Model construction and comprehensive evaluation of quality infrastructure capability building model in the equipment manufacturing industry

Abstract

Quality Infrastructure serves as a crucial foundation for the high-quality development of the equipment manufacturing industry, encompassing numerous factors and constituting a complex systems engineering project. Addressing the current challenges of incomplete elements and insufficient integration in the industry’s quality infrastructure construction, this paper focuses on the construction needs of the equipment manufacturing industry, it clarifies the constituent elements of the industry’s quality infrastructure and constructs an overall framework for capability building based on the “Regulatory System–Management System–Technical System.” To tackle the problems of lacking evaluation indicators and strong subjectivity in evaluating quality infrastructure capability, a quality infrastructure capability evaluation model and indicator system for the equipment manufacturing industry are proposed from the dimensions of industry influence, institutional construction, resource supply, and equipment quality assurance. Based on fuzzy theory and the VIKOR method, a comprehensive evaluation method for quality infrastructure capability in the equipment manufacturing industry is proposed. Ultimately, an application in a specific aviation equipment manufacturing sector is undertaken to validate the effectiveness of the proposed method.

Keywords

equipment manufacturing industry quality infrastructure capability comprehensive evaluation model construction fuzzy theory VIKOR

Highlights

Build QI framework across regulatory, management, technical systems.

Propose hierarchical model with 4-14-26 indicators.

Integrate fuzzy theory and VIKOR for objective evaluation.

Aviation case (2020–2024): rising index; resources, institutions critical.

Introduction

The equipment manufacturing industry is a vital reflection of economic and social development, national security, and international competitiveness.¹ The level of its quality infrastructure (QI) construction is crucial for ensuring the overall quality equipment. Currently, the industry faces challenges such as an unstable foundation for quality development and difficulties in guaranteeing overall equipment quality, highlighting inadequacies in the construction capability and effectiveness of the industry’s quality infrastructure.^2,3 Quality Infrastructure (QI), first proposed by the German Federal Institute of Physics (PTB) in 2002, consists of three elements: metrology, standards, and conformity assessment. It was formally introduced to the public by the UN Trade and Development (UNCTAD) and the World Trade Organization (WTO) in 2005.^4,5 In 2017, relevant international organizations jointly recognized QI as “a system comprising public and private institutions, as well as the policies, legal, regulatory frameworks, and practices needed to support and enhance the quality, safety, and health environment of goods, services, and processes.” Its essence is a framework system and practice of institutions, laws, policies, regulations, and practical activities, playing a fundamental and supportive role in industry development and equipment quality improvement.⁵

Current research on quality infrastructure capability building and evaluation primarily focuses on the national or regional level. For example: The US government initiated National Quality Infrastructure (NQI) construction as early as the 1980s, issuing a series of policy measures to provide various technical consulting services for enterprise development.² The Gesellschaft für Internationale Zusammenarb (GIZ) actively promotes the implementation of NQI. Based on an assessment of Ethiopia’s quality infrastructure construction level, GIZ guided Ethiopia to invest 11.7 million euros over three years in quality infrastructure construction, achieving significant results.⁴ Theoretical methods related to quality infrastructure are gradually expanding into industries such as trade, health, and safety.^6,7 In terms of evaluation indicators, there is currently a lack of an authoritative international indicator system for measuring the comprehensive level of QI. Various experts, scholars, and research institutions have conducted exploratory work. For instance, the United Nations Industrial Development Organization (UNIDO) developed the Trade Standards Compliance Index (TSSCI), which includes 10 sub-indices and 73 indicators covering standardization, metrology, certification, accreditation, inspection, testing, quality management, technical regulations, etc.⁸ Hüseyin Uğur proposed a comprehensive evaluation method for assessing the social and economic impact of NQI, collecting basic data from 15 European and Central Asian countries for evaluation.⁹ Jiang et al.¹⁰ analyzed NQI evaluation indicators from capability and effectiveness perspectives, combining them to form an NQI development level index, which mirrors the potential service capability and direct service effectiveness at the national level. In terms of evaluation methods, traditional evaluation methods rely heavily on subjective expert judgment, significantly influenced by the experts’ professional level and cognition. For example, the evaluation of the TSSCI mainly involves distributing questionnaires to relevant institutions for qualitative descriptions from specific aspects of NQI, dividing results into 5 levels to reflect NQI capability.^5,10

Regarding the application of quality infrastructure capability building in the equipment manufacturing industry, some enterprises have undertaken exploratory work, effectively supporting equipment manufacturing quality. For example: Boeing emphasizes the application of quality infrastructure elements like standards, metrology, inspection/testing, and certification or accreditation. In product design and manufacturing, 38% of operational data, 39% of engineering data, and 40% of product definition data originate from standards. Siemens’ quality infrastructure construction focuses on digitalization and intelligence as core strategies, supporting quality management, technological innovation, and digital transformation.^11,12 However, there are still some issues in quality infrastructure construction and capability evaluation in the equipment manufacturing industry:

The constituent elements of quality infrastructure in the industry are unclear, leading to a lack of a construction model and hindering effective support and guarantee of equipment quality levels.

Current quality infrastructure evaluations mainly target national or regional levels, misaligning with the focus and requirements of industry-level construction, making direct application difficult.

Quality infrastructure capability evaluation relies heavily on qualitative analysis, resulting in strong subjectivity and difficulty in objectively characterizing capability levels.¹³

Therefore, building upon national or regional requirements for quality infrastructure construction and evaluation, this paper combines the quality management requirements of the equipment manufacturing industry to construct a quality infrastructure construction model.^14,15 Based on fuzzy theory and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method, it proposes a comprehensive evaluation method for assessing the quality infrastructure capability building level within the equipment manufacturing industry, providing methodological support for enhancing its quality infrastructure capability.

To address these issues, this paper makes the following contributions. First, the key elements of quality infrastructure in the equipment manufacturing industry are clarified. Second, a capability-building framework is constructed based on the “Regulatory System–Management System–Technical System.” Third, an evaluation model and indicator system are developed from four dimensions: industry influence, system construction, resource supply, and equipment quality assurance. Finally, a fuzzy theory and VIKOR-based evaluation method is proposed and validated through a case study. These contributions form a complete chain from framework construction to quantitative evaluation.

