Analysis and Optimization of the Effectiveness of Production Safety Standardization Construction Based on Set-Pair Analysis

Abstract

The industry and trade sector is a crucial part of China’s national economy, yet its development is frequently accompanied by numerous safety incidents, leading to significant casualties and property damage. To enhance safety practices, the Chinese government introduced standardized production safety assessment criteria. Despite improvements in overall safety management in recent years, the implementation process often emphasizes scoring over substance, causing enterprises to overlook key elements directly related to production safety. Additionally, the current assessment system, which ranks enterprises based solely on scores, fails to accurately reflect their true safety management levels. To overcome the limitations of the current evaluation results of standardized work safety construction and to establish a method for scientifically assessing the safety management level and predicting the future safety development trends of enterprises, this study employs the principles of similarity and contrast, utilizing Set-Pair Analysis (SPA) as a quantitative tool. By targeting thirteen critical elements of the safety standardization framework, a five-element linkage function model was constructed. This model calculates linkage degree, set-pair potential, pessimistic potential, optimistic potential, and difference degree to evaluate safety standardization efforts across enterprises within and between industries. The study’s findings indicate that the five-dimensional linkage model based on SPA is both reasonable and reliable. A positive correlation was observed between the weights of evaluation elements and the optimistic potential values of enterprises, particularly with key elements such as Elements Seven and Eight, which are critical in determining an enterprise’s actual safety capabilities. Enhancing these elements can significantly improve intrinsic safety levels. Additionally, the model’s calculated metrics allow for precise and quantitative ranking of enterprises’ true safety management levels. Moreover, the model provides an accurate quantitative assessment of the true safety management hierarchy, offering practical and adaptable applications in other sectors.

1. Introduction

China’s production safety standardization can be traced back to the late 1980s, with the introduction of the ISO9001 [1] series of international quality standard systems and total quality management in the domestic enterprises. In 2003, China’s national coal mine safety and quality standardization work conference was held, and the concept of safety and quality standardization was first put forward in China. Since then, China has formed a production safety standardization system with Chinese characteristics while learning from the advanced experience of foreign standards and has successively issued a series of relevant laws, regulations, and standards to continuously refine the requirements for production safety standardization [2].

At present, China is in the key period of the development of economic focus on the real economy; the important foundation of the real economy is the manufacturing industry, the main body of the manufacturing industry is the industry and trade industry enterprises, and the important development of the industry and trade industry enterprises is the basis of production safety [3]. In recent years, the number of enterprises in the industry and trade industry has continued to grow, and a lack of attention and investment in production safety management has resulted in frequent production safety accidents [4]. According to China’s National Bureau of Statistics, in 2023, there were 1.224 deaths related to production safety accidents for every 100,000 people employed by enterprises in the industry, mining, and trade sectors. For the time being, the production safety situation in China’s industry and trade sector remains severe, with a great impact on social stability and national economic development [5].

The industry and trade sector in China comprises eight major industries: metallurgy, non-ferrous metals, building materials, machinery, light industry, textiles, tobacco, and commerce. According to the National Bureau of Statistics, small- and medium-sized industrial enterprises account for over 90% of all industrial enterprises in the country. To effectively regulate work safety, the government has continuously issued laws, regulations, and standards to refine safety standardization requirements. Infractions of safety standards and procedures are frequently highlighted as a causal element that leads to accidents and other expected outcomes [6]. The industrial and commercial sectors must accelerate the implementation of production safety standardization to improve the national production safety management capacity [4]. The purpose of China’s production safety standardization construction is to regulate enterprise production safety management, improve enterprise production safety conditions, raise the level of enterprise production safety, improve enterprise production safety performance, implement the main responsibility of enterprise production safety, establish a long-term mechanism for enterprise production safety, and play a vital role in effectively preventing all kinds of accidents.

Production safety standardization refers to an enterprise assuming primary responsibility for production safety by involving all staff in the entire process. This includes establishing and maintaining a comprehensive production safety management system that controls safety and occupational health across all aspects of production and operations. It covers quality of personnel, improvements to the operating environment, equipment and facilities upgrades, and technological transformations, with an emphasis on scientific, standardized, innovative, systematic, and continuous improvement [7,8]. The construction process is divided into ten stages, starting from the planning and preparation phase, where a leadership team is established, and extending through the entire lifecycle of standard construction and operation. These stages include setting construction objectives, conducting standardization training, mapping and inspection, rectification and validation, self-assessment, external evaluation, continuous improvement, and re-assessment upon expiry.

At present, in the small- and medium-sized industrial and trade enterprises in the construction and operation of production safety standardization, there is the phenomenon of the assessment of the merits and demerits of only the scores, resulting in the neglect of important elements affecting the actual production safety of enterprises. At the same time, due to the industrial and trade industry safety production standardization assessment results by the assessment scores for the grade division. This approach makes it difficult for enterprises of the same level to effectively assess their safety management strengths and weaknesses and to predict future safety trends. There is very little research in the field of production safety standardization in China, and almost no detailed study of the construction of production safety standardization in Chinese industrial and trade enterprises has been retrieved.

