Assessing the Degradation of Safety Management Performance in Large Construction Projects: An Investigation and Decision Model Based on Complex Network Modeling

Abstract

Modern safety control theory suggests that the accumulation of safety management defects at the organizational level can lead to a degradation in the overall safety management performance. This problem is exacerbated by the increasing complexity of safety management in large construction projects. The theoretical frameworks proposed by existing studies can provide generalized guidance for identifying safety management defects, but they are not flexible enough to address the complexity of a safety management system (SMS) in specific large construction projects. This study proposed an investigation and decision model based on a complex network model of SMSs. The main purpose was to accurately assess the degradation of safety management performance through the comprehensive identification of safety management defects for large construction projects. The functional components and their interactions in SMSs were graphically represented in a complex network using the fuzzy DEMATEL technique. Based on this, deep-seated safety management defects were identified by tracing the path of influence between the functional components and their roots. Furthermore, the results of this identification were used to support the assessment of the degradation of the safety performance of the overall SMS. The proposed model was verified with a large-scale wastewater treatment plant construction project in Lanzhou City, China. The degradation of the functional components could be presented in a complex visual network map to facilitate an understanding of the weak points or risk-sensitive areas throughout the SMS. Especially in the case of false safety perceptions, deep-seated safety management defects can be identified in time to prevent a sudden collapse of the SMS through early warnings. In addition, it also facilitates timely short-term improvement strategies and systematic long-term improvement strategies for long-term sustainability and increased resilience.

1. Introduction

The traditional approach to accident prevention is to prevent or reduce errors in production activities, such as failings, deviations, and even near misses [1]. However, through the development of the accident causation theory, errors are considered to be consequences instead of causes [2,3]. Modern safety control theory suggests that accidents attributed to errors have their root causes in safety management defects at the organizational level [4,5]. Merely preventing or reducing errors cannot eliminate the deeper safety management defects that cumulatively degrade the overall safety management performance, creating an environment that is conducive to safety-related incidents [6]. This problem is exacerbated by the increasing complexity of safety management systems (SMSs) in large construction projects [7,8,9]. From a resilience perspective [10], the comprehensive identification of safety management defects and the accurate assessment of the degradation of safety management performance in large construction projects has become a major challenge to ensure the sustainability of safety management performance in the long term.

According to epidemiological principles, safety management defects are not independent of each other but are interrelated in a complex and non-linear way [11]. However, many processes investigating construction projects’ safety can identify only the proximal failures that led to the incident, rather than the more systemic safety management defects [12]. Fragmented identification results may lead to an inadequate understanding of safety performance by those making safety-related decisions, leaving them vulnerable to adopting “firefighting” control thinking [13]. Furthermore, isolated control measures do not address the deep-seated or hidden safety management defects, which may again lead to new safety problems. Ultimately, this makes it difficult to achieve effective accident prevention and control the degradation of safety management performance in complex SMSs.

From the perspective of non-linear safety control [6,14,15], classical studies have constructed systematic frameworks that can assist in the identification of safety management defects, such as the systems theoretical accident model and processes (STAMP) and the viable system model (VSM). As a non-linear accident causation model, the STAMP describes the generalized safety control structure to assist in the identification of control defects that may lead to violation of the constraints [14]. As an organizational control model, the VSM describes an appropriate organizational structure for an SMS and helps to diagnose pathological defects in the organization [16]. While these frameworks can provide generalized guidance for identifying safety management defects, they are not sufficient to address the complexities of safety management in specific large construction projects. In response, it has been suggested that the interactions among the system’s components can provide clues for identifying deeper safety management defects [15]. Meanwhile, complexity science suggests that managing the complexity of a project involves studying the interactions within systems [17,18]. Therefore, a clear understanding of the functional components of an SMS and their interactions is essential for identifying safety management defects and assessing the degradation of safety management performance.

In this context, this study aimed to establish an investigation and decision model based on complex network modeling of SMSs in large construction projects. The main purpose was to accurately assess the degradation of safety management performance through the comprehensive identification of safety management defects. The functional components and their interactions in the SMS were graphically represented in a complex network using the fuzzy DEMATEL technique. With this method, it is expected that deep-seated safety management defects can be identified by tracing the path of influence between the functional components and their roots. In addition, by assessing the degradation of the performance of the functional components and the overall SMS, more timely and effective control strategies can be developed to promote the long-term sustainability of safety management performance.

Following the introduction (Section 1), this article reviews the literature (Section 2). Then, the investigation and the decision model are presented (Section 3). Through a case study, the proposed model was verified, as shown in Section 4. Discussion for this paper is shown in Section 5. Finally, the conclusions are addressed in Section 6.

