3.1 WBS of automotive styling design tasks

The WBS is a project-management tool that decomposes an automotive styling design project into manageable tasks. First, automotive styling design development is defined as the first level overall objective. Based on the general automotive styling design process and the project lifecycle theory [36], the automotive styling design work was divided into phases following the Initiation, Planning, Execution, Control, and Closing cycle. In combination with the CATARC styling guidelines and the phased design processes commonly adopted by major Chinese automakers such as Dongfeng, SAIC, and Geely during full-vehicle development, the overall objective was decomposed into five second level strategic stages: Project initiation and preparation, creative design and exploration, design refinement and digital model development, physical model verification and evaluation, final delivery and archiving. These stages cover the entire process from early conceptual exploration to final production support.

Within the creative design, digital surface development, and physical model evaluation stages, the WBS is constructed according to the physical structure of the automobile and the principle of physical modular decomposition among system units [37]. Automotive styling consists mainly of exterior and interior sections, each divided into multiple modules, and each module consists of several components. Together, they constitute the full WBS of styling design. For example, the exterior consists of three major modules-body, front fascia, and rear fascia. The body module includes the A-pillar surface, B-pillar surface, C-pillar surface, D-pillar surface, roof surface, windows, doors, front or rear fenders, wheels, etc. To ensure the rationality and industry applicability of the WBS structure, domain experts were invited to review and revise the preliminary structure after its initial construction (detailed information about the experts is proSect 3.3vided in Sect 3.3). In addition, the task hierarchy and module divisions were further verified by referencing the complete vehicle development process and relevant project experience, ultimately resulting in the WBS structure adopted in this study. The corresponding WBS structure is shown in Fig 2.

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Fig 2. WBS Decomposition Diagram for Automotive Styling Design.

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3.2 RBS of automotive styling-design tasks

The risks in automotive styling design mainly arise from the potential adverse impacts of styling decisions, including exterior appearance, structural layout, materials, proportions, and detailed design, on safety, functionality, human–machine interaction, manufacturability, and regulatory compliance [38]. Referring to the IEC 31010:2009 Risk Management—Risk Assessment Techniques standard as the overall risk management framework, and drawing on relevant international and domestic standards (including the GB/T 34590 series, ISO 21448, ISO 15005, and GB/T 43407), as well as the CATARC styling process guidelines and enterprise design processes used by major automotive manufacturers (such as Dongfeng, SAIC, and Geely), the risk factors throughout the automotive styling design process are classified into five dimensions: technical risk, schedule risk, cost risk, resource and collaboration risk, and external and compliance risk.

1. (1). Technical risk

During the transition from sketches to digital models, geometric distortion or inconsistency in form may occur. In addition, styling solutions may conflict with engineering structures, material processes, or regulatory requirements, leading to repeated design revisions or even complete redesign. For example, the stamping feasibility of key body surfaces (such as the hood and tailgate) must be verified, while aggressive styling features, such as a low-profile body or a large rear wing, may result in an excessively high aerodynamic drag coefficient.

1. (2). Schedule risk

Due to the highly parallel and iterative nature of automotive design projects, critical tasks are often affected by competition for resources or delays in decision-making, which compress the available time for design activities. For instance, repeated revisions of CAS data may delay its release, which in turn postpones clay model production, while disputes regarding Class-A surfaces may prevent design data from being delivered to engineering teams on schedule.

1. (3). Cost risk

Cost risk includes both explicit expenses, such as mold modifications and prototype remanufacturing caused by design changes, and implicit costs associated with material or process premiums. For example, the cost of special styling components, such as customized grilles or fastback tailgates, may exceed the planned budget, while color, material, finishing (CMF) schemes involving special paint processes or new environmentally friendly materials may also increase costs.

1. (4). Resource and Collaboration risk

The loss of key personnel may disrupt the continuity of design language, while cross-team collaboration may be hindered by unclear responsibilities, inefficient communication, or system failures, creating information barriers that obstruct task coordination. For example, the departure of a lead exterior designer may make it difficult to maintain the established front-end styling language, or the steeply inclined A-pillar preferred by the styling team may conflict with the field of view safety requirements of the engineering team.