The current reliance on score-based evaluations fails to accurately reflect the true safety management levels of these enterprises. To address this issue and to develop a method for scientifically predicting future safety development trends, this study will undertake comprehensive research and data collection. The research will examine both safety standardization construction and actual safety management practices within small- and medium-sized industrial and trade enterprises, ensuring that the sample selection process is scientifically rigorous and that the study’s findings are broadly applicable and generalizable. This study employs the concept of similarity and contrast, utilizing Set-Pair Analysis (SPA) to develop a five-element linkage model; the SPA can be employed in the quantification of the severity of the safety production standardization results [9]. By integrating SPA with the operational aspects of safety standardization in industrial and commercial enterprises, the study conducts qualitative and quantitative analyses of the safety production standardization results. The results demonstrate that the five-element linkage model based on Set-Pair Analysis is both robust and reliable. A positive correlation was found between the weight of safety standard evaluation elements in the industry and trade sector and the optimistic potential of the enterprises. High-weighted elements are critical determinants of an enterprise’s actual safety capabilities and production performance, with improvements in these areas significantly enhancing the enterprise’s intrinsic safety. Furthermore, the index calculations from the five-element linkage function model provide a quantitative framework for assessing the effectiveness of the safety standardization efforts and ranking safety management levels. Therefore, it is essential to study the improvement and enhancement of safety production standardization construction and evaluation using the Set-Pair Analysis method. This approach not only fills the gaps in current research on safety production standardization and evaluation but also provides targeted guidance to enterprises by scientifically predicting the impact of safety standardization improvement projects on their future safety management capabilities. As a result, it enables enterprises to continuously strengthen and elevate their safety management capabilities and overall safety performance.

2. Research Subjects and Methods

2.1. Selection of Research Subjects

According to the latest data from China’s National Bureau of Statistics, the industries with the largest number of legal entities in China’s industry and trade sector are machinery manufacturing, light industry, building materials, and textiles. In China, obtaining a Level 3 certification in work safety standardization is sufficient to meet the requirements of most small- and medium-sized enterprises, making this the primary target for most companies in their safety standardization efforts. Therefore, this study focuses on the on-site research and data collection of work safety standardization among small- and medium-sized enterprises in the industrial and trade sectors. More than 20 enterprises were surveyed, and 15 typical companies were selected as the primary data sources for this study.

To effectively conduct a comparative study between enterprises within the same industry and across different industries, five companies from the machinery manufacturing sector—representing the largest proportion of enterprises in the industrial and trade sector—were selected. Additionally, 10 companies from various other industries, including musical instrument manufacturing, measurement and control, concrete mixing, pharmaceutical, biotechnology, vacuum engineering, electrical machinery, and textiles, were chosen. This selection ensured a balanced representation of the different industries within the industrial and trade sectors, thereby enhancing the accuracy and credibility of the study’s findings. The study will compile the safety standardization evaluation reports of these 15 selected enterprises, and both qualitative and quantitative analyses will be conducted based on the scoring results and specific demerit points across each evaluation element.

2.2. Set-Pair Analysis (SPA) Theory

The Set-Pair Analysis (SPA) theory, first proposed by Zhao [10], is now widely used in security assessments as a systematic method for quantifying both deterministic and uncertain problems [11,12]. SPA analyzes the common (same), differing (different), and opposing (opposite) characteristics of two sets under a given precondition. This method metrically inscribes these characteristics and calculates the degree of same–different–opposite linkage. It can also be extended to situations involving more than two sets, allowing for new, in-depth research that evaluates objectively existing uncertainties [13]. The degree of linkage is expressed by the following equation:

$$\mu ={\displaystyle \frac{S}{N}}+{\displaystyle \frac{F}{N}}i+{\displaystyle \frac{P}{N}}j$$

(1)

where

• μ is the degree of association;
• N is the total number of features in the two sets;
• S is the number of common features in the two sets;
• P is the number of similar features in the two sets;
• F is the number of opposing features in the two sets;
• i is the coefficient of the degree of dissimilarity, ranging from −1 to 1;
• j is the coefficient of opposition, with a constant value of −1.

For Equation (1), ${\displaystyle \frac{S}{N}}$ is called the degree of congruence, ${\displaystyle \frac{F}{N}}i$ is called the degree of difference, ${\displaystyle \frac{P}{N}}j$ is called the degree of opposition, and a, b and c are their respective linkage components [14]. Therefore, Equation (1) can be simplified to Equation (2).

$$\mu =a+bi+cj$$

(2)

In practical use, scenarios often involve more than one set. The ternary linkage function of Equation (2) may not adequately address the complexity of such situations. Therefore, to accommodate this complexity, the linkage degree is expanded to different levels, resulting in Equation (3), which represents a multivariate linkage number function and can be expressed as follows:

$$\mu =a+b{i}_1+b{i}_2+\cdot \cdot \cdot b_{n-2}{i}_{n-2}+cj$$

(3)

Set-Pair Analysis (SPA) theory provides a robust framework for quantifying relationships between deterministic and uncertain variables within two or more sets. By extending the degree of same–different–opposite linkage across multiple sets, SPA allows for a comprehensive analysis of complex situations, which is crucial for accurately assessing security risks and uncertainties. This expanded model lays the foundation for more refined evaluations in subsequent sections.