Quality infrastructure construction model for the equipment manufacturing industry

Constituent elements of quality infrastructure in the equipment manufacturing industry

Based on the quality assurance needs of the equipment manufacturing industry and national quality infrastructure research theory, this paper posits that the industry’s quality infrastructure is a technical system composed of professional elements such as metrology, standards, inspection or testing, certification or accreditation, it includes elements like standardization, metrology, conformity assessment, and general quality characteristics of equipment, as well as regulatory systems, regulatory frameworks, organizational structures, talent teams, and practical activities that support each element4. The capability level of this infrastructure is determined by:

Industry quality infrastructure capability

Industrial quality foundation supply capability

Ancillary quality support capability

General quality characteristics assurance capability

Industry quality supervision capability

Construction model for quality infrastructure in the equipment manufacturing industry

Quality infrastructure construction in the equipment manufacturing industry involves multiple domains such as standards, metrology, inspection or testing, certification or accreditation, industrial data, and general quality characteristics, potentially facing issues of fragmented management and coordination difficulties. Therefore, in order to comprehensively advance this construction, this paper builds upon national quality infrastructure construction requirements and industry characteristics.¹¹ Focusing on constituent elements like standardization, metrology, conformity assessment (including inspection or testing, certification or accreditation), and equipment general quality characteristics, it proposes a construction model from three dimensions: regulatory system, management system, and technical system. The regulatory system provides the essential basis for equipment quality supervision; the management system is the direct guarantee for standardizing equipment quality; the technical system is the vital foundation for ensuring industry development. The construction model is shown in Figure 1.

(1) Regulatory system

Figure 1.

Overall framework of quality infrastructure for the equipment manufacturing industry.

The regulatory system for the equipment manufacturing industry, under the guidance of national laws, consists of industry laws, administrative regulations, departmental rules, normative documents, and management measures for frontline scientific R&D. It ensures the sustainable development of the industry’s quality infrastructure. Relevant administrative regulations mainly include national laws, rules issued by national competent authorities, and industry regulatory requirements.

(2) Management system

Leveraging the existing management systems within the industry, we should further refines the responsibilities for quality infrastructure management and clarifies quality management requirements. It can be divided into four layers according to management hierarchy: governance layer, management layer, support layer, and execution layer.

The governance layer is responsible for organizing the management of industry plans, policies, standards, and regulations, supervising their implementation, proposing overarching governance requirements, defining quality policies and top-level frameworks, and centrally managing the industry’s quality infrastructure. The governance layer primarily refers to industry competent authorities.

The management layer is responsible for implementing governance requirements and leading the construction of industry quality infrastructure. It mainly includes enterprise headquarters’ competent departments and relevant industry associations.

The support layer establishes and improves the industry quality infrastructure management system based on the construction requirements set by the Governance and Management Layers. It primarily consists of industry professional technical institutions and industry management laboratories.

The execution layer includes all units within the industry, serving as the main participants and direct users of quality infrastructure construction.

(3) Technical system

Facing the professional composition of quality infrastructure, the technical system comprises four parts: standardization technical system, metrology technical system, inspection and testing technical system, and equipment general quality characteristics technical system. Among them:

The industry standardization technical system includes standardization fundamental technology, standardization management technology, standard specification development technology, and standard digitalization technology.

The industry metrology technical system scientifically categorizes and delineates metrology technologies based on systems engineering principles, the system covers four fields: scientific theory frontiers, special value transfer, R&D and production support, and professional fundamental sharing.

Inspection and testing are divided into quality testing and technical safety & environmental testing based on different purposes. Quality testing includes non-destructive testing, metrological testing, physical and chemical testing, and product testing, technical safety & environmental testing includes energy conservation and environmental protection testing, vacuum testing, electrostatic protection testing, intelligent video inspection, etc.

The equipment general quality characteristics technical system mainly includes design analysis and test verification technologies for general quality characteristics such as reliability, maintainability, testability, supportability, safety, and environmental adaptability.

This section clarifies the constituent elements of quality infrastructure and establishes an integrated construction framework for the equipment manufacturing industry. The next section further develops a corresponding evaluation model and indicator system based on this framework.

Comprehensive evaluation indicator system for quality infrastructure capability in the equipment manufacturing industry

Comprehensive evaluation model for industry quality infrastructure capability

To enhance the construction level of quality infrastructure in the equipment manufacturing industry, it is necessary to conduct capability evaluations to provide inputs for targeted and continuous improvement. Rooted in the national industrial base, the industry’s quality infrastructure primarily serves the complex equipment construction field, effectively ensuring equipment quality, promoting industrial upgrading, and supporting equipment R&D activities, thereby achieving high-quality development.

This paper focuses on enhancing the quality assurance capability of the equipment manufacturing industry. By integrating the constituent elements and construction model of the quality infrastructure capability in the equipment manufacturing industry, and drawing on the evaluation approach of the National Quality Infrastructure Development Level Index, this paper comprehensively considers the goal of the quality infrastructure in the equipment manufacturing industry serving the quality assurance of equipment development and production. It establishes a comprehensive evaluation model from the dimensions of industry influence, system construction, resource supply, and equipment quality assurance, this model comprises 4 first-level indicators, 15 second-level indicators (see Figure 2), and 26 third-level indicators.

(1) Industry Influence

Figure 2.

Comprehensive evaluation model for the equipment manufacturing industry.

Industry influence primarily evaluates the influence of the industry within its technical domain. The evaluation focus is on possessing metrology, standards, accreditation, and conformity assessment systems recognized internally and externally, leading national/industry-related quality infrastructure regulations, and the construction of professional institutions related to quality infrastructure.

(2) System construction

Having a relatively complete regulatory system at the industry level is the foundation for ensuring the sound operation of the quality infrastructure system. When evaluating the regulatory system, it is necessary to build upon national quality infrastructure regulations, while also taking into account the current development status and needs of the specific industry or enterprise, and carrying out targeted evaluations of regulatory construction.