1. (5). External and Compliance risk

Changes in the external environment are highly uncertain. Updates in domestic or international regulations may require mandatory design modifications, supply chain fluctuations may affect the availability of key components, and public opinion pressure may also lead to redesign. For instance, the hood shape may need to be modified to meet updated pedestrian protection regulations, or a large screen interior layout may require redesign if it fails to meet crash safety standards in the target market.

RBS decomposes risks into hierarchical categories and subcategories, enabling systematic identification and analysis. Based on the above analysis, a multi-level risk indicator system for automotive styling design is developed, as illustrated in Fig 3.

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Fig 3. RBS Decomposition Diagram for Automotive Styling Design Project.

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3.3 Construction of the WBS-RBS Matrix

The WBS-RBS method combines the WBS and RBS to identify potential risks through a cross analysis of project tasks and associated risk factors. The construction process consists of the following steps:

1. (1). Constructing the WBS-RBS matrix

All work packages in the WBS are arranged as the rows of the matrix, while all risk factors in the RBS serve as the columns. The intersections between rows and columns represent potential risk factors associated with each specific design task. The risk value of the j-th risk factor in the i-th styling design task is denoted as .

1. (2). Determination of the matrix cell risk value

Within automotive styling design projects, the probability that risks occur during design, production, or delivery processes, as well as the magnitude of the loss incurred, cannot be accurately quantified. Consequently, the abstract notion of risk must be transformed into specific, measurable numerical values. To this end, a cardinal fuzzy evaluation approach is adopted, whereby integers ranging from 0 to 9 are used to represent the severity level, with 0 indicating the lowest and 9 indicating the highest magnitude. According to system safety engineering theory and the Likelihood-Exposure-Consequence evaluation method [39], the magnitude of risk is related to both the probability of occurrence and the severity of potential losses. The basic formulation defines risk as the product of the probability of an accident and the magnitude of the resulting loss. Accordingly, the risk value is calculated as the following Eq (1).

(1)

where denotes the degree of risk associated with risk factor j at WBS task node i; represents the probability of occurrence of risk factor j at task node i; and denotes the loss severity associated with risk factor j at task node i.

For each task node, the values of P and L are assigned by an expert panel in automotive styling design, based on collective discussion and professional judgement. The specific rating criteria for P and L are shown in Table 1.

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Table 1. Rating criteria for risk occurrence probability and loss severity.

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In combination with the WBS decomposition and risk factor analysis described in the preceding sections, a WBS-RBS matrix for the automotive styling design process is constructed, as shown in Fig 4. The cell values in the matrix are determined based on expert scoring by an automotive styling design specialist panel from a major automobile manufacturer. To ensure the scientific validity and reliability of the scoring results for the risk occurrence probability and loss severity in the WBS-RBS matrix, and to avoid potential risk overlap and repeated measurement among different risk factors, this study adopts a collective expert evaluation approach to assign risk parameters for each design task node. In addition, a risk identification and overlap verification mechanism is introduced during the scoring process. The expert panel consists of seven members, all from well-known domestic automobile manufacturers’ styling design and related support departments. Experts were selected based on their professional experience, job relevance, and participation in vehicle development projects. The panel covers the fields of styling design, styling engineering interface, and project management. Specifically, three members are exterior/interior styling design experts with 8–15 years of experience in vehicle development, two are styling engineering interface specialists familiar with engineering feasibility and manufacturing constraints, and the remaining two are product project managers or styling management personnel.

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Fig 4. WBS-RBS Risk Matrix for Automotive Styling Design.

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During the evaluation process, experts independently scored the risk occurrence probability and loss severity for each WBS task node under different RBS risk factors according to unified risk definitions and scoring criteria (see Table 1), combined with their experience in automotive styling design projects. To reduce the interference of risk overlap on the evaluation results, the scoring results were cross-checked through group discussions to identify potential duplicate evaluations or logical conflicts among different risk factors. The relevant scores were then adjusted according to the underlying mechanisms of risk occurrence to mitigate the influence of overlapping risks. In addition, to reduce subjective bias, multiple rounds of discussion and result aggregation were conducted. The final scores were obtained by averaging the opinions of all experts and used as the input parameters of the matrix, thereby improving the reliability and robustness of the risk evaluation results.