2. Literature Review

With the development of safety science, safety management is viewed as a multi-level non-linear control problem [15]. Accordingly, the accumulation of safety management defects (shortages, design deviations, or poor implementation) at the organizational level is considered to be the root cause of the degradation of safety performance and contributes to the occurrence of safety-related incidents [13,19]. From an accident causation perspective, according to the traditional linear accident models (the domino model developed by Heinrich [20], Reason’s Swiss Cheese model [21], the ARAMIS methodology [22], etc.), some researchers have pointed out that accidents are not always attributed to individual safety management defects alone (i.e., a failure to impose safety constraints), but are emergent phenomena that cannot be controlled as a result of the complex and non-linear interactions within the SMS [23,24,25]. Thus, non-linear analysis models have been proposed to assist practitioners in identifying the organizational defects that lead to accidents, such as FRAM [6], STAMP [14], Accimap [26], etc. In parallel, from an organizational control perspective, many authors have argued that an SMS is an organic system consisting of interrelated components [11,13,27]. Several organizational control models have been proposed to assist in identifying safety management defects at the organizational level, such as VSM [16], the control theoretic framework of organizational safety [28], etc. On the basis of these, Kazaras proposed a joint STAMP–VSM framework to bridge the gap between non-linear accident causation analyses and organizational control analyses to help safety analysts search deeper for safety management defects in SMSs [13]. Overall, these analytical frameworks provide generalized guidance for identifying safety management defects, but their application to specific construction projects is not flexible enough to address the complexity of safety management and relies on the practitioners having a good understanding of the project’s SMS.

Some studies have been conducted to analyze the patterns and factors of safety management failures in construction organizations [28]. Karen identified stagnating safety practices in the face of technological advances, declining safety consciousness, and eroding safety goals as the main challenges to maintaining SMSs [29]. Rajaprasad confirmed the enormous driving force of management commitment and the wide-ranging influence of safety policies for SMSs [30]. Based on a survey of the SMSs of 59 construction companies, Okonkwo found that the most common safety management defects related to accountability and incentives for employee participation, management of subcontractors, and employee competence and training [31]. Love revealed that learning from and management errors was an important aspect neglected by most construction organizations, making the large number of repetitive errors and rework a major problem for declining safety performance [32]. In addition, a systematic approach divides safety management defects into five categories, namely inadequate formulation of safety policies and goals, inadequate adaptation to change, inadequate assignment of authority and responsibility for control, inadequate design and ineffective implementation of safety plans, and inadequate modeling of the state of safety performance [13], which provides a systematic reference for safety analysts. Overall, safety management defects can be categorized into two main types. The first type of safety management defect is caused by poorly designed and updated SMSs, reflecting a mismatch between the system function and technology or environment, such as the lack of essential functions or impractical functional designs [24,33]. Such defects can limit the performance of the SMS in the long term, and will continue to worsen with changes in technology and environment. The second type of safety management defect is caused by external pressures and chronic deterioration within the organization during the implementation, reflecting actual performance below expectations [1,13]. Such defects are characterized by concealment, randomness, repetition, and decentralization, and will gradually weaken SMS performance over time.

As modern systems and organizations have become increasingly complex, it has been suggested that practitioners should move towards safety models that are sensitive to the creation of system defects and organizational vulnerabilities, rather than just their eventual existence [34]. In response, considerable research has been devoted to the development of models for assessing the performance of SMSs in construction projects. Three methods have been summarized for assessing the effectiveness of an SMS: the results-based approach (which analyses the number of accidents, injuries, incidents, etc.), the compliance-based approach (which examines the degree of compliance of the SMS with a standard), and the process-based approach (which independently measures the performance of each management process that makes up the SMS) [35]. However, the results-based approach has been criticized for its passivity, as results showing a deterioration only reveal the existence of management defects and do not precisely identify the organizational defects [36]. Relatively, the other two methods are more proactive in identifying safety management defects. Although the compliance-based approach is easy to use, it relies on the rationality of the standard, and lacks flexibility and dynamic adaptability in practical applications [37]. Due to the emphasis on the performance of each management process in an SMS, the process-based approach is widely recognized for its flexibility and ability to provide an early warning regarding the safety performance of organizations [33,38]. Several studies have focused on the development of the leading indicators of safety performance to effectively identify safety management defects at an early stage [1,39,40]. However, some of the indicators are discrete and are insufficient to capture the complexity of an SMS in a systematic and clear way.