2.3. Potential

2.3.1. Set-Pair Potential

In evaluating enterprise safety standards, the set-pair potential is determined by the ratio of the congruence degree aa to the contradiction degree cc when cc is non-zero. The linkage coefficient μ directly indicates the strengths and weaknesses of the enterprise’s comprehensive safety assessment results. This potential serves as a reflection of the enterprise’s actual safety status, categorized by specific levels as detailed in

Table 1. The level of each set, its corresponding potential, and each set’s order relationship.

No.	Rating	Name of the Set of Potentials	a, b1, b2, b3, c Interrelationships	Meaning
I	homogeneous potential $a>\mathrm{c}$	quasi-homogeneous potential	$b_1+b_2+b_3=0$	Homogeneous potential is completely determined.
II		strong homogeneous potential	$c>b_1+b_2+b_3$	Homogeneous potential is predominant.
III		weak homogeneous potential	$a>b_1+b_2+b_3>c$	Homogeneous potential exists but is relatively weak.
IV		slight homogeneous potential	$b_1+b_2+b_3>a$	Homogeneous potential exists but is weaker.
I	equilibrium potential $\mathrm{a}=\mathrm{c}$	slight equilibrium potential	$b_1+b_2+b_3>a$	Equilibrium potential not dominant, uncertainty trend dominant.
II		weak equilibrium potential	$a=b_1+b_2+b_3$	Uncertainty evident, equilibrium potential weaker.
III		strong equilibrium potential	$a>b_1+b_2+b_3$	Equilibrium potential dominates.
IV		quasi-equilibrium potential	$b_1+b_2+b_3=0$	Homogeneous potential and opposite potential are enemies.
I	Opposite potential $\mathrm{a}<\mathrm{c}$	quasi-opposite potential	$b_1+b_2+b_3=0$	Opposite potential completely determined.
II		strong opposite potential	$a>b_1+b_2+b_3$	Opposite potential dominates.
III		weak opposite potential	$c>b_1+b_2+b_3>a$	Opposite potential exists but is weaker.
IV		slight opposite potential	$c<b_1+b_2+b_3$	Opposite potential exists but is weaker.
uncertain homogeneous potential			$c=0, a>b_1+b_2+b_3$	Uncertainty is evident, homogeneous potential exists.
Uncertainty of uncertainty			$c=0, a\le b_1+b_2+b_3$	Uncertainty dominates.

[15].

2.3.2. Pessimistic Potential

The concept of pessimistic potential [16] adopts a perspective where all differences within the subject of study are construed as degrees of opposition. It assesses the developmental trajectory of the subject by examining the ratio of congruence to opposition degrees. For scenarios where the linkage degree is intermediate, the pessimistic potential is expressed by Formula (4).

$$SHI(B)={\displaystyle \frac{a}{b+c}}$$

(4)

Pessimistic potential provides a key metric for evaluating the possibility of adverse outcomes by focusing on opposition degrees within a given set. It serves as a critical tool for assessing scenarios where uncertainty and opposition are prominent factors, aiding in more effective risk management.

2.3.3. Optimistic Potential

Optimistic potential [17] adopts an optimistic perspective where all differences within the subject of study are interpreted as degrees of similarity. It evaluates the developmental trajectory of the subject by analyzing the ratio of similarity to opposition degrees. For scenarios where the linkage degree is intermediate, the optimistic potential is expressed by Equation (5).

$$SHI(C)={\displaystyle \frac{a+b}{c}}$$

(5)

Optimistic potential offers an effective method for highlighting the potential for positive outcomes and scientifically identifying trends in an organization’s safety management level, fostering confidence in its future development.

2.4. Construction of the Linkage Degree Equation of the Set-Pair Homogeneous Inverse Hierarchy Method

According to the “National Metallurgy and Other Industrial and Commercial Enterprises Safety Production Standardization Assessment Methods”, safety production standardization in industrial and commercial enterprises is evaluated using a scoring system, with a maximum score of 100 points. The grading criteria are as follows: Grade I is awarded for scores ≥90 points, Grade II for scores ≥75 points, and Grade III for scores ≥ 60 points.

The normalized linkage number μ ranges from −1 to 1, categorizing the degree of linkage into four domains through equal division principles. These domains correlate with the hazard levels of the evaluated objects, as detailed in

Table 2. Hazard Classification Criteria.