4.1 Determining risk-factor weights with improved FAHP

Automotive styling design projects involve numerous and complex risk factors. When the AHP is directly applied to identify risk nodes, two main problems arise. First, it is difficult to capture the inherent fuzziness of human cognition when assessing relationships among factors. Second, when the judgment matrix fails to satisfy the consistency requirement, repeated procedures of adjustment, verification, readjustment, and re-verification are required. Although FAHP introduces fuzzy numbers to better describe the fuzziness of expert judgments, it still suffers from strict consistency requirements, complex computation, and insufficient stability of results. Therefore, this study adopts an improved FAHP method to determine the risk weights [40]. This method is based on constructing a fuzzy consistency matrix and solving the weight vector using vector norms. The fuzzy consistency matrix directly calculates weights through vector norms, thereby avoiding the consistency testing and eigenvector iteration procedures required in traditional AHP methods and significantly reducing computational complexity. In addition, the infinity norm avoids complex eigenvalue iteration operations and improves computational efficiency and numerical stability while maintaining ranking consistency. As a result, the accumulation of computational errors is reduced, and the reliability of weight results in automotive styling design risk evaluation is enhanced. Through fuzzy representation, matrix consistency transformation, and norm-based weight calculation, the improved FAHP method overcomes the shortcomings of traditional FAHP methods, such as complicated consistency testing, large computational burden, and high sensitivity of results. Consequently, it is more suitable for multi-criteria evaluation problems characterized by strong subjectivity and uncertainty, such as the risk assessment of automotive styling design tasks. The construction procedure is described as follows.

Step 1: Construct Fuzzy Judgment Matrix

Based on the WBS-RBS matrix described in Sect 3.3, according to the Eqs (2) and (3) construct fuzzy judgment matrix A for all factors.

(2)

(3)

Here, and denote the relative importance of risk factor i and j, respectively, and the relative importance is expressed by the degree of risk at a given task node associated with the corresponding risk factor. The comparison result of risk factor iii relative to factor j is denoted by .

Step 2: Calculate the Consistency Judgment Matrix

First, sum the elements of fuzzy judgment matrix A row by row to obtain , Then The following mathematical transformation was applied: , resulting in the consistency judgment matrix . The construction of a consistent matrix enables the elements of the matrix to satisfy additive or multiplicative consistency relationships. This property avoids the computational burden and instability caused by the strict consistency tests required in traditional AHP. Moreover, the proposed approach does not rely on the eigenvector iterative solution commonly used in classical FAHP methods. Instead, the weight vector is directly calculated through the norm of the matrix row vectors, thereby significantly reducing computational complexity.

Step 3: Initialize the weight Vector

Apply the row-sum normalization method to derive the initial weight vector,using the following Eq (4).

(4)

Step 4: Construct the Reciprocal Matrix

Transform the fuzzy consistency judgment matrix into reciprocal matrix by .

Step 5: Iterative Solution of Final Weight Vector

Take the initial weight vector as the initial vector V ⁰ for the power iteration method, and further compute a more accurate weight vector . Given the initial vector , use the iterative formula V ^k+1 = EV ^k to obtain V ^k+1. Calculate the infinity norm . If , then is regarded as the maximum eigenvalue . After normalizing according to the Eq (5), the resulting vector is obtained as the weight vector, and the iteration process terminates. For a non-negative consistent matrix, the sum of the elements in each row vector (the infinity norm) reflects the relative importance of the corresponding criterion compared with other criteria, while maintaining directional consistency with the principal eigenvector of the matrix. According to the Perron-Frobenius theorem, the largest eigenvalue of a positive matrix corresponds to a unique positive eigenvector. Therefore, normalization based on the infinity norm can approximate this principal eigenvector without explicitly solving for the eigenvalues, thereby enabling efficient weight calculation.

