risks associated with the product design process and helps to make the right decisions about where to use what kinds of resources to avoid the potential impact of the identified risks.
Subsequently, the PFDA is applied, the purpose of which is to minimize uncertainty in human decision-making when classifying factors S, O, D.
Step 1: Creation of an SME team of experts. Tab. 3 presents a group of three experts who are labelled as SME1, SME2, SME3. SME experts analysed a machine part named Wheel axle 022-09-005 (Fig. 2). The wheel axle is a stationary machine part that helps to transmit machine movement.

Figure 2 -Wheel Axle 022-09-005 (ICS Ice Cleaning Systems Slovakia)
Step 2: Assigning weights to experts. The weight is assigned to each expert depending on his experience and knowledge in the researched area (Tab. 4). To comply with the condition of eq. 3, that the total weight assigned to experts has a value in the range of 0 to 1, in this case study each SME expert is assigned the same weight (1/3), since the degree of expertise of each SME is in the analysed issue the same. Step 3: A team of SME experts identifies potential failure modes of the machine part. Experts in the design phase of a machine part suggest potential failure modes that have a direct or indirect impact on the part design process. For this purpose, a group of experts created and agreed on a list of 17 potential failure modes listed in Tab. 5. The product exceeds the specified production costs The production plant is not ready to start production Notes: I -innovation (a new idea, design, product or method, or development or use of a new idea, design, product or method); Q -quality (the degree to which an object or entity, e.g., process, product, or service satisfies a specified set of attributes or requirements); T -time (time period or time section), Bbudget (an estimation of revenue and expenses over a specified future period of time).
Step 4: Perform FMEA using linguistic values. A team of SME used the list of linguistic values listed in Tab. 5, which include the following areas: innovation (I), quality (Q), time (T), budget (B). Each of these areas is divided into levels of influence: low (L), neutral (N), high (H), and a team of SME assigned individual values and levels their member and non-member functions.  Step 5: Calculate and perform PFDA-FMEA. PFDA is applied through eq.3; subsequently, eq. 2 (both given in chapter Methodology) is used to defuzzify fuzzy values and obtain data. The calculation results obtained through the PFDA-FMEA are presented in Tab. 8 and include the calculation results for S, O, D.  For calculating membership values = for S -severity, the first part of eq. 3 was used: For calculating non-membership values A= , the second part of eq. 3 was used: To defuzzify the values, eq. 2 was used: = 0.5773 − 0.4649 = 0.1171 (6) Step 6: PFDA-FMEA index. Values listed in Tab. 7 were used to calculate the PFDA-FMEA Index (S×O×D). The results are presented in Tab. 9 and potential failure modes are listed according to the value of the risk number. Step 7: Determine the ranking of potential failure modes. The results are sorted to identify those potential failure modes for which action needs to be taken. This assessment of potential failure modes reveals the future scenario to be considered when assessing risk in the design of a machine component. In this sense, PFM4 -Long delivery time of raw material for production (steel) represents the greatest risk because it has the highest index number.
It is evident from the PFDA-FMEA ranking of potential failure modes listed in Tab. 10 that the lowest number represents the PFM with the highest risk.

DISCUSSION AND CONCLUSION
FMEA is an advanced tool that can be defined as simple and intuitive providing added value to the risk management process (Juhaszova, 2013). Based on the literature survey in the introduction chapter, it can be concluded that the application of FMEA in risk assessment is criticized by the professional public mainly because of the uncertainty present in risk classification. According to Turisova and Kadarova (2015), the FMEA method is usually developed by a team of experts. Analysis means team responsibility, where individual problems arising are solved by consensus, i.e. that the opinion of the most active members is accepted.
In the case study, the proposed PFDA-FMEA method has the advantage over the conventional FMEA that it compensates the possible uncertainty with linguistic values and their influence levels. Although there are currently various approaches proposed to improve FMEA, for example the harmonized edition of AIAG & VDA FMEA (Česká společnost pro jakost, 2019) focused not on the product of factors S, O, D but on the priority for action especially from the point of view of the severity of the impacts on the production plant, customer or final consumer. Unlike the conventional FMEA method, the proposed PFDA-FMEA method combines PFS, dimensional analysis and FMEA itself, thereby improving the current FMEA methodology.
Risk identification is the process of finding, recognizing, and describing risks. Risk analysis is a process to understand the nature of risk and to determine the level of risk, that is -the magnitude of a risk or combination of risks expressed in terms of the combination of consequences and their likelihood (Lengyel, Zgodavová and Bober, 2012). Fig. 3 shows the current state of risk assessment in the design of a machine component in company ICS ICE Cleaning Systems, which is complexly organized and risk identification in this case is quite difficult. In comparison with the proposed state, which results from the case study, it is clear how it is possible to proceed in the future in the identification of potential failures modes and which areas can be affected or are the most critical. This visualization makes it possible to assign resources to those areas where they are needed to mitigate the identified risks. Areas (quality, innovation, time, budget) help classify the goals to be achieved. Fig. 4 shows a comparison of potential failure modes against the values for severity, occurrence and detection, where it is clear that PFM4, PFM5, PFM6 and PFM14 had the highest values for the severity of impacts. After reviewing the literature there is room for improvement in the topic of risk analysis in the new product design process, but the presented integrated PFDA-FMEA method overcomes the main identified shortcomings and provides an advanced solution for risk assessment methods. The main benefits of the method include: 1. Elimination of uncertainty in human judgment in risk assessment due to the diversity of opinions and views in the cross-sectional team; 2. Determining the sequence of risks (allows to focus on resources at the right time in the right area);