(3) Resource supply

A robust quality infrastructure for the equipment manufacturing industry requires the guarantee capability of relevant resources, serving as a crucial foundation for ensuring its smooth operation. Besides ensuring the supply of resources for metrology, standards, accreditation, and conformity assessment, it is also important to focus on evaluating the supply of human resources, funding, and the construction of technical basic data resource platforms in professional institutions.¹⁶

(4) Equipment quality assurance

During equipment R&D and production, specialized fields such as standardization, metrology, and general quality characteristics are the main quality infrastructure elements ensuring equipment development. Emphasis should be placed on evaluating whether corresponding quality assurance system has been established within the current equipment development process and whether relevant assurance professionals have been appointed.

Evaluation indicator system for quality infrastructure capability in the equipment manufacturing industry

Based on the constructed “Industry Influence–System Construction–Resource Supply–Equipment Assurance” comprehensive evaluation model and its indicator system (4 first-level, 15 second-level, 26 third-level indicators), this paper presents quantitative calculation methods for each third-level indicator to enhance the operability and accuracy of the evaluation index calculations. The comprehensive evaluation indicator system is shown in Table 1.

Table 1.

Evaluation indicator system for quality infrastructure capability in the equipment manufacturing industry.

First-level indicator	Second-level indicator	Third-level indicator	Evaluation points
Industry influence	Scope of influence	External influence	Number of relevant organizations joined, number of standards led in drafting, etc. \|
	Scope of influence	Internal Influence	Number of relevant technical organizations undertaken within the industry, industry-level standards led in drafting, metrology institutions, measurement standards, etc.
	System construction	Capability of Professional Technical Institutions	Number of institutions at industry level or above
System construction	Regulations	Regulation construction	Number of industry-level regulations, number of enterprise-level regulations, etc.
	Regulations	Quality policy environment	Comprehensive quality policies, strategies, or plans, etc.
	Supervision	Technical supervision system construction	Construction and operation of the quality supervision management system
	Supervision	Technical supervision system development	Technical supervision systems covered in quality management systems
Resource supply	Data platform resources	Shared platform construction	Quality infrastructure data platform shared and used within the industry
	Data platform resources	Professional platform construction	Industry-shared standard data platforms, metrology data platforms, product quality data platforms, etc.
	Standard resources	Leading formulation	Number of industry/enterprise standards led in drafting
	Metrology resources	Metrology specifications/standards	Number of national/industry metrology technical specifications led in drafting, measurement standards preserved, types of specialized reference materials, types of reference materials, etc.
	Metrology resources	Metrology Laboratories	Number of metrology R&D laboratories
	Certification/accreditation resources	certification/accreditation qualification capability	Number of certificates with industry certification, units qualified for equipment manufacturing, units licensed for equipment R&D and production, etc.
	Inspection/testing resources	inspection/testing capability	Number of laboratories within the industry (or group) certified at national/industry level
	Human resources	personnel engaged in QI construction	Number of technical personnel specifically engaged in QI construction, national/industry-level specialized talents
	Funding resources	R&D/technical renovation funding	Annual R&D/technical renovation funding for QI-related specialties
Equipment quality assurance	Standardized equipment quality assurance	Equipment product standardization work	Construction status of the equipment standards system
	Metrology equipment quality assurance	Equipment metrology work	Number of specialized metrology and testing equipment for equipment, average inspection/calibration rate of measurement equipment equipped for R&D and production, etc.
	General quality characteristics	Equipment general quality characteristics work	Degree of dependence on external quality and reliability technology projects, self-completion of general quality characteristics tests, utilization of environmental test and observation information, autonomy in natural environmental testing, etc.
	Equipment quality assurance personnel	Personnel engaged in standardization, metrology, and GQC	Proportion of dedicated GQC personnel, proportion of professionals with senior technical titles

This section establishes a comprehensive evaluation model and constructs a multi-level indicator system for assessing quality infrastructure capability. Based on these indicators, the next section proposes the evaluation methodology for data processing, weight determination, and capability calculation.

Comprehensive evaluation methodology for quality infrastructure capability in the equipment manufacturing industry

Building upon the established evaluation indicator system for quality infrastructure capability in the equipment manufacturing industry, methods for quantifying evaluation data, determining index weights, and comprehensive evaluation are proposed.¹⁷

Fuzzy theory-based quantitative processing method for evaluation data

Due to variations in personnel knowledge, experience, and engineering backgrounds, expert evaluation information exhibits ambiguity and uncertainty. To improve the accuracy of evaluation results, this paper employs fuzzy theory to quantitatively process subjective evaluation data.^18,19

(1) Fuzzy Theory

Fuzzy theory quantifies ambiguous information in natural language, effectively addressing the fuzziness and uncertainty inherent in human judgment.²⁰

Let $U$ be the universe of discourse, $U = {u_{1}, u_{2}, \dots, u_{n}}$ , and $\tilde{A}$ be a set of ordered pairs: $\tilde{A} = {(u_{1}, f_{\tilde{A}} (u_{1})), (u_{2}, f_{\tilde{A}} (u_{2})), \dots, (u_{n}, f_{\tilde{A}} (u_{n}))}$ , where $f_{\tilde{A}}$ is the membership function of $\tilde{A}$ , $f_{\tilde{A}} : U \to [0, 1]$ , $f_{\tilde{A}} (u_{i})$ is the level of the membership function of $u_{i}$ in the fuzzy set $\tilde{A}$ . Only if $\forall u_{i}, u_{j}$ in $U$ satisfies the following conditions, the fuzzy set $\tilde{A}$ is convex, the fuzzy set $\tilde{A}$ is convex, it satisfies²¹ as equation (1):

\begin{matrix} f_{\tilde{A}} (η u_{i} + (1 - η) u_{j}) \geq \min (f_{\tilde{A}} (u_{i}), f_{\tilde{A}} (u_{j})) \end{matrix}

(1)