With the increasing complexity of projects, traditional project management practices have become ineffective [41]. How to manage the complexity of construction projects is receiving increasing attention from scholars and practitioners [42,43,44]. Complexity science suggests that managing the complexity of a project means studying the interactions within a system [17,18,45]. Wahlström pointed out that the interactions between a system’s components can provide clues for identifying the deeper safety management defects [15]. Dikmen suggested that modeling the non-linear relationships among the complex variables in construction projects is necessary for developing an effective strategy to control the risk and complexity [46]. In the application of accident analysis and crisis management, Dekker has used more flexible descriptions of organizations and advocated that structures and functions can emerge in different shapes [47]. Furthermore, some other studies have used different approaches to model the complexity of construction projects, such as the fuzzy analytical network process (ANP) [44], structural equation modeling (SEM) [48], the decision-making trial and evaluation laboratory (DEMATEL) [7], etc. Overall, the DEMATEL approach shows good flexibility and simplicity for quantifying the interactions among complex variables in organizations. The main limitation of the ANP is the assumption of the same relationships between clusters, which may be different from the perspective of the decision makers [49]. SEM is mainly used to validate research hypotheses of the interactions among complex variables [48], which makes it difficult to describe a project’s complexity in a flexible way. It should be noted that existing research on managing the complexity in construction projects supports the assessment of safety management performance to some extent, but does not integrate it with the identification of safety management defects.

A literature review has shown that grasping the complexity of SMSs in different construction projects is crucial for the comprehensive identification of safety management defects and for assessing safety management performance. Therefore, it is necessary to develop a more flexible investigation and decision model that allows complex network modeling of the functional components and their interactions to support a deeper identification of the safety management defects and to quantitatively assess the degradation of the overall SMS, thus providing a clear basis for the development of precise improvement strategies. In risk analyses, the proposed model may be used to provide an early warning of declining safety management performance. In accident analyses, the proposed model may be used to investigate the deeper organizational causes that contributed to an accident.

3. Model Development

Figure 1 summarizes the five main phases of the investigation and decision-making model: (1) a team of experts with extensive work experience and detailed knowledge of the complexity pf organizational management is assembled to support the entire process of investigation and decision-making; (2) the functional components in the SMS are identified by applying the process analysis approach; (3) the fuzzy DEMATEL technique is applied to map the complex network of the functional components; (4) a comprehensive inspection of the safety management defects is conducted by tracing the root causes based on the complex network of the SMS; and (5) the degree of degradation of the safety management performance is assessed, and improvement strategies are formulated. The details are presented in the following subsections.

3.1. Assembling a Team of Experts

To ensure the accuracy of the entire investigation and the decision-making process, it is imperative to assemble a team of experts with extensive work experience and detailed knowledge of the complexities of organizational management. The members of the team should primarily consist of the construction manager, the safety manager, and supervisors at the organizational level, as they have a thorough understanding of the safety management process and the status of the construction project. In addition, it is necessary to include safety management experts or researchers with experience in the same type of construction project to provide a more accurate opinion from an outside perspective. It can be assumed that the team of experts will reach a decision by consensus. Therefore, the Delphi method was adopted, as it allows the investigating decision makers to obtain opinions from a team of experts through systematic multiple sequential rounds of intensive questionnaires with controlled feedback [50]. This approach is ideal for obtaining a reliable consensus in a complex SMS.

3.2. Identifying the Functional Components

Functional components are the basic units of an SMS. They interact with each other and operate according to a specific process in order to jointly achieve safety goals. Therefore, process analysis is considered to be a suitable method for the systematic identification of the functional components. This method is easy to understand, simple to apply, and has been widely used in many different fields [51]. Process analysis views the organization as a network of interrelated processes that aim to achieve the organization’s goals [34], which is consistent with the starting point of this study. In addition, the functional components identified should have a specific function and relative independence. The experts were asked to identify the functional components in the SMS of the target construction project through process analysis. The functional components identified through the consensus of the expert team can be represented as $Ci (i=1,2,\cdots ,n)$.

3.3. Mapping the Complex Network of the Functional Components

Complexity in an SMS mainly refers to the varying degrees of interactions among functional components [11,25,44]. To achieve a clear understanding of the SMS, a feasible approach is to visualize the interactions among the functional components by mapping a complex network [7]. It is also necessary to determine the importance of the functional components, as well as the type and degree of the interactions among them during the process of modeling complex networks. It should be noted that although there are differences in the composition of SMSs for different construction projects, they all share the common goal of ensuring the integrated safety of the construction process [31], including the safety of humans, equipment, and the environment.

A literature review showed that the DEMATEL method is the most suitable technique for quantifying the interactions among the functional components in the SMSs of large construction projects [7]. Among the existing methods, the DEMATEL method or its variants have been widely used to visualize and illustrate the interactions among the elements in a complex non-linear system [52,53]. This method allows the researchers to represent complex variables in an intelligent structural model consisting of a cause group and an effect group, thus grasping the interdependence among the different systems [54]. To address the fuzziness caused by the subjective judgment of experts, triangular fuzzy numbers (TFNs) were introduced to process the initial direct relationship matrix, improving the accuracy of the DEMATEL method [55,56]. This approach is more in line with human reasoning when making an approximation or decisions involving uncertainty, thus better ensuring the quality of the data and the accuracy of the results. The defuzzification algorithm proposed by Opricovic was adopted as a bridge to combine TFNs with DEMATEL to meet DEMATEL’s input requirement of crisp values [57]. Therefore, the complex network of SMSs for large construction projects can be realized by fuzzy DEMATEL as follows.