Rating	Secure	General Security	Hazard
degree of linkage μ	[0.33,1]	[−0.33,0.33]	[−0.33,−1]

.

According to the safety standard evaluation criteria for industry and trade, Equation (6) establishes the calculation of the five-element linkage degree for extended applications.

$$\mu =a+b_1{i}_1+b_2{i}_2+b_3{i}_3+cj$$

(6)

According to the hierarchy theory of Set-Pair Analysis, a set-pair homogeneous inverse hierarchy can be established, as illustrated in Figure 1 [18].

Based on the set-pair homogeneous inverse hierarchy, the linkage degree method [19] is derived by integrating Equation (3) with the calculation equation specified in

Table 3. Calculation equation for the linkage degree of the set-pair homogeneous inverse hierarchical method.

Linkage Degree μmk	${\mathit{q}}_{\mathit{x}}$
$1+0i_1+0i_2+0i_3+0j$	$d\ge q_0$
${\displaystyle \frac{1}{2}}{\displaystyle \frac{d-q_1}{q_0-q_1}}+{\displaystyle \frac{1}{2}}{i}_1+{\displaystyle \frac{1}{2}}{\displaystyle \frac{q_0-d}{q_0-q_1}}{i}_2+0i_3+0j$	$q_0>d\ge q_1$
$0+{\displaystyle \frac{1}{2}}{\displaystyle \frac{d-q_2}{q_1-q_2}}{i}_1+{\displaystyle \frac{1}{2}}{i}_2+{\displaystyle \frac{1}{2}}{\displaystyle \frac{q_1-d}{q_1-q_2}}{i}_3+0j$	$q_1>d\ge q_2$
$0+0i_1+{\displaystyle \frac{1}{2}}{\displaystyle \frac{d-q_3}{q_2-q_3}}{i}_2+{\displaystyle \frac{1}{2}}{i}_3+{\displaystyle \frac{1}{2}}{\displaystyle \frac{q_2-d}{q_2-q_3}}j$	$q_2>d\ge q_3$
$0+0i_1+0i_2+0i_3+j$	$d<q_3$

Where: d is the evaluation score of the security standard element of industrial and commercial enterprises; q_x is the evaluation grade line of the security standard evaluation of industrial and commercial enterprises; m represents the security standard evaluation element of the mth enterprise; k represents the kth evaluation element of the enterprise.

.

According to the evaluation criteria for safety standards in industrial and commercial enterprises, the scores of thirteen elements are converted into percentages, yielding the weight coefficients 0.02, 0.03, 0.04, 0.10, 0.05, 0.26, 0.23, 0.08, 0.06, 0.06, 0.03, 0.02, and 0.02. Considering these weights of safety standard evaluation elements, the weight linkage degree is expressed by Equation (7).

$${\mu }_m={\displaystyle {\sum }_{m=1}^s{W}_k}{\mu }_{mk}$$

(7)

where

• μ_m is the linkage degree of the mth enterprise;
• W_k is the weight of the kth security standard evaluation element;
• μ_mk is the linkage degree of the security standard evaluation element k of the mth enterprise.

The linkage degree equation provides a comprehensive framework for assessing the safety standardization of industrial and commercial enterprises. By utilizing a normalized linkage number, it becomes possible to categorize the degree of safety into distinct levels, which correlate directly with potential hazards. This approach allows for a more precise evaluation of safety management performance and offers clear guidance for future improvements.

3. SPA-Based Analysis of Safety Standard Assessments in Industrial and Trade Enterprises

3.1. Comprehensive Analysis of Standardized Production Safety Assessment Scores

In China’s national standard, “Guidelines for Standardized Construction of Production Safety in Industry and Trade”, the framework for standardized production safety in industrial and trade enterprises is divided into 13 elements. These elements encompass the entire life cycle of the enterprise’s production and operations. The elements, listed sequentially, are as follows: objectives; organizational structure and responsibilities; safety inputs; laws, regulations, and safety management; education and training; production equipment and facilities; operational safety; hazard identification and management; major hazard monitoring; occupational health; emergency response; accident reporting, investigation, and handling; and continuous improvement.

According to the aforementioned assessment report on the safety standardization of the fifteen enterprises selected as typical industries of industry and trade,

Table 4. Average scores on safety standardization assessment elements for small- and medium-sized industrial and trade enterprises.

Thirteen Elements of Work Safety Standardization	Average Score	Thirteen Elements of Work Safety Standardization	Average Score
1. Objectives	87.67%	8. Identification and management of hidden dangers	76.55%
2. Organizational structure and responsibilities	53.33%	9. Monitoring of major sources of danger	60.48%
3. Inputs to production safety	69.19%	10. Occupational health	76.61%
4. Laws, regulations, and safety management	54.33%	11. Emergency relief	68.97%
5. Education and training	58.53%	12. Accident reporting, investigation, and handling	80.00%
6. Production equipment and facilities	59.15%	13. Continuous improvement	75.41%
7. Operational safety	62.26%	Composite score rate for each element	67.88%

presents a statistical analysis of the thirteen safety standard evaluation elements for each enterprise. The analysis reveals that, aside from a low score in the “target” element, small- and medium-sized enterprises show deficiencies in safety management. To investigate and compare the safety management levels among enterprises at the same standard level, as well as across different industries, Set-Pair Analysis (SPA) was applied. This approach aimed to analyze the safety standard results and forecast the development trends of small- and medium-sized industrial and commercial enterprises within and across industries.