Where, $η \in [0, 1]$ , only when $\exists u_{i} \in U, f_{\tilde{A}} (u_{i}) = 1$ , the fuzzy set $\tilde{A}$ is normal, and a fuzzy number is a fuzzy subset of $U$ , which is both convex and normal. Using $\tilde{A} α$ to represent the $α -$ “cut” of fuzzy numbers,the $α -$ “cut” of a fuzzy number $\tilde{A} α$ is defined as equation (2):

\begin{matrix} \tilde{A} α = {(u | f_{\tilde{A}} (u_{i})) \geq α}, α \in [0, 1] \end{matrix}

(2)

(2) Fuzzy numbers

Triangular fuzzy numbers are a commonly used method for describing fuzzy sets, let $\tilde{A} = (a, b, c)$ , where $0 \leq a \leq b \leq c (a, b, c \in R)$ , with its membership function defined as equation (3):

\begin{matrix} f_{\tilde{A}} (x) = {\begin{matrix} \frac{x - a}{b - a}, & x \in [a, b] \\ \frac{c - x}{c - b}, & x \in [b, c] \\ 0, & otherwise \end{matrix} \end{matrix}

(3)

As shown in Figure 3, when $x = b$ , $f_{\tilde{A}} (x) = 1$ , indicating $x$ completely belongs to the set, when $x \leq a$ or $x \geq c$ , $f_{\tilde{A}} (x) = 0$ indicating $x$ don’t belong to the set, here, $a$ and $c$ are respectively called the lower and upper boundaries of the support, while $b$ represents the median value.^22,23

(3) Linguistic Variables

Figure 3.

Triangular fuzzy number.

When evaluating assessment indicators, it is difficult to provide precise descriptions, typically, linguistic variables or interval numbers are employed to characterize evaluation results. Therefore, when analyzing evaluation indicators, it is necessary to construct corresponding linguistic term sets.^24,25 Let the term set be denoted as $S^{l} = {s_{i} | i = 0, 1, 2, \dots, l}$ , where $l$ represents the number of terms in the set. This set must satisfy the following characteristics:

Ordering: $s_{a} > s_{β}$ , when $a > β$ ;

Maximum property: $\max (s_{a}, s_{β}) = s_{a}$ , when $s_{a} > s_{β}$ ;

Minimum property: $\min (s_{a}, s_{β}) = s_{a}$ , when $s_{a} < s_{β}$ ;

Negation operation: $Neg (s_{a}) = s_{β}$ , where $a + β = l$ .

$S^{l}$ is called a linguistic term set, where $l$ represents the granularity of the term set, indicating the number of terms at different levels, the fuzzy linguistic variables for evaluating quality infrastructure capability indicators are shown in Table 2. Referring to the 9-scale method of the Analytic Hierarchy Process (AHP), the evaluation grades are divided into nine levels. In order to facilitate calculation, the evaluation values are mapped to the range of 0–10, and are expressed with 1.2 as the scale interval.

Table 2.

Triangular fuzzy linguistic variables for evaluation indicators.

Evaluation level	Fuzzy linguistic term set for evaluation indicators		Triangular fuzzy number
Evaluation level	Industry level	Quality assurance level of supporting equipment	Triangular fuzzy number
9	Very high	Fully Compliant: Fully supports high-quality equipment development	(8.4,10.0,10.0)
8	High	Highly Compliant: Highly supports high-quality equipment development	(7.2,8.4,9.6)
7	Relatively high	Compliant: Supports high-quality equipment development well	(6.0,7.2,8.4)
6	Medium high	Compliant: Supports high-quality equipment development	(4.8,6.0,7.2)
5	Medium	Partially Compliant: Partially supports high-quality equipment development	(3.6,4.8,6.0)
4	Medium low	Partially Non-Compliant: Partially does not support high-quality equipment development	(2.4,3.6,4.8)
3	Low	Non-Compliant: Does not support high-quality equipment development	(1.2,2.4,3.6)
2	Very low	Highly Non-Compliant: Highly does not support high-quality equipment development	(0.0,1.2,2.4)
1	Extremely low	Extremely Non-Compliant: Completely does not support high-quality equipment development	(0.0,0.0,1.2)

After determining the correspondence between the linguistic term set and triangular fuzzy numbers, T experienced experts are invited to evaluate the indicators. The selected experts should have more than 10 years of theoretical foundation and rich practical experience related to quality infrastructure, and be able to transform fuzzy and complex evaluation problems into quantifiable indicators, as well as identify key influencing factors. Let the evaluation information provided by the k-th expert be denoted as equation (4):

\begin{matrix} E M^{k} = [\begin{matrix} x_{11}^{k} & x_{12}^{k} & \dots & x_{1 n}^{k} \\ x_{21}^{k} & x_{22}^{k} & \dots & x_{2 n}^{k} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ x_{m 1}^{k} & x_{m 2}^{k} & \dots & x_{mn}^{k} \end{matrix}], k = 1, 2, \dots, T (4) \end{matrix}

(4)

Where, $m$ represents the number of evaluation indicators, $n$ denotes the number of rating levels (here, $n = 3$ ), $x_{ij}^{k}$ is the rating value assigned by the $k -$ “th” expert for quality influence factor $i$ under evaluation indicator $j$ , is the scoring matrix of quality influence factors provided by the $k - th$ expert.

Convert each expert’s evaluation information into a triangular fuzzy number matrix according to Table 2, then aggregate the evaluations from all experts to obtain the comprehensive evaluation index $x_{ij}$ for factor $i$ on dimension $j$ , as equation (5):

\begin{matrix} x_{ij} = (\frac{1}{T} \sum_{k = 1}^{T} a_{ij}^{k}, \frac{1}{T} \sum_{k = 1}^{T} b_{ij}^{k}, \frac{1}{T} \sum_{k = 1}^{T} c_{ij}^{k}), \\ i = 1, 2, \dots, m, j = 1, 2, 3 \end{matrix}

(5)

Where, $a_{ij}^{k}, b_{ij}^{k}, c_{ij}^{k}$ is the triangular fuzzy number corresponding to $x_{ij}^{k}$ .