• Step 1: Experts evaluate the interactions among the functional components in an SMS by using TFNs.

In this study, five linguistic expressions formed by using TFNs were defined (

Table 1. The linguistic expressions and triangular fuzzy numbers of influence among the functional components.

Linguistic Expression of Influence	Triangular Fuzzy Number
No influence (N)	(0, 0, 0)
Low influence (L)	(0, 1, 2)
Medium influence (M)	(1, 2, 3)
High influence (H)	(2, 3, 4)
Very high influence (VH)	(3, 4, 4)

), where 1 denotes the least influence, and 4 denotes the highest influence. The experts were asked to evaluate the interactions among the functional components using the TFNs in Table 1. The initial fuzzy direct influence matrix $H^k$ was obtained.

$$H^k={\left(\begin{array}{cccc}0& {\tilde{x}}_{1-2}^k& \cdots & {\tilde{x}}_{1-n}^k\\ {\tilde{x}}_{2-1}^k& 0& \cdots & {\tilde{x}}_{2-n}^k\\ ⋮& ⋮& \ddots & ⋮\\ {\tilde{x}}_{n-2}^k& {\tilde{x}}_{n-2}^k& \cdots & 0\end{array}\right)}_{n\times n}(k=1,2,\cdots ,K)$$

(1)

where the triangular fuzzy number ${\tilde{x}}_{i-j}^k$$(i\ne j)$ is the result of the evaluation by the kth expert, which represents the direct influence of functional component $Ci$ on $Cj$ $(i=1,2,\cdots ,n;j=1,2,\cdots ,n)$, i.e., ${\tilde{x}}_{i-j}^k=\left(l_{i-j}^k,m_{i-j}^k,u_{i-j}^k\right)$, where $l$, $m$, $u$ refer to the smallest value, the most likely value, and the largest value, respectively. When $i=j$, ${\tilde{x}}_{i-j}^k=(0,0,0)$.

• Step 2: Defuzzify the triangular fuzzy numbers into crisp values.

The defuzzification algorithm proposed by Opricovic is used to convert the triangular fuzzy numbers into crisp values [57], which reflect the exact evaluation results of the expert team for the same object. The specific steps are as follows:

• Normalize the triangular fuzzy numbers with Formulas (2)–(4).

$$y{l}_{i-j}^k=\frac{l_{i-j}^k-\min l_{i-j}^k}{\max u_{i-j}^k-\min l_{i-j}^k}$$

(2)

$$y{m}_{i-j}^k=\frac{m_{i-j}^k-\min l_{i-j}^k}{\max u_{i-j}^k-\min l_{i-j}^k}$$

(3)

$$y{u}_{i-j}^k=\frac{u_{i-j}^k-\min l_{i-j}^k}{\max u_{i-j}^k-\min l_{i-j}^k}$$

(4)

2.

The left-hand ($yls$) and right-hand ($yrs$) normalized values are calculated with Formulas (5) and (6).

$$yl{s}_{i-j}^k=\frac{y{m}_{i-j}^k}{1+y{m}_{i-j}^k-y{l}_{i-j}^k}$$

(5)

$$yr{s}_{i-j}^k=\frac{y{u}_{i-j}^k}{1+y{u}_{i-j}^k-y{m}_{i-j}^k}$$

(6)

3.

The total normalized values are calculated with Formula (7).

$$y_{i-j}^k=\frac{[yl{s}_{i-j}^k(1-yl{s}_{i-j}^k)+{(yr{s}_{i-j}^k)}^2]}{[1-yl{s}_{i-j}^k+yr{s}_{i-j}^k]}$$

(7)

4.

Crisp values of the evaluation results of the kth expert are calculated with Formula (8).

$$v_{i-j}^k=\min l_{i-j}^k+y_{i-j}^k(\max u_{i-j}^k-\min l_{i-j}^k)$$

(8)

5.

The crisp direct influence matrix is calculated with Formula (9).

$$V=(\frac{1}{K}){\displaystyle \sum _{k=1}^K{v}_{i-j}^k}={\left(\begin{array}{cccc}0& v_{1-2}& \cdots & v_{1-n}\\ v_{2-1}& 0& \cdots & v_{2-n}\\ ⋮& ⋮& 0& ⋮\\ v_{n-1}& v_{n-2}& \cdots & 0\end{array}\right)}_{n\times n}$$

(9)

where $v_{i-j}$ is the crisp value reflecting the direct influence of functional component $Ci$ on $Cj$.

• Step 3: Normalize the crisp direct influence matrix with Formula (10).

$$G=V/\lambda$$

(10)

where the normalized factor is defined as the sum of all elements of the matrix $V$, i.e., $\lambda ={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{v}_{i-j}}}$.