3.2. SPA Analysis of Safety Standard Assessment Results of Enterprises in the Same Industry

Among the fifteen enterprises, five machinery manufacturing enterprises (numbered I to V) were selected for research. The linkage function model was applied to analyze their SPA. The percentage scores of each element of the safety standard evaluation for these five machinery manufacturing enterprises are presented in

Table 5. Analysis of the results of the assessment of the safety standardization of five machinery manufacturing enterprises.

Enterprise	Element 1	Element 2	Element 3	Element 4	Element 5	Element 6	Element 7	Element 8	Element 9	Element 10	Element 11	Element 12	Element 13	Overall Score
I	90.00	53.33	70.00	53.00	58.00	57.89	69.32	82.86	65.38	75.00	73.08	80.00	77.78	66.01
II	90.00	53.33	70.00	53.00	58.00	57.89	68.92	77.14	65.38	75.00	73.08	80.00	77.78	65.25
III	90.00	53.33	70.00	53.00	58.00	57.89	71.74	62.86	65.38	75.00	73.08	80.00	77.78	64.79
IV	55.00	36.67	52.78	65.00	54.00	64.42	65.38	71.25	28.57	73.17	42.31	80.00	60.00	61.93
V	90.00	53.33	70.00	53.00	58.00	57.89	46.53	82.86	65.38	75.00	73.08	80.00	77.78	61.33

.

Taking machinery manufacturing Enterprise I, as an example, the set-pair homogeneous anti-hierarchical method was employed to calculate the five-dimensional linkage degree equation for each evaluation element of the enterprise’s safety standard. The results of the calculation for each linkage category of the safety standard elements are presented in

Table 6. Enterprise I safety production standardization evaluation elements of the five-element linkage degree calculation.

Element	$\mathit{a}$	$\mathit{b}1$	$\mathit{b}2$	$\mathit{b}3$	$\mathit{c}$	Element	$\mathit{a}$	$\mathit{b}1$	$\mathit{b}2$	$\mathit{b}3$	$\mathit{c}$
μI11	1	0	0	0	0	μI18	0	131/500	1/2	119/500	0
μI12	0	0	0	0	1	μI19	0	0	59/329	1/2	135/421
μI13	0	0	1/3	1/2	1/6	μI10	0	0	1/2	1/2	0
μI14	0	0	0	0	1	μI11	0	0	109/250	1/2	8/125
μI15	0	0	0	0	1	μI12	0	1/6	1/2	1/3	0
μI16	0	0	0	0	1	μI13	0	24/259	1/2	200/491	0
μI17	0	0	233/750	1/2	71/375	—	—	—	—	—	—

.

According to the weight linkage calculation, Equation (7), combined with the linkage and weight of each element of the safety standard in the industrial and trade industry, the linkage function of the assessment result of the safety standard of Enterprise I is calculated by Equation (8).

$${\mu }_1={\displaystyle \frac{1}{50}}+{\displaystyle \frac{4}{153}}{i}_1+{\displaystyle \frac{29}{146}}{i}_2+{\displaystyle \frac{48}{151}}{i}_3+{\displaystyle \frac{45}{88}}j$$

(8)

Using the special values method [20], the coefficients of the degree of difference are taken as $i_1=0.5$, $i_2=0$, and $i_3=-0.5$. The degree of connectedness of Enterprise I is obtained as ${\mu }_1=-0.637$, and the results for other enterprises are shown in

Table 7. Five machinery manufacturing enterprises safety standardization assessment results for the set of analysis indicators.

Enterprise	Linkage Degree	Set-Pair Potential	Level of Set-Pairing Potential	Pessimistic Potential	Optimistic Potential
I	−0.637	0.039	weak opposition potential	0.029	0.393
II	−0.670	0.039	weak opposition potential	0.028	0.391
III	−0.692	0.038	weak opposition potential	0.028	0.399
IV	−0.621	0.000	weak opposition potential	0.000	0.373
V	−0.759	0.029	weak opposition potential	0.025	0.192

.

The size of the linkage degree is directly proportional to the quality of the comprehensive assessment results for enterprise security standardization. From the calculation results, it can be observed that the comprehensive assessment results for Enterprises I to V decrease sequentially. This is consistent with the order of comprehensive assessment results shown in Table 5, and the potential values lie between the pessimistic and optimistic potentials. This consistency verifies the reliability and reasonableness of the established five-dimensional linkage degree calculation model for analyzing the standardization results of industrial and commercial enterprises with the same enterprise safety standardization assessment.