During the implementation of indicator evaluation, for objective evaluation data, in order to ensure the accuracy of the evaluation results, relevant business data from the equipment manufacturing industry are collected, including annual reports, quality manuals, capability lists, and other supporting materials, and the statistical analysis requirements for different indicators are clearly specified. Meanwhile, since the indicators differ in dimensions and orders of magnitude, they cannot be directly compared or aggregated through weighted summation. To maintain consistency with the expert evaluation results, the extreme value method is adopted to map the indicator values into a dimensionless interval of [0, 10], where the industry benchmark value is taken as the maximum value and the minimum requirement is taken as the minimum value.

For subjective evaluation indicators, an expert team for quality infrastructure capability evaluation is established. Experts with extensive experience in quality infrastructure management are invited to conduct quantitative assessments of the capability level of each evaluation indicator, based on the constructed fuzzy linguistic evaluation dataset and the corresponding fuzzy numbers.

VIKOR-based evaluation indicator weight calculation

By comprehensively considering the overall impact of the evaluation indicators on equipment operational effectiveness, mission reliability, and equipment quality level (including product physical quality, organizational quality, and process assurance quality), the greater the degree of influence, the larger the weight value of the evaluation indicator. Accordingly, a VIKOR-based method for calculating the weights of evaluation indicators is proposed.

(1) Basic Theory

The VIKOR method is a multi-attribute decision-making algorithm based on the ideal point method. It assumes that multiple attributes of a thing are conflicting and different, making it difficult or impossible to achieve an optimal result satisfying all attributes simultaneously in practical calculations.^26,27 The VIKOR method finds a suboptimal solution closest to the ideal solution by comprehensively considering both maximizing group utility and minimizing individual regret, thereby obtaining a compromise ranking for multi-attribute decision-making that makes the ranking results more scientific and accurate.²⁸ For fuzzy number-based compromise programming, the weighted metric the weighted metric $Lp$ is defined as equation (6):

\begin{matrix} L_{p, i} = {\sum_{j = 1}^{n} {(ω_{j} \frac{X_{j}^{*} - x_{ij}}{X_{j}^{*} - X_{j}^{-}})}^{p}}^{\frac{1}{p}}, 1 \leq p \leq \infty, i = 1, 2, \dots m \end{matrix}

(6)

Where, $X_{j}^{*}$ and $X_{j}^{-}$ are the ideal solution and negative-ideal solution for the $j - th$ attribute respectively, $ω_{j}$ is the weight of the $j - th$ attribute, $n$ is the number of attributes, $m$ is the number of decision alternatives, $p$ is the weight for the maximum deviation of intermediate attributes from the ideal solution.²⁹

$L_{1, i}$ (group utility) and $L_{\infty, i}$ (individual regret) are used as ranking measures, ranking based on $L_{1, i}$ maximizes group utility, while ranking based on $L_{\infty, i}$ minimizes individual regret.

(2) Weight Calculation Process

The process for calculating evaluation indicator weights is as follows:

1) Determine the ideal solution and negative-ideal solution for the weight influencing factors.

Calculate the ideal solution $X_{j}^{*}$ and negative-ideal solution $X_{j}^{-}$ for the triangular fuzzy numbers of each evaluation indicator based on the three impact dimensions (physical quality, organizational quality, process quality assurance)³⁰ as equation (7):

\begin{matrix} X_{j}^{*} = \max_{1 \leq i \leq m} x_{ij}, X_{j}^{-} = \min_{1 \leq i \leq m} x_{ij} \end{matrix}

(7)

Here, $X_{1}^{*}, X_{2}^{*}, X_{3}^{*}$ corresponds to the triangular fuzzy number representing the factor with the highest impact degree on the respective quality dimension (physical, organizational, process). $X_{1}^{-}, X_{2}^{-}, X_{3}^{-}$ corresponds to the factor with the lowest impact degree.

2) Calculate Group Utility Maximization Ranking and Individual Regret Minimization Ranking

The proximity to the ideal solution is measured by calculating the distance between the analysis results of the weight influencing factors and the ideal solution. A smaller value indicates closer proximity to the ideal solution, meaning the corresponding factor has a greater influence on the weight. Thus, based on Lp, calculate the group utility maximization ranking $L_{1, i}$ and individual regret minimization ranking $L_{\infty, i}$ for each influencing factor i. The calculation formulas for the rankings are as equation (8):

\begin{matrix} L_{1, i} = \sum_{j = 1}^{3} ω_{j} [\frac{X_{j}^{*} - x_{ij}}{X_{j}^{*} - X_{j}^{-}}], i = 1, 2, \dots m \\ L_{\infty, i} = \max_{j = 1, 2, 3} ω_{j} [\frac{X_{j}^{*} - x_{ij}}{X_{j}^{*} - X_{j}^{-}}], i = 1, 2, \dots m \\ \sum_{j} ω_{j} = 1, ω_{j} \geq 0 \end{matrix}

(8)

Where $ω_{j}$ are the weights for each impact dimensions, generally obtained based on the importance of each dimension and expert experience.

3) Calculate the Compromise Ranking for the Quality Influencing Factors as equation (9):

\begin{matrix} Q_{i} = v [\frac{L_{1}^{*} - L_{1, i}}{L_{1}^{*} - L_{1}^{-}}] + (1 - v) [\frac{L_{\infty}^{*} - L_{\infty, i}}{L_{\infty}^{*} - L_{\infty}^{-}}], i = 1, 2, \dots m \\ L_{1}^{*} = \max_{1 \leq i \leq m} L_{1, i}, L_{1}^{-} = \min_{1 \leq i \leq m} L_{1, i} \\ L_{\infty}^{*} = \max_{1 \leq i \leq m} L_{\infty, i}, L_{\infty}^{-} = \min_{1 \leq i \leq m} L_{\infty, i} \end{matrix}

(9)

Where, $v$ is the weight for the strategy of maximum group utility, when $v > 0.5$ , it emphasizes maximum group utility; when $v = 0.5$ , it represents a balanced approach; when $v < 0.5$ , it emphasizes minimizing individual regret.³¹

In order to defuzzify the calculated, Let $Q_{i} = (a_{i}, b_{i}, c_{i}), i = 1, 2, \dots, m$ , then the importance value for influencing factor $i$ is calculated as equation (10):

\begin{matrix} {\tilde{Q}}_{i} = \frac{a_{i} + 2 b_{i} + c_{i}}{4} \end{matrix}

(10)

A smaller value of x indicates closer proximity to the ideal solution, meaning the influencing factor $i$ has a greater impact on the weight.