• Step 4: Calculate the total influence matrix $T$ with Formula (11).

$$T={\left(t_{i-j}\right)}_{n\times n}=\underset{l\to \infty }{\lim }(G^1+G^2+\cdots )=G\times {(I-G)}^{-1}$$

(11)

where $t_{i-j}$ denotes the total influence of functional component $Ci$ on $Cj$, including both direct and indirect influences, and $I$ denotes the identity matrix.

• Step 5: Calculate the degree of influential impact $r_i$ with Formulas (12).

$$r_i={\displaystyle \sum _{j=1}^n{t}_{ij}}$$

(12)

Unlike the original DEMATEL method, the degree of influential impact $r_i$ is set as an index of the degree of importance of each component to reflect its influence in the whole SMS. In other words, the higher the value of $r_i$, the more important the functional component $Ci$ is, in terms of its overall relationship to the other functional components.

• Step 6: Map the complex network of the functional components in the SMS according to the crisp influence matrix $V$ and the degree of influential impact $r_i$.

3.4. Conducting a Comprehensive Inspection of the Safety Management Defects

Safety management defects in construction projects can be classified into three categories: (i) a lack of essential functions, such as the lack of the necessary safety training for employees, the lack of a safety assessment system, etc.; (ii) impractical functional designs, including ambiguous safety rules, inadequate systematicity of the safety management programs, blurred safety responsibilities among different departments, etc.; (iii) inadequate execution of functions, such as insufficient implementation of the mechanism of reporting safety problems, an emergency system with unverified applicability, etc. [13]. Overall, due to the complexity and uncertainty of large construction projects, safety management defects exhibit the characteristics of randomness, repetition, and concealment. It is important to note that the various safety management defects are not independent of each other but instead accumulate to gradually weaken the safety management performance based on the non-linear interaction of the complex network in the SMS. This requires an inspection of the safety management defects to focus on both regular and obvious defects, as well as deep-seated safety management defects. Failure to address deeper safety management defects over a long period of time may lead to new defects or problems. Therefore, based on the mindset of tracing the root cause, this study proposes a thorough method of inspecting the safety management defects in the complex network of an SMS. The specific steps are as follows.

• Step 1: Identify the obvious regular safety management defects in the SMS through routine safety inspections;
• Step 2: On the basis of the influence path of the complex network in the SMS, investigate the deeper safety management defects in the former functional components related to the defects identified in Step 1;
• Step 3: Repeat Step 2 until no new safety management defects can be identified.

3.5. Assessing the Degradation of Safety Management Performance

To accurately assess the degradation of safety management performance, it is important to evaluate the functional components, including the integrity of the functional composition, the practicality of the design, and the adequacy of the implementation. Experts are tasked with assessing the performance of these components on the basis of the identified safety management defects. Because of the ambiguity of the experts’ judgment process, triangular fuzzy numbers are used to obtain the evaluation results, which are then defuzzified to obtain crisp values. In addition, the degree of the influential impact ($r_i$) of each functional component in the SMS’s complex network can be converted into corresponding weight values using the normalization method. Finally, the overall safety management performance of the SMS and the corresponding degree of degradation is determined by weighted integration. Moreover, by using the SMS’s complex network, it is possible to obtain the degradation of safety management performance throughout the entire organization. This can then facilitate the development of targeted strategies to improve safety management performance.

It is important to emphasize that improvement strategies need to be developed with due regard to the timely effectiveness of improvements to the proximal and distal functional components of the integrated safety of the complex network [12]. If the functional components prioritized for improvement are distant from the integrated safety status, it will be difficult to achieve an improvement in the integrated safety status in the short term, leaving more time for the incubation of accidents. In view of the above, it is necessary to prioritize improvements in the proximal functional components in the short term and thus reinforce the fundamental barrier guaranteeing the integrated safety of the frontline. In the long term, it is necessary to systematically improve the distal functional components in order to fully enhance the drivers and performance of safety management at the organizational level.

• Step 1: Experts evaluate the safety management performance of the functional components using TFNs, based on the results of identifying the safety management defects.

Four linguistic expressions formed by using TFNs were defined (

Table 2. The linguistic expressions and triangular fuzzy numbers of safety management performance.

Linguistic Expression of Performance	Triangular Fuzzy Number
Poor performance (P)	(0, 0, 1)
Limited performance (L)	(0, 1, 2)
Moderate performance (M)	(1, 2, 3)
Good performance (G)	(2, 3, 4)
Sufficient performance (S)	(3, 4, 4)

), where 1 denotes poor performance, and 4 denotes adequate performance. The experts were asked to evaluate the safety management performance of the functional components using the TFNs in Table 2. The initial fuzzy assessment $E^k$ was obtained.

$$E^k=\left(\begin{array}{cccc}{e}_1^k& e_2^k& \cdots & e_n^k\end{array}\right)(k=1,2,\cdots ,K)$$

(13)

where the triangular fuzzy number $e_i^k$ is the evaluation of the kth expert, which represents the safety management performance of functional component $Ci (i=1,2,\cdots ,n)$.