(5)

If the convergence condition is not satisfied, calculate using the following formula (6) as the new initial vector for the next iteration.

(6)

4.2 Quantifying design-task risks using the VIKOR method

The risks associated with automotive styling design tasks involve multiple mutually conflicting criteria, including creative alignment, cost control, and schedule progress. Among MCDM methods, commonly used ranking approaches include Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE), and VIKOR, which differ in theoretical assumptions and decision preferences. The VIKOR method is based on the concept of a compromise solution. It seeks a balance between maximizing group utility and minimizing individual regret and is capable of highlighting the influence of the most unfavorable risk factors. Therefore, it is suitable for decision-making scenarios involving critical bottleneck risks [41]. By contrast, TOPSIS assumes full compensability among indicators. However, in automotive styling design, severe problems related to regulatory compliance or engineering feasibility often cannot be offset by advantages in other indicators [42]. PROMETHEE relies on the specification of preference functions and threshold parameters, and its results are sensitive to parameter selection, which may reduce the stability and consistency of the ranking results [43]. In contrast, the VIKOR method introduces the individual regret indicator, preventing advantages in certain indicators from completely offsetting severe deficiencies in others. Furthermore, it allows the decision coefficient to be adjusted to reflect different risk preference scenarios, providing better interpretability and operability. In addition, risks in automotive styling design tasks exhibit strong stage characteristics. Different stages emphasize different aspects of overall risk control and critical risk avoidance. The VIKOR method can reflect such changes in decision preference simply by adjusting the parameter without modifying the original risk matrix structure. This feature makes it suitable for capturing the dynamic nature of styling design task risks and avoiding risk misjudgment caused by single-dimensional evaluation.

The specific procedure for calculating the WBS node risk level using the VIKOR method is as follows:

Step 1: Standardize the WBS-RBS matrix

Each cell value in the WBS-RBS matrix is normalized using range normalization for each indicator, as expressed below.

(7)

where Z_ij denotes the normalized value of represents the value of the j-th risk factor for the i-th WBS node; and, represent the maximum and minimum values of column j, respectively.

Step 2: Calculate the positive and negative ideal solutions

For each column j of the normalized WBS-RBS matrix, determine the positive and negative ideal solutions, i.e., the maximum and minimum values in that column (, ).

Step 3: Calculate group utility S and individual regret R

S represents the sum of the relative distances from the optimal object and reflects the overall deviation of an evaluated object from the positive ideal solution, with smaller values indicating better performance. R represents the maximum relative distance of any single indicator from the optimal object, where smaller values again correspond to superior performance.

(8)

Where denotes the weight of the j-th risk factor.

Step 4: Calculate the benefit ratio Q

Based on the obtained and , compute the benefit ratio by using the following Eq (9).

(9)

where denotes the benefit ratio; v denotes the decision-making coefficient with a value range of [0,1]. When , the evaluation result is more inclined to group utility and therefore tends toward risk preference; when , equal consideration is given to group utility and individual regret, representing a risk-balanced pattern; when , emphasis is placed on individual regret, thereby reflecting a risk-averse pattern. and denote the maximum and minimum values of S, while and denote the maximum and minimum values of R.

Step 5: Determine the ranking of WBS nodes

Sort the calculated Q values in ascending order, where a higher Q indicates higher compatibility with design objectives and therefore lower risk, and vice versa. The classification of risk levels is established based on the characteristics of the benefit ratio Q derived from the VIKOR method. It also draws on the risk grading principles of ISO 31000 and ISO 31010, as well as the interval division concept of the LEC evaluation method, while incorporating the specific risk distribution characteristics of automotive styling design tasks. By categorizing the continuous evaluation results into three levels—high, medium, and low risk—the proposed scheme not only enhances the interpretability of the risk identification results but also facilitates hierarchical decision-making and resource allocation in engineering management. The detailed criteria are shown in Table 2.

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Table 2. Risk level classification criteria for automotive styling design.