From the set of potentials, it is evident that the selected enterprises exhibit a “weak opposite potential”. This indicates that although the enterprises have reached the third level of production safety standardization, there is a trend toward opposition. Consequently, the overall safety situation is in a “dangerous” state, and this trend is worsening. The “opposite potential” state should not be confused with pessimistic potential [21].

Optimistic potential, on the other hand, reflects the enterprise’s capability to take positive countermeasures and achieve better safety standard assessment results. A higher optimistic potential signifies a stronger trend towards improved safety standards. As shown in Table 7, Enterprise III, despite having lower linkage and safety standard assessment results compared to Enterprises I and II, has a higher optimistic potential. This indicates that Enterprise III is more likely to achieve better overall safety standard assessment results.

When analyzing the score rate of each element of the safety standard evaluation of the five machinery manufacturing enterprises in Table 5, it is observed that Enterprise III has a higher score rate in Element 7, “Operational Safety”, compared to Enterprises I and II. The score rates for the other elements are similar across these enterprises. This suggests a correlation between the high optimism of Enterprise III and its high score rate in Element 7. In the industry and trade industry safety standardization assessment Element 7, contains four secondary assessment elements: production site management and production process control, operational behaviors management, warning signs, and related party management. At the same time, there are detailed evaluation criteria for each secondary evaluation element. To explore this further, statistical analyses were conducted on the most important Element 7 items for Enterprises I to III, with the results presented in

Table 8. Seven major demerit points for safety standardization elements in machinery manufacturing enterprises.

Secondary Elements	Achievement of Standards	Company I and Company II	Company III
7.1 Production site management and production process control	Identify, assess, and grade the risks and hidden dangers that exist at the production site and in the production process and environment, and formulate appropriate control measures.	Failure to carry out risk identification of plant layout and earth moving operations; inaccurate risk assessment of storage and use of flammable and explosive chemicals.	Failure to identify the risks of spray booth equipment and facilities, confined space operations, and spray-painting operations.
	Provide emergency lighting; emergency lighting should be able to start automatically when the normal lighting is interrupted.	——	The office building is not equipped with emergency evacuation lighting signs; emergency lights cannot be fully illuminated.
	Establish a management system for “three violations”, and clarify the responsibilities, methods, records, assessment, and other matters of monitoring.	Lack of records of inspection and assessment of “three violations” behaviors.	Lack of records of inspection and assessment of “three violations” behaviors.
	Establish a safety management system for hazardous operations, specifying the responsible departments, personnel, scope of authorization, approval procedures, and authorization issuers.	Failure to formulate the Safety Management System for Cross-over Operations; the Approval System for Dangerous Operations does not cover the approval of operations in confined spaces.	The Management System for Pyrotechnic Operations and the Management System for Restricted Spaces have not been adjusted to the latest norms.
	The safety management of hazardous operations is carried out by means of an operating license, which should contain an analysis of hazardous elements and safety measures.	Temporary electricity operation ticket is not filled in the analysis of hazardous elements, no signature of the guardian; temporary electricity, fire operation, work tickets do not contain hazardous elements identification, not set up the information column of the guardian	Inadequate identification of hazards in the restricted space operation ticket, no time filled in the signatures of all levels of personnel, no gas analysis and detection values, no completion acceptance
7.2 Operational behaviors management	Identify human unsafe behaviors during production operations and develop appropriate control measures.	Failure to carry out risk identification for welding operations and refrigeration operations.	Failure to carry out risk identification for welding operations.
	A permit and work ticket system is in place for hazardous operations.	Fire operation ticket without construction acceptance; results of combustible gas testing not reported.	——
	Employees shall be equipped with labor protective equipment that meets national or industry standards appropriate to their jobs and supervised and educated to wear and use them in accordance with their rules of use.	Labor protective equipment was not classified and managed and the quantities received did not correspond to actual needs.	——
7.3 Warning signs	Safety warning signs and safety colors are installed in workplaces with greater risk elements or on related equipment.	No height restriction on crossing shelves, evacuation sign on the first floor of the workshop is not light type.	Paint booths, sewage treatment tanks, and pool treatment are without warning signs.
	Special warehouses for hazardous chemicals, special equipment, and jobs that produce serious occupational hazards should be marked and warned in accordance with the relevant regulations.	Some of the “ovens” were not labelled with a “beware of high temperatures” warning sign; the office premises failed to provide a visually continuous lighted evacuation indicator sign.	——
	Setting up warning areas and warning signs at the operation sites of equipment and facilities inspection and maintenance, construction, lifting, etc.	Failure to provide warning signs for earth moving operations.	——
	Places where gas is likely to leak and accumulate should be marked with conspicuous warning signs.	Empty acetylene cylinders were stored in an abandoned facility with a large amount of flammable material piled up around them, and no warning signs were set up.	——
7.4 Related party management	Manage the pre-qualification and selection of contractors, suppliers, and other related parties; pre-service preparation; supervision of the operational processes, products and technical services provided; and performance evaluation and renewal of employment; and establish a directory and file of related parties.	Failure to include the construction engineering team in the list of related parties.	Some of the parties involved have no established management files.
	Regularly identify service behavior risks based on the nature and behavior of the service operations provided by the relevant parties, adopt effective risk control measures, and monitor their safety performance.	Lack of targeting of service risk controls for related parties in the product and service categories.	——
	Engineering projects should not be contracted out to units that do not possess the appropriate qualifications. The contracting agreement for the project should clearly stipulate the production safety responsibilities and obligations of both parties.	Failure to provide the relevant party’s special operator certificate.	——

.