• Step 2: Defuzzify the triangular fuzzy numbers to obtain crisp values using Formulas (2)–(9), resulting in the crisp assessment results $E$. Accordingly, the degree of degradation of the safety management performance of each functional component can be calculated using Formula (15).

$$E^{}= e_i=\left(\begin{array}{cccc}{e}_1^{}& e_2^{}& \cdots & e_n^{}\end{array}\right)$$

(14)

$$d_i=1-\frac{e_i}{4}\%$$

(15)

• Step 3: The degree of influential impact $r_i$ is converted into the corresponding weight value $w_i$ using Formula (16). It should be noted that the weighted results can be considered to be relatively stable over a specific period of time.

$$w_i=\frac{r_i}{{\displaystyle \sum r_i}}$$

(16)

• Step 4: The assessment result $P$ of the safety management performance is obtained by Formula (17). In turn, the degree of degradation of the overall safety management performance of the SMS can be calculated by Formula (18). The results of this assessment can be combined with the complex network in the SMS to visualize the degree of degradation of the safety management performance.

$$P=e_i{w}_i$$

(17)

$$D=1-\frac{P}{4}\%$$

(18)

• Step 5: Develop short- and long-term improvement strategies to improve the organization’s safety management performance, taking full account of the proximal and distal functional components of the integrated safety in the complex network of the SMS.

4. Illustrative Example: Guiding the Investigation and Decision-Making Process for Safety Management Defects in a Project to Construct a Wastewater Treatment Plant

In this section, we demonstrate how the proposed model can be used to guide an appropriate investigation of the safety management defects and an assessment of the degradation of the safety management performance of the SMS in a large-scale construction project (a wastewater treatment plant). The project is a new municipal project in Lanzhou City, China, which uses the EPC (engineering, procurement, construction) contract management model. It has a construction area of 60,990.17 m² and covers an area of 52,776.62 m². The underground reinforced concrete water tank has a total length of 271.00 m and a total width of 101.00 m. The project was selected because of the complexity and challenging nature of managing its safety, which could result in huge losses in the event of a safety-related incident.

4.1. Assembling a Team of Experts

The selection of the members of the expert panel plays a crucial role in the success of the overall investigation and decision-making process. First, the construction manager, safety manager, safety inspector, safety supervisor, frontline team leader, and financial manager of the wastewater treatment plant construction project were invited to be members of the expert team. This is because they are directly involved in managing the safety of this project. In addition, experts and researchers with extensive experience in construction-related safety management were invited to join the expert team. In total, nine experts formed the expert team.

Table 3. Backgrounds of the experts.

No.	Organization	Degree	Experience (Years)
1	Construction manager	Undergraduate	19
2	Safety manager	Undergraduate	16
3	Safety inspector	Bachelor	8
4	Safety supervisor	Undergraduate	16
5	Frontline team leader	Bachelor	6
6	Financial manager	Undergraduate	13
7	Consultant	Doctor	15
8	Consultant	Undergraduate	12
9	Researcher	Doctor	13

shows the background information of the experts.

4.2. Identifying the Functional Components

In order to fully identify the functional components, the expert team was invited to conduct a 1-week systematic survey of the SMS of the wastewater treatment plant construction project. On this basis, the first round of open-ended questionnaires was distributed. The experts were asked to identify the functional components by using process analysis. The results were collated to form an initial list of the functional components, with which a second round of the questionnaire was constructed. In the second round, the participants were advised to comment on or question any point in the questionnaire. In the third round, the results were reviewed and refined through semi-structured interviews and group discussions. Finally, 30 functional components of the SMS were identified (

Table 4. Functional components of the SMS.

No.	Functional Component	No.	Functional Component	No.	Functional Component
C1	Idea and promotion of safety culture	C11	Safety meetings	C21	Management of the equipment, facilities, and electricity for construction
C2	Safety management regulations	C12	Verification of practical qualification	C22	Civil construction
C3	Safe operating instructions	C13	Safety input	C23	Management of the frontline team
C4	Safety-related communication and coordination	C14	Management of safety-related materials and facilities	C24	Engineering changes
C5	Safety goals and their breakdown	C15	Safety education and training	C25	Acceptability of construction quality
C6	Leadership decisions and safety programs	C16	Safety-related technical guidance	C26	Fire management
C7	Hazard identification	C17	Safety inspections	C27	Emergency management
C8	Risk assessments	C18	Tracking hazardous waste disposal	C28	Living security
C9	Planning to organize the construction	C19	Management of personal protection	C29	Safety incentives and penalties
C10	Management of safety-related information	C20	Management of labor intensity	C30	Reporting unsafe incidents

). The details of each functional component are shown in

Table A1. Details of the functional components.