4) Calculate Evaluation Indicator Weights

The importance of evaluation indicators is determined by sorting ${\tilde{Q}}_{i}$ , ${\tilde{L}}_{1, i}$ and ${\tilde{L}}_{\infty, i}$ in ascending order: ${\tilde{Q}}_{(1)} \leq {\tilde{Q}}_{(2)} \leq \dots \leq {\tilde{Q}}_{(m)}$ , ${\tilde{L}}_{1, (1)} \leq {\tilde{L}}_{1, (2)} \leq \dots \leq {\tilde{L}}_{1, (m)}$ , ${\tilde{L}}_{\infty, (1)} \leq {\tilde{L}}_{\infty, (2)} \leq \dots \leq {\tilde{L}}_{\infty, (m)}$ , the weight values of the indicators are then calculated based on their determined importance ranking.³²

Step 1: Identify the indicators with the most significant influence on weights based on the following two criteria:

Criterion 1: Acceptable Advantage, whose evaluation method is shown in equation (11).

\begin{matrix} {\tilde{Q}}_{(2)} - {\tilde{Q}}_{(1)} \geq \frac{1}{(m - 1)} \end{matrix}

(11)

Where, ${\tilde{Q}}_{(1)}$ and ${\tilde{Q}}_{(2)}$ are the first and second smallest values in the sorted ${\tilde{Q}}_{i}$ sequence, respectively, m is the total number of evaluation indicators.

Condition 2 (Acceptable stability in decision making): The factor corresponding to ${\tilde{Q}}_{(1)}$ must also be the best ranked by ${\tilde{L}}_{1, (1)}$ or ${\tilde{L}}_{\infty, (1)}$ .

If both conditions are satisfied, the factor corresponding to ${\tilde{Q}}_{(1)}$ is the most important, ranked 1, if one condition fails, compromise solutions are considered, if Condition 2 fails, both factors corresponding to ${\tilde{Q}}_{(1)}$ and ${\tilde{Q}}_{(2)}$ are ranked 1, if Condition 1 fails, find $m'$ using, as equation (12):

\begin{matrix} m' = \max_{i = 1, 2, \dots, m} {i | {\tilde{Q}}_{(i)} - {\tilde{Q}}_{(1)} \geq \frac{1}{(m - 1)}} \end{matrix}

(12)

The factors corresponding to ${\tilde{Q}}_{(1)}, {\tilde{Q}}_{(2)}, \dots, {\tilde{Q}}_{(m')}$ are all considered the most important and ranked 1.

Step 2: Remove the most important factor(s) identified in Step 1 from the set, sort the remaining factors in ascending order according to the values of ${\tilde{Q}}_{i}$ , ${\tilde{L}}_{1, i}$ , and ${\tilde{L}}_{\infty, i}$ , repeat the conditions in Step 1 to select the best or compromise solution ranked 1 at this stage, the corresponding factor is the next most important, ranked 2.

Step 3: Calculate the weight values of the evaluation indicators by sequentially determining the importance of each indicator and computing their respective contribution degrees, where the contribution rate value of the sorted influencing factors to quality impact is defined as equation (13)

\begin{matrix} R_{(i)} = \frac{\frac{1}{{\tilde{Q}}_{(i)}^{2}}}{\sum_{i} \frac{1}{{\tilde{Q}}_{(i)}^{2}}} \end{matrix}

(13)

Representing the degree of influence each evaluation indicator has on the comprehensive assessment, thereby serving as the weight value for each respective evaluation indicator.

Comprehensive evaluation of quality infrastructure capability

To conduct a comprehensive evaluation of quality infrastructure capability in the equipment manufacturing industry and enable comparative analysis of results, the comprehensive capability index (QI Index) is calculated based on the constructed evaluation hierarchy and the weights of each indicator.³³ The formula is as equation (14):

\begin{matrix} {QI}_{M} = \sum_{j = 1}^{m} R_{(j)} [\sum_{i = 1}^{m} R_{(i, j)} p_{(i, j)}] \end{matrix}

(14)

Where, ${QI}_{(M)}$ is the comprehensive quality infrastructure capability index for enterprise M; $p_{(i, j)}$ is the score of the $i - th$ indicator at the $j - th$ level, $R_{(i, j)}$ is the weight of that indicator within its parent group, $R_{(j)}$ is the weight of the parent group.

Based on the calculated comprehensive capability index, we can not only conduct comparative analysis on the quality infrastructure capability levels of different enterprises, but also evaluate the quality infrastructure capability construction levels of the same enterprise at different times. This helps understand the enterprise’s quality infrastructure capability building level and provides a decision-making basis for subsequent continuous improvement.^34,35

This section proposes a fuzzy theory and VIKOR-based evaluation methodology to quantify indicators and calculate the overall capability index. The following section applies the proposed method to an aviation equipment manufacturing case study for validation.

Case study

This paper selected an aviation equipment manufacturing enterprise for a pilot application, which undertakes the R&D and production of various types of aviation equipment. In terms of quality infrastructure capability building, it has continuously strengthened the construction of the industry’s technical foundation through investments in upgrading its quality management system, intelligent manufacturing transformation, industrial chain collaboration optimization, and talent cultivation, playing a significant role in technological research, service, and supervision for high-quality aviation equipment development.

Evaluation data collection and processing

Following the constructed comprehensive quality infrastructure capability evaluation indicator system, evaluation data was collected for the period 2020–2024. For subjective indicators, to reduce the subjectivity of evaluation data, 3 experienced industry experts were invited to determine evaluation grades based on the enterprise’s quality infrastructure capability construction status and its support for aviation equipment development. These grades were then converted into quantitative evaluation data.