In the element of “production site management and production process control”, the management level of Enterprises I and III is similar. However, in the elements of “work behaviors management” and “warning signs”, Enterprise III significantly outperforms Enterprises I and II. Enterprise III has established a better management workflow and a comprehensive supervision and inspection mechanism for hazardous work practices and work protection products, resulting in superior management outcomes. Specifically, in managing “warning signs”, Enterprise III has nearly eliminated issues of missing safety warning signs, ensuring they are present for work processes, emergency evacuation routes, and gas storage areas.

Additionally, for the “related party management” element, Enterprise III has thoroughly identified risks associated with related-party operations, strictly verified the qualifications of related enterprises and personnel, and maintained complete records of changes. The only shortfall was the absence of management files for a few related parties. Overall, these practices demonstrate Enterprise III’s strong commitment to maintaining high safety standards and effective management processes.

Based on the analysis of Element 7 “Operational Safety”, Enterprise II demonstrates better management procedures compared to Enterprise I, with identified deficiencies being more manageable for improvement. Despite having a lower linkage and overall assessment score initially, Enterprise II shows higher optimism, suggesting a stronger potential to achieve improved assessment scores after implementing enhancement measures. Therefore, when considering safety standard scores, linkage, and optimism, the production safety situation of Enterprise II appears more favorable than that of Enterprise I.

3.3. SPA Analysis of Safety Standard Assessment Results in Different Industries

Industrial and trade enterprises encompass a variety of sectors, including metallurgy and eight others. This study focuses on five representative industrial enterprises: concrete mixing, electrical machinery, machinery manufacturing, textile, and pharmaceutical companies (labeled I to V, respectively). These enterprises were chosen to analyze the implementation of safety standardization using SPA.

Table 9. Analysis of the results of the assessment of work safety standardization of five enterprises in different industries.

Enterprise	Element 1	Element 2	Element 3	Element 4	Element 5	Element 6	Element 7	Element 8	Element 9	Element 10	Element 11	Element 12	Element 13	Overall Score
I	90.00	53.33	70.00	53.00	58.00	83.85	46.53	82.86	65.38	75.00	73.08	80.00	77.78	66.76
II	90.00	53.33	70.00	53.00	58.00	57.89	69.32	82.86	65.38	75.00	73.08	80.00	77.78	66.01
III	90.00	53.33	70.00	53.00	58.00	57.89	71.74	62.86	65.38	75.00	73.08	80.00	77.78	64.79
IV	90.00	53.33	70.00	53.00	58.00	57.89	60.49	82.86	65.38	75.00	73.08	80.00	77.78	64.02
V	90.00	53.33	70.00	53.00	58.00	51.80	46.53	82.86	65.38	75.00	73.08	80.00	77.78	60.14

displays the scores across the thirteen elements for these enterprises, offering insights into their safety standardization efforts.

According to the weight linkage calculation, Equation (7), the linkage, set-pair potential, pessimistic potential, and optimistic potential of the enterprises numbered I to V can be computed by integrating the linkage and weight of each element of the industrial and trade safety standard. The results of these calculations are presented in

Table 10. Five enterprises in different industries and their safety standardization assessment results for the set of analysis indicators.

Enterprise	Linkage Degree	Set-Pair Potential	Level of Set-Pairing Potential	Pessimistic Potential	Optimistic Potential
I	−0.47	0.046	weak opposition potential	0.032	0.471
II	−0.64	0.039	weak opposition potential	0.029	0.393
III	−0.69	0.038	weak opposition potential	0.028	0.399
IV	−0.70	0.035	weak opposition potential	0.027	0.308
V	−0.76	0.029	weak opposition potential	0.025	0.192

.

The degree of weight linkage decreases consistently from Enterprise I to Enterprise V, aligning precisely with the comprehensive assessment scores of the safety standards shown in Table 9. The set of potential values ranges between pessimistic and optimistic potentials, affirming the reliability and validity of the established five-dimensional linkage calculation model used to analyze safety standardization assessment results across various industries within industrial and trade enterprises.