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5.1 Construction of the WBS-RBS matrix for exterior styling

1. (1). Establishing the WBS of automotive exterior styling design

Based on the WBS construction process described in Sect 3.1, the creative exterior styling design of an SUV is decomposed into three major categories, namely front-end design, rear-end design, and body design. Each category consists of multiple exterior components, resulting in a total of 27 WBS work packages, as shown in Table 3.

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Table 3. WBS decomposition of creative exterior styling design for a certain SUV.

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1. (2). Building the WBS-RBS Matrix

The above 27 lowest-level WBS work packages are taken as the rows of the matrix, and the 16 lowest-level RBS risk factors described in Sect 2.2 are taken as the columns to form the WBS-RBS coupling matrix. The expert panel on automotive styling design then assigns P and L scores for each of the 16 risk factors at each of the 27 WBS task nodes, followed by calculating the risk value for each matrix cell according to Eq (1). The final results are shown in Table 4.

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Table 4. WBS-RBS risk matrix for creative exterior styling design of an SUV.

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5.2 Calculation of risk-factor weights

To illustrate the calculation process, the front headlamp assembly (W₁₁) is used as an example. Because certain risk factors (e.g., R₁₄, R₃₁, R₃₂, R₄₃) do not apply during early styling concept development, they are assigned zero risk. Corresponding judgment matrices W-R, W-R₁, W-R₂, W-R₄, and W-R₅ are constructed (Table 5).

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Table 5. Fuzzy judgement Matrix.

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Using the W-R judgment matrix as an example, the corresponding consistency judgment matrix P is obtained as follows.

The initial weight vector obtained by the row sum normalization method is as follows.

The reciprocal judgment matrix E is as follows.

With a convergence precision of 0.0001 and four iterations, the final weights obtained by iterative computation are as follows.

Following this procedure, both the risk factors and risk indicators weights are obtained, as shown in Table 6. Ranking the indicators further determines which risk factors dominate at this node.

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Table 6. Risk factor weights for creative exterior styling design of an SUV.

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For the creative design of the front headlamp assembly (W₁₁), the results obtained from the improved FAHP-based weight calculation indicate that technical risk accounts for the largest proportion, followed by schedule risk, while cost risk contributes the least. This suggests that the risk at this task node is primarily dominated by the difficulty of styling realization and engineering feasibility constraints, with the design iteration cycle also exerting a significant influence on the overall risk level. Further sensitivity analysis reveals that small variations in the weight of technical risk lead to the most pronounced changes in the overall risk ranking, whereas fluctuations in cost risk weights have a relatively limited impact. This demonstrates that the proposed model exhibits high sensitivity to critical risk factors and is capable of effectively identifying the dominant drivers of task level risk, thereby validating both the rationality of the weight allocation and the robustness of the model results.

5.3 Quantitative risk assessment and analysis

According to Eq (7), the WBS-RBS matrix is standardized, from which the maximum and minimum values of each column (, ) are obtained. Combined with the FAHP derived risk weights at W₃₅, the group utility S₃₅ and individual regret R₃₅ are calculated using Eq (8), the same procedure is applied to the remaining 26 WBS nodes.

In the risk evaluation of automotive styling design tasks, regulatory compliance and engineering feasibility risks often exhibit a “veto effect,” while schedule and cost risks mainly reflect overall project performance. If a large value of () is adopted, the ranking results will tend to favor solutions with the optimal overall average risk level, which may mask critical risk factors. Conversely, if a small value of () is used, the evaluation results may be excessively influenced by a single indicator, reducing the comprehensiveness of the assessment [44]. Therefore, this study sets to achieve a balanced trade-off between group utility and individual regret, which better conforms to the decision-making requirements of automotive styling design, where both overall optimization and critical risk control must be considered. Finally, based on Eq (9), the benefit ratio Q of each node is computed and subsequently ranked. According to Table 2, each WBS node is then classified into corresponding risk levels. The results are summarized in Table 7.

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Table 7. Summary of VIKOR results (risk-balanced type).