The evaluation data for each indicator of the aviation manufacturing enterprise from 2020 to 2024 is shown in Table 3.

Table 3.

Evaluation data of quality infrastructure capability indicators for an aviation manufacturing enterprise (2020–2024).

First-level indicator	Second-level indicator	Third-level indicator	Evaluate the fusion results
First-level indicator	Second-level indicator	Third-level indicator	2020	2021	2022	2023	2024
Industry influence	Scope of influence	External influence	5.2	5.6	5.6	5.6	7.2
	Scope of influence	Internal Influence	6.4	6.8	6.8	7.2	7.6
	System construction	Capability of Professional Technical Institutions	5.6	5.2	6.4	6.4	6.4
System construction	Regulations	Regulation construction	6	6.4	7.2	7.2	8
	Regulations	Quality policy environment	5.6	6.8	6	7.2	7.6
	Supervision	Technical supervision system construction	5.6	4.4	5.2	6.4	6.4
	Supervision	Technical supervision system development	5.2	6.8	6.4	6.4	7.2
Resource supply	Data platform resources	Shared platform construction	4	4.4	4.4	5.6	7.6
	Data platform resources	Professional platform construction	5.2	5.2	5.6	5.6	5.6
	Standard resources	Leading formulation	6.4	6.4	6.8	7.6	8
	Metrology resources	Metrology specifications/standards	6	6.8	6.4	7.2	7.6
	Metrology resources	Metrology Laboratories	6	6.4	6.8	6.4	7.6
	Certification/accreditation resources	certification/accreditation qualification capability	3.6	4	3.6	6	5.6
	Inspection/testing resources	inspection/testing capability	4.4	4.8	5.6	6	6.4
	Human resources	personnel engaged in QI construction	6.4	6.8	7.2	7.2	8
	Funding resources	R&D/technical renovation funding	5.6	7.2	6.4	6.8	7.6
Equipment quality assurance	Standardized equipment quality assurance	Equipment product standardization work	6.8	6.8	6.8	6.8	7.6
	Metrology equipment quality assurance	Equipment metrology work	4.4	5.6	6.4	6.4	6.4
	General quality characteristics	Equipment general quality characteristics work	6.4	6	7.6	7.6	8
	Equipment quality assurance personnel	Personnel engaged in standardization, metrology, and GQC	6	6	5.6	6.4	7.2

Calculation of comprehensive evaluation indicator weights

Considering the impact degree of each quality infrastructure capability evaluation indicator on enterprise organizational quality, process assurance quality, and equipment physical quality, the weights of each indicator were calculated using the VIKOR-based method proposed in this paper.

First, the ideal solution ( $X_{j = 1}^{*}$ ) and negative-ideal solution ( $X_{j = 1}^{-}$ ) were determined based on the three impact dimensions: organizational quality, process assurance quality, and equipment physical quality, as shown in Table 4.

Table 4.

The ideal solution and negative-ideal solution.

	Enterprise organizational quality		Process assurance quality		Equipment physical quality
Evaluation indicator	Ideal solution	Negative-ideal solution	Ideal solution	Negative-ideal solution	Ideal solution	Negative-ideal solution
Results	(8.4,10,10)	(0,0,1.2)	(8.4,10,10)	(2.4,3.6,4.8)	(8.4,10,10)	(2.4,3.6,4.8)

Then, the group utility maximization ranking and individual regret minimization ranking for each indicator were calculated, the compromise ranking was solved under the principle of balancing approval and rejection ( $v = 0.5$ ), as shown in Table 5. In the table, P represents the calculation result of the group utility maximization ranking; R represents the calculation result of the individual regret minimization ranking; and Q represents the calculation result of the compromise ranking.

Table 5.

Ranking based on P, R, and Q.

First-level indicator	Second-level indicator	Third-level indicator	P	Ranking	R	Ranking	Q	ranking
Industry influence	Scope of influence	External influence	1.525	9	0.961	4	0.631	12
	Scope of influence	Internal Influence	1.272	15	0.591	15	1.288	4
	System construction	Capability of Professional Technical Institutions	1.459	12	0.756	12	0.927	10
System construction	Regulations	Regulation construction	0.757	18	0.386	19	1.851	2
	Regulations	Quality policy environment	1.287	14	0.795	10	0.961	9
	Supervision	Technical supervision system construction	0.488	19	0.361	19	1.999	1
	Supervision	Technical supervision system development	1.272	15	0.591	15	1.288	4
Resource supply	Data platform resources	Shared platform construction	2.650	1	0.961	4	0.062	19
	Data platform resources	Professional platform construction	2.536	2	1.000	1	0.050	20
	Standard resources	Leading formulation	1.388	13	0.646	14	1.128	8
	Metrology resources	Metrology specifications/standards	1.808	8	0.906	6	0.513	13
	Metrology resources	Metrology Laboratories	2.051	4	0.906	6	0.411	16
	Certification/accreditation resources	certification/accreditation qualification capability	2.256	3	1.000	1	0.177	18
	Inspection/testing resources	inspection/testing capability	0.951	16	0.776	11	1.131	7
	Human resources	personnel engaged in QI construction	0.943	17	0.551	17	1.474	3
	Funding resources	R&D/technical renovation funding	1.460	11	0.551	17	1.246	6
Equipment quality assurance	Standardized equipment quality assurance	Equipment product standardization work	1.879	6	0.906	6	0.490	14
	Metrology equipment quality assurance	Equipment metrology work	1.879	6	0.906	6	0.490	14
	General quality characteristics	Equipment general quality characteristics work	1.906	5	1.000	1	0.338	17
	Equipment quality assurance personnel	Personnel engaged in standardization, metrology, and GQC	1.588	10	0.756	12	0.866	11

Finally, determine the importance of each evaluation indicator sequentially and calculate their contribution degrees, which are assigned as the weight values for the respective indicators, the results are shown in Table 6.

Table 6.

Calculation of evaluation indicator weights.