Based on the set-pair potential, all five of the different industrial and trade enterprises exhibit a “weak opposite potential”. Despite achieving the third level of production safety standardization, these enterprises show a concerning trend towards worsening safety conditions, deepening the overall “dangerous” state. Referring to the analysis indicators in Table 10, Enterprise III has a lower degree of linkage and safety standard assessment score compared to Enterprise II but displays an opposite optimistic trend. Consequently, Enterprise III is poised to achieve better overall safety assessment results.

Upon analyzing the element score rates of Enterprises II and III in Table 9, it becomes apparent that these rates differ significantly, particularly in Element 7 and Element 8. When examining the safety standard evaluation results within the same industry, Element 7’s score rate shows a positive correlation with the enterprise’s optimistic potential, even when other element scores are similar. However, between Enterprises II and III from different industries, Enterprise III exhibits a slightly higher score rate in Element 7 and a significantly higher rate in Element 8 compared to Enterprise II. Despite this, Enterprise II still maintains a higher optimistic potential than Enterprise III, suggesting that Element 8’s influence on optimistic potential is less pronounced than that of Element 7.

This difference can be attributed to varying total scores and weight distributions among the safety standard evaluation elements in the industrial and trade sectors. For instance, Element 7 carries a weight of 0.23, whereas Element 8 holds a weight of only 0.08. Consequently, the magnitude of these weights directly determines their impact on enterprise optimism. Therefore, enhancing the construction of enterprise safety standardization should prioritize elements with higher weights to achieve more rapid and effective improvements.

4. Results

4.1. The Model Based on Quintic Linking Number Calculus Is Constructed Rationally and Efficiently

Based on the principle of similarity, contrast, and opposition, the Set-Pair Analysis (SPA) method was employed here to develop a five-element linkage calculation formula and model for evaluating safety standards in the industrial and trade sectors. This model calculates the linkage, set-pair potential, and optimistic potential for each enterprise by considering the evaluation rates and weights of safety standard elements specific to industrial and trade settings. Comparing these results with the comprehensive safety standard evaluation scores of each enterprise reveals consistent trends in strengths and weaknesses. This validates the applicability of the five-element linkage formula and model for conducting detailed analyses of safety standard evaluation outcomes in small- and medium-sized industrial and trade enterprises.

4.2. Breaking the Standard of Assessing Results Based on Scores

Introducing key safety standard evaluation indices such as linkage degree, pessimistic potential, and optimistic potential enables a thorough analysis of safety standard construction outcomes in small- and medium-sized industrial and trade enterprises. This approach facilitates quantitative assessments of safety standard effectiveness and provides insights into the enterprise’s safety management hierarchy. Moreover, it allows for predictions regarding future safety trends, enhancing evaluation criteria for safety production standardization in these enterprises’ construction and operational phases. This refinement contributes to improving overall safety standards within the industrial and trade sectors.

4.3. The Weighting of Evaluation Elements Determines the Development Trend of Enterprise Security

The influence of each safety standard evaluation element’s weight in small- and medium-sized industrial and trade enterprises directly affects the enterprise’s optimistic potential in safety standard construction. This relationship underscores the importance of prioritizing elements with higher weights during continuous improvement efforts. Focusing on these key safety standard elements ensures more effective enhancements, leading to a swift elevation of the overall safety management standards within the enterprises.

5. Discussion

This study has developed a model based on quintic linking number calculus for evaluating safety standards in the industrial and trade sectors. Utilizing the Set-Pair Analysis method, the model calculates the linkage degree, set-pair potential, and optimistic potential for enterprises, considering the specific evaluation rates and weights of safety standard elements. The results demonstrate that the model effectively reflects the strengths and weaknesses in safety standard evaluations of small- and medium-sized enterprises (SMEs), validating the applicability of the five-element linkage formula and model in these settings.

Although this study focused on SMEs, the findings are highly relevant and applicable to the broader industry context, given that SMEs constitute the majority in the industrial and trade sectors in China. Large enterprises are often subject to confidentiality agreements that limit access to detailed safety standard evaluation reports, which restricts their inclusion in this research. Nonetheless, since safety production standardization elements and evaluation criteria are consistent across different enterprise sizes in China, the insights gained from this study remain valuable for the safety standardization efforts across the entire sector.

By incorporating key safety standard evaluation indices such as linkage degree, pessimistic potential, and optimistic potential, this study provides a comprehensive analysis of safety standard outcomes in SMEs. This approach enhances the quantitative assessment of safety standard effectiveness and offers insights into the enterprise’s safety management hierarchy. Moreover, it allows for predictions regarding future safety trends, thereby refining evaluation criteria and contributing to the overall improvement of safety standards within the industrial and trade sectors.

The study also highlights that the weighting of the evaluation elements significantly influences the development trend of the enterprise safety standards. Emphasizing elements with higher weights during continuous improvement efforts is crucial for achieving more effective enhancements and rapidly elevating overall safety management standards within enterprises.

Future research should aim to include large enterprises to provide a more comprehensive assessment of safety production standardization across various enterprise sizes. Such studies would offer more targeted safety management measures and further enhance safety management levels across different scales of enterprises.