No.	Functional Component	Department	Connotations
C1	Idea and promotion of safety culture	R1; R2	Integration of the idea of safety culture with construction; acceptability of the idea of safety culture; promotion of the idea of safety culture
C2	Safety management regulations	R1; R2	Safety-related responsibility regulations; safety inspection regulations; occupational health and safety management regulations; etc.
C3	Safe operating instructions	R2; R3; R4	Standard operating procedures and safety precautions for construction activities
C4	Safety-related communication and coordination	R1; R2	Organizational fairness; respect and support for employees; conflict resolution
C5	Safety goals and their breakdown	R2; R3	Realistic and clear safety goals; specific and quantifiable breakdowns of safety goals; adjustment of the safety goals
C6	Leadership decision and safety programs	R1; R2; R3	Senior management’s attitudes and decisions regarding implementing the safety program; planning and implementation of the safety program
C7	Hazard identification	R3; R4	Classification and updating of the sources of hazard; dynamic identification and level of the sources of hazard
C8	Risk assessments	R3	Identification of uncertain factors; assessment of construction safety risks; measures to control the safety risks
C9	Planning to organize the construction	R1; R4	Preparation plan for the construction; construction scheme; organization and management plan for the construction; resource allocation and use plan
C10	Management of safety-related information	R3; R4	Standardization of safety information; storage, recall, transfer, and sharing of safety-related information; updates of safety-related information and knowledge
C11	Safety meetings	R2	Identification of key safety issues; analysis of the safety status; adjustment of the safety plan and program
C12	Verification of practical qualifications	R3; R5	Verification of the practical qualifications of subcontractors, suppliers, and construction workers
C13	Safety input	R1; R3; R6	Planning, disbursement, and adjustment of safety inputs, including staff, facilities, funding, etc.
C14	Management of safety-related materials and facilities	R3; R7	Procurement, verification, and storage of safety-related materials and facilities
C15	Safety education and training	R3	Education on safety awareness and safety-related knowledge; training in safety skills
C16	Safety-related technical guidance	R4	Guidance on safe operation, potential hazards, protection of personnel, and emergency responses
C17	Safety inspections	R3	Content, mode, frequency, and analysis of safety inspections
C18	Tracking hazardous waste disposal	R3	Corrective measures, dynamic tracking, and verification reports for identified hazards
C19	Management of personal protection	R3; R4	Issuing, using, and checking personal protective equipment during construction work
C20	Management of labor intensity	R4	Appropriate workloads; reasonable working hours; monitoring of worker fatigue
C21	Management of the equipment, facilities, and electricity for construction	R3; R4	Compliance regarding the use and maintenance of the equipment and facilities; compliance regarding the installation, acceptance, and removal of large equipment; compliance regarding the distribution and use of electricity
C22	Civil construction	R3; R4	Integrated management of the site’s cleanliness, hygiene, safety, environmental protection, and orderliness
C23	Management of the frontline team	R3; R4	The organizational ability of the team leader; standardization of the construction processes; safety climate in the team; communication and cooperation; democratic management
C24	Engineering changes	R3; R4	The necessity of engineering changes; completeness of the plans for the changes; timeliness of executing the changes
C25	Acceptability of construction quality	R4	Compliance with quality acceptance procedures and standards
C26	Fire management	R3; R4	Fire prevention plan; fire safety equipment; fire drills
C27	Emergency management	R1; R2; R3; R7	Emergency response mechanisms; emergency plans; rescue plans; facilities; emergency drills
C28	Living security	R8	Dietetic hygiene; environmental hygiene; heat protection and warmth; medical and emergency issues; leisure and recreation
C29	Safety incentives and penalties	R2; R3	Safety incentives (bonus, honor, promotion); safety penalties (fines, criticism, job reassignment)
C30	Reporting unsafe incidents	R3; R4	Scope of unsafe incidents; reporting procedures and requirements; reporting channels; the level of involvement of all employees

Note: R1 denotes the project leadership, R2 denotes the safety management committee, R3 denotes the safety management department, R4 denotes the construction technology department, R5 denotes the general management department, R6 denotes the finance department, R7 denotes the material management department, and R8 denotes the logistic support department.

(Appendix A).

4.3. Mapping the Complex Network of the Functional Components

In order to fully reflect the complex network of the SMS, the non-functional components (the safety of personnel, the environment, and equipment) were set as end nodes, designated C31, C32, and C33, respectively. Firstly, the expert team identified and reached a consensus on the influencing relationships between the functional components through a symposium. In this way, the scope of assessing the degree of influence between the functional components was sufficiently reduced. The influencing relationships were mainly reflected by the aspects of guarantees, constraints, and promotion. Then, the degree of influence between the functional components was determined by the experts using the TFNs listed in Table 1. To clarify the comparative terms for all participants, examples were introduced to illustrate the degree of influence of one particular variable on another one in the questionnaire. The initial fuzzy direct influence matrix $E^k$ was then obtained. To construct the crisp direct influence matrix $V$ (

Table A2. Crisp direct-influence matrix.