First-level indicator	Weights	Second-level indicator	Weights	Third-level indicator	Weights
Industry influence	0.164	Scope of influence	0.111	External influence	0.036
		Scope of influence	0.111	Internal Influence	0.074
		System construction	0.053	Capability of Professional Technical Institutions	0.053
System construction	0.352	Regulations	0.162	Regulation construction	0.107
		Regulations	0.162	Quality policy environment	0.055
		Supervision	0.190	Technical supervision system construction	0.115
		Supervision	0.190	Technical supervision system development	0.074
Resource supply	0.357	Data platform resources	0.006	Shared platform construction	0.004
		Data platform resources	0.006	Professional platform construction	0.003
		Standard resources	0.065	Leading formulation	0.065
		Metrology resources	0.053	Metrology specifications/standards	0.030
		Metrology resources	0.053	Metrology Laboratories	0.024
		Certification/accreditation resources	0.010	certification/accreditation qualification capability	0.010
		Inspection/testing resources	0.065	inspection/testing capability	0.065
		Human resources	0.085	personnel engaged in QI construction	0.085
		Funding resources	0.072	R&D/technical renovation funding	0.072
Equipment quality assurance	0.126	Standardized equipment quality assurance	0.028	Equipment product standardization work	0.028
		Metrology equipment quality assurance	0.028	Equipment metrology work	0.028
		General quality characteristics	0.020	Equipment general quality characteristics work	0.020
		Equipment quality assurance personnel	0.050	Personnel engaged in standardization, metrology, and GQC	0.050

The Figure 4 shows that the trend of the weights calculated by this paper’s method aligns with that calculated by the traditional averaging method, indicating that the proposed method effectively characterizes the relative magnitude of each indicator. Furthermore, since the calculation method considers the comprehensive results of factors influencing the importance of different indicators, the evaluation results show greater differentiation compared to the traditional averaging method, better reflecting the importance of each indicator.

Figure 4.

Overall framework of quality infrastructure for the equipment manufacturing industry.

Analysis of comprehensive evaluation results

Based on the evaluation results of each indicator and their weights, the comprehensive quality infrastructure capability evaluation index for the aviation enterprise from 2020 to 2024 was calculated, as shown in Table 7.

Table 7.

Comprehensive evaluation index of quality infrastructure capability for an aviation manufacturing enterprise (2020–2024).

First-level indicator	2020	2021	2022	2023	2024
Industry influence	0.97	0.99	1.05	1.08	1.17
System construction	1.98	2.07	2.18	2.38	2.55
Resource supply	2.04	2.25	2.30	2.45	2.67
Equipment quality assurance	0.74	0.77	0.80	0.84	0.91
Quality infrastructure capability	5.73	6.08	6.33	6.76	7.31

The trend of the enterprise’s comprehensive quality infrastructure capability index is shown in the Figure 5 below. Since 2020, the index has gradually increased, reflecting the steady improvement in the enterprise’s quality infrastructure capability level and the continuous enhancement of equipment quality assurance capability. Furthermore, with the promotion and application of new technologies and methods, the quality infrastructure capability has grown even faster.

Figure 5.

Overall framework of quality infrastructure for the equipment manufacturing industry.

From the perspective of first-level evaluation dimensions, the industry influence, system construction level, resource supply capability, and equipment quality assurance capability all showed gradual improvement, the resource supply capability and system construction level increased more significantly and at a faster rate, reflecting the enterprise’s high emphasis on system construction. Additionally, as depicted in Figure 6, since 2023, the quality infrastructure index of the enterprise has grown faster, reflecting a higher emphasis on the level of quality infrastructure capability building. Moving forward, efforts should be intensified to bolster influence and improve equipment quality assurance capabilities.

Figure 6.

Overall framework of quality infrastructure for the equipment manufacturing industry.

The case study results demonstrate that the proposed method can effectively reflect the capability level and development trend of quality infrastructure. The final section summarizes the conclusions and discusses future research directions.

Conclusion

This paper addressed the current problems of incomplete elements and insufficient integration in the equipment manufacturing industry’s quality infrastructure construction. It focused on enterprise requirements for quality infrastructure construction, clarified the constituent elements of the industry’s quality infrastructure, and constructed a capability building model based on the dimensions of “regulatory system–management system–technical system.” To enable comparative analysis of quality infrastructure capability levels among equipment manufacturing enterprises and solve problems like missing evaluation indicators and strong subjectivity, an evaluation model and indicator system for quality infrastructure capacity in the equipment manufacturing industry are constructed from four dimensions: industry influence, system construction, resource supply, and equipment quality assurance, and a comprehensive evaluation method based on fuzzy theory and the VIKOR was proposed, it has advantages over traditional methods in quantifying objectivity and accuracy. Validation was conducted through a case study of an aviation equipment manufacturer, where analysis of quality infrastructure development data from 2020 to 2025 calculated the enterprise’’s composite capability index, quantitatively assessed its evolution, revealed 5-year development trends, drove continuous improvement initiatives, and confirmed the methodology’s effectiveness.

In the context of intelligent manufacturing, the evaluation of quality infrastructure capability should evolve from a static measurement of resource supply toward a dynamic, system-level assessment of intelligent operational support capacity. Future research should incorporate industrial Internet security evaluation mechanisms,³⁶ function–performance coupling analysis,³⁷ digital twin integration,³⁸ and “soft quality infrastructure” elements such as adaptive scheduling³⁹ and intelligent small-shift detection into the framework, thereby enhancing cyber-security resilience, real-time monitoring sensitivity,⁴⁰ and decision-support capability. At the methodological level, greater attention should be given to the interrelationships among evaluation indicators, as highly correlated indicators may result in repeated calculations and implicit weight amplification. Therefore, correlation identification methods such as Pearson correlation analysis and causal modeling should be introduced to detect redundancy, merge or eliminate strongly correlated indicators, and improve the robustness and accuracy of the evaluation system, ultimately promoting a more integrated, dynamic, and intelligent quality infrastructure assessment model.

Footnotes

Handling Editor: Aarthy Esakkiappan

ORCID iD

Jinglu Wei

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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