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From Table 7 there are five high-risk nodes (18.5%), nine medium-risk nodes (33.3%), and thirteen low-risk nodes (48.2%). The high-risk nodes include W₁₂ (upper air-intake surface), W₁₃ (front bumper surface), W₁₄ (lower air-intake surface), W₂₆ (lidar surface), and W₃₄ (rear bumper surface). These nodes show a high level of risk across most of the five major dimensions. Specifically, the front-end design tasks W₁₂, W₁₃, and W₁₄ show relatively high technical risk (R₁) and schedule risk (R₂). In order to enhance brand recognition, designers often adopt relatively aggressive styling languages, which may lead to deviations from the brand DNA (R₁₁: stylistic deviation from brand DNA) and generate conflicts with engineering feasibility (R₁₃: abrupt engineering hard-points) and aerodynamic performance (R₁₂: insufficient CAS surface continuity). As a result, these tasks frequently undergo repeated modifications during cross-departmental reviews (R₂₂: Prolonged review and decision-making chain), which may ultimately lead to schedule delays and increased project costs. Node W₂₆, which is associated with intelligent and connected vehicle components, presents risks not only from the technical challenges of integrating sensor layouts with styling design (R₁), but also from potential regulatory changes (R₅₁: regulatory updates). Adjustments in regulatory requirements may trigger design rework. Similar to the front-end design tasks, node W₃₄ requires repeated trade-offs between compliance with crash regulations (R₅₁) and maintaining desired styling proportions (R₁₁). In addition, it involves strong coordination constraints with components such as taillights and exhaust systems, which increases the likelihood of design rework and introduces additional schedule and cost risks.

The medium-risk nodes include W₁₁, W₁₅, W₂₁, W₂₃, W₂₁₀, W₂₁₂, W₂₁₅, W₃₂ and W₃₃, whose risks characteristics are relatively dispersed and are typically concentrated in specific risk factors. For instance, nodes W₁₁ and W₃₂ are mainly affected by the technical implementation challenges associated with complex light-and-shadow styling surfaces (R₁₂) and the cost pressure of special materials (R₃₃: Material price fluctuation). Structural body components such as W₁₅, W₂₁, and W₂₃ are primarily constrained by the interactions among styling requirements, ergonomics, and safety regulations (R₁₃, R₅₁), which may lead to localized rework and schedule impacts. Furthermore, the risks associated with nodes W₂₁₀, W₂₁₂, and W₃₃ are mainly reflected in resource coordination and collaboration factors (R₄₂: lack of cross-departmental interface personnel). Issues such as panel gaps and surface mismatches often increase communication and iteration costs during the design process. Node W₂₁₅, on the other hand, involves trade-offs between lightweight design and structural strength, making its technical risk (R₁) and cost risk (R₃) relatively prominent.

From the perspective of risk distribution, high-risk nodes are mainly concentrated in front-end design, rear-end design, and intelligent component design such as the lidar surface. Medium-risk nodes are primarily associated with body structural components and optical elements, while low-risk nodes mainly correspond to components with mature technologies and weak dependency relationships, such as the fuel filler or charging port door and vehicle windows. This distribution pattern is consistent with engineering practice in automotive styling design. The front-end and rear-end regions represent the core elements of vehicle styling identity, where design complexity is high and conflicts with engineering feasibility and regulatory requirements are more likely to occur, resulting in higher risk levels. Intelligent components such as the lidar surface are subject to both technological constraints and regulatory requirements, which also leads to elevated risks. Body structural components must balance styling requirements, ergonomics, and safety considerations, and therefore involve a moderate level of risk. In contrast, the design processes of mature components are highly standardized, leading to relatively lower risk levels.

From the perspective of risk driving mechanisms, high and medium risk nodes are mainly concentrated in three categories. First, tasks with high design complexity, represented by front and rear styling, where risks arise from the strong coupling between styling innovation and multiple engineering constraints. Second, tasks driven by engineering and manufacturing constraints, such as body structural components, where risks primarily stem from conflicts between manufacturability and regulatory compliance. Third, tasks characterized by technological uncertainty, represented by lidar related surfaces, where risks are influenced by both the integration of emerging technologies and potential regulatory changes. In addition, some medium risk nodes exhibit pronounced cross departmental coordination characteristics, further contributing to their risk profiles. The detailed classification of WBS nodes is presented in Table 8.

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Table 8. Classification of medium-risk and high-risk nodes.

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5.4 Comparative analysis

To further verify the effectiveness and superiority of the proposed FAHP-VIKOR method in identifying risks in automotive styling design tasks, three different evaluation methods are selected for comparative analysis: (1) the single FAHP weighted evaluation method [11]; (2) the FAHP-TOPSIS method [45], This method ranks risks by calculating the relative closeness coefficient (CC) of each alternative to the positive and negative ideal solutions, where a larger CC value indicates a higher level of risk; (3) the traditional FAHP–VIKOR method [44]; (4) the improved FAHP-VIKOR method proposed in this study. All four methods are based on the same WBS-RBS risk matrix and the same FAHP-derived risk factor weights to ensure that differences in the results arise solely from the ranking mechanisms. The code for implementing each method can be found in the supplementary S1 File. The initial WBS nodes classification used in the study and the original WBS-RBS risk matrix are presented in the supplementary S2 File. The matrices, weight values, return rates, and risk levels of each WBS task node involved in the calculation process of each method in the study can be found in the supplementary S3 File. The specific risk identification results are shown in Table 9.

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Table 9. Risk identification results of automotive styling task nodes under different methods.

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From the overall results, the three methods show a high degree of consistency in identifying extreme risk nodes. For example, node W₁₃ (front bumper surface) and node W₃₄ (rear bumper surface) are identified as high-risk nodes by all three methods, while node W₂₁₄ (Fuel Flap or Charging Port Door) consistently falls within the low-risk nodes. This indicates that the constructed WBS-RBS risk matrix is structurally reasonable and that the improved FAHP weighting system exhibits good stability and consistency.

From the results of the single FAHP method, the risk level of each WBS node is calculated through linear weighted summation, which represents a typical fully compensatory model. For example, node W₃₂ is classified as high-risk under FAHP, whereas it is identified as medium-risk under FAHP-TOPSIS, FAHP-VIKOR and the improved FAHP-VIKOR. Similarly, node W₁₆ is classified as medium-risk under FAHP but adjusted to low-risk under the other two methods. These differences indicate that the single weighted model is sensitive to locally high-risk values and may elevate the overall risk level when a particular indicator has a relatively large value.

From the perspective of the FAHP-TOPSIS method, the ranking discrimination is improved compared with the single FAHP method. For example, nodes W₁₆, W₂₂, W₂₄, and W₂₅ are all classified as low-risk under TOPSIS, which better corresponds to the engineering reality that these mature structural modules usually involve relatively low risk. However, compared with the improved FAHP-VIKOR method proposed in this study, differences appear in the high-risk boundary interval (rank positions 22–26). For instance, node W₁₄ is identified as medium-risk under TOPSIS. The underlying reason is that TOPSIS evaluates alternatives based on the Euclidean distance from positive and negative ideal solutions. As long as the overall distance is relatively favorable, an alternative may obtain a better ranking even if it performs poorly on a critical risk factor. While this distance-based compensation mechanism is mathematically reasonable, it may weaken the influence of “critical bottleneck” risks in the context of automotive styling design.

From the results of the FAHP combined with the VIKOR method, it can be observed that although the compromise solution concept of VIKOR is introduced compared with FAHP–TOPSIS, the weight determination process still relies on the traditional FAHP approach. Conventional FAHP requires consistency testing and eigenvector iteration, which become computationally complex when the dimension of the judgment matrix increases. This may lead to convergence issues or distortion in weight allocation. In terms of ranking results, the traditional FAHP–VIKOR and the improved FAHP–VIKOR methods show a generally consistent trend, but differences can be observed for certain nodes. For example, node W22 is classified as medium risk under the traditional FAHP–VIKOR method, whereas it is identified as low risk using the improved FAHP–VIKOR approach. Considering that this node involves fewer styling constraints and a high level of engineering maturity, it is more reasonably classified as low risk. The discrepancy arises because traditional FAHP relies on consistency testing and eigenvector solutions, without incorporating consistency transformation and norm-based optimization, resulting in limited weight stability and the amplification of local errors during the VIKOR ranking process.

Overall, based on the data presented in the table, it can be concluded that the single FAHP method is sensitive to local extreme values, while the FAHP–TOPSIS method suffers from the limitation of full compensability. Although the FAHP–VIKOR method alleviates this issue to some extent, its results remain affected by the instability of weight calculation. In contrast, the improved FAHP–VIKOR method proposed in this study enhances both the weight determination process and the ranking mechanism, producing results that better reflect the engineering reality that critical risks are non-compensatory in automotive styling design tasks. Therefore, in terms of rationality, stability, and interpretability of risk identification, the improved FAHP–VIKOR method demonstrates stronger applicability and decision-support capability in the context of this study.

5.5 Management recommendations

In the management of automotive styling design projects, traditional project scheduling is mainly based on experience to determine task durations, which makes it difficult to fully reflect the influence of potential risks on task execution. Therefore, integrating risk identification results into project schedule management is of great significance for improving the efficiency of design management. To visually demonstrate the supporting role of risk identification results in project management decision-making, this study first constructs a WBS based task Gantt chart of the automotive styling design project prior to risk identification in the Oracle Primavera P6 Enterprise Project Portfolio Management (Oracle P6 EPPM) system, based on the Work Breakdown Structure (WBS) of the automotive styling design project (as shown in Fig 6).

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Fig 6. Gantt chart of WBS tasks for the automotive styling design project before risk identification.

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On this basis, the improved FAHP-VIKOR method is applied to conduct risk identification for the WBS tasks of the styling design project. In the Oracle P6 EPPM environment, tasks with different risk levels are marked using different colors. Compared with Fig 6, the optimized Gantt chart (Fig 7) can clearly distinguish the risk levels associated with various styling design tasks.

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Fig 7. Optimized Gantt chart of WBS tasks for the automotive styling design project after risk identification.

https://doi.org/10.1371/journal.pone.0352278.g007

For high-risk nodes W₁₂, W_13, W₁₄, W₂₆, and W₃₄, proactive and strengthened management measures should be adopted. These tasks are typically located at key decision-making stages of the styling design process and are characterized by broad influence and high rework costs. Therefore, greater schedule buffers and design resources should be allocated to these tasks at the early stage of the project. For example, during the front-end styling design stage, the scheme review period can be appropriately extended, and joint verification of engineering feasibility and aerodynamics can be conducted in advance to reduce potential rework caused by engineering constraints or performance issues in later stages. For nodes significantly influenced by regulatory requirements, such as the W₂₆ lidar surface design task, a regulatory monitoring mechanism should be established and sufficient design adjustment space should be reserved to cope with uncertainties arising from potential policy changes.

The management focus for medium-risk nodes lies in targeted control and local optimization. Although these tasks do not directly determine the success or failure of the project, local problems may affect the overall schedule through cumulative effects. For instance, for optical component design nodes such as W₁₁ and W₃₂, coordination between optical performance and styling design should be strengthened. For components involving structural and ergonomic constraints, including nodes W₁₅, W₂₁, and W₂₃, early-stage virtual validation can be implemented to reduce potential design conflicts. For nodes with strong cross departmental dependencies, including nodes W₂₁₀, W₂₁₂, and W₃₃, interface responsibilities should be clearly defined and communication processes optimized to reduce coordination costs.

For low-risk nodes, standardized process management can be adopted. These tasks generally involve mature technologies and relatively weak dependency relationships. Their implementation can be promoted through modular design and experience reuse, thereby allowing more project resources to be concentrated on critical risk nodes and improving overall resource allocation efficiency.

Compared with the original schedule, the optimized Gantt chart allocates time more reasonably for key high-risk tasks and introduces moderate risk-buffer mechanisms, making the overall project schedule more consistent with the risk distribution characteristics of the design tasks.