Component	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15	C16	C17
C1	0	2.871	0	3.857	0	3.519	2.372	2.412	2.162	2.542	3.374	0	2.253	0	2.514	2.341	2.312
C2	0	0	0	1.741	2.432	3.131	2.413	2.483	2.313	2.251	2.139	2.546	2.464	2.162	2.338	2.473	2.475
C3	0	0	0	0	3.451	2.875	3.647	3.339	3.417	0	0	0	3.174	3.518	3.372	3.761	3.613
C4	0	0	0	0	0	3.114	0	0	0	0	3.253	0	0	0	0	0	0
C5	0	0	0	3.372	0	3.274	0	0	2.912	3.274	0	2.813	2.961	2.517	2.747	2.874	3.174
C6	0	0	0	0	0	0	0	0	0	2.861	2.847	2.637	3.346	2.753	2.852	2.951	3.267
C7	0	0	0	0	0	0	0	3.514	2.751	0	0	0	0	0	0	2.738	3.251
C8	0	0	0	0	3.196	2.814	0	0	2.947	0	2.872	0	2.913	2.637	2.641	0	0
C9	0	0	0	0	0	0	0	0	0	0	0	0	0	2.462	0	2.457	0
C10	0	0	3.172	3.017	0	2.943	3.274	2.871	2.813	0	0	3.318	2.547	2.414	2.732	2.747	3.151
C11	0	0	0	2.417	0	0	0	1.742	2.573	0	0	0	0	0	0	0	0
C12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C13	0	0	0	0	0	0	0	2.514	0	3.174	0	0	0	3.714	2.871	0	2.548
C14	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C15	0	0	0	2.431	0	0	2.303	0	0	0	0	0	0	0	0	2.722	0
C16	0	0	0	0	0	0	3.372	0	0	0	0	0	0	0	0	0	0
C17	0	0	0	0	0	0	0	3.151	0	0	0	0	0	0	0	0	0
C18	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C19	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C20	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C21	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C22	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C23	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2.875	0
C24	0	0	0	0	0	2.874	0	0	2.613	0	0	0	0	0	0	0	0
C25	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C26	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C27	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C28	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C29	0	0	0	0	0	0	0	2.413	0	0	0	0	0	0	0	2.437	2.512
C30	0	0	0	0	0	0	2.743	0	0	0	0	0	0	0	0	0	0
C31	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C32	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C33	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Component	C18	C19	C20	C21	C22	C23	C24	C25	C26	C27	C28	C29	C30	C31	C32	C33
C1	0	0	0	0	0	3.417	0	0	0	0	0	0	0	0	0	0
C2	2.272	2.317	2.174	2.214	2.257	2.373	2.159	2.217	2.274	2.232	2.347	2.174	2.272	0	0	0
C3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C4	2.716	0	0	0	0	2.963	3.159	0	0	0	0	0	3.362	0	0	0
C5	2.441	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C6	2.613	2.752	2.314	2.562	2.519	2.843	2.451	2.747	2.416	2.754	2.521	2.835	0	0	0	0
C7	3.313	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C9	0	0	2.852	2.597	2.472	2.863	0	0	2.374	2.414	0	0	0	0	0	0
C10	3.132	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C11	0	0	0	0	0	0	0	0	0	0	0	0	2.316	0	0	0
C12	0	3.148	0	3.727	2.753	3.174	0	0	3.171	0	0	0	0	0	0	0
C13	0	0	0	0	0	0	0	0	0	0	2.464	0	0	0	0	0
C14	0	2.972	0	2.671	2.942	0	0	0	2.416	2.379	2.276	0	0	0	0	0
C15	2.163	2.435	1.943	2.417	2.354	2.514	0	0	2.382	2.351	0	0	2.374	0	0	0
C16	0	3.368	2.874	2.913	2.853	2.847	0	0	2.614	2.417	0	0	0	0	0	0
C17	2.952	2.714	2.617	2.791	2.543	2.975	2.473	0	2.743	2.572	2.317	0	0	0	0	0
C18	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2.514	2.427
C19	0	0	0	0	0	0	0	0	0	0	0	0	0	3.886	0	0
C20	0	0	0	0	0	0	0	0	0	0	0	0	0	2.954	0	0
C21	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2.427	3.475
C22	0	0	0	0	0	0	0	0	0	0	0	0	0	0	3.772	0
C23	2.412	2.679	2.641	2.476	2.391	0	0	0	2.347	2.624	0	0	2.572	2.841	0	0
C24	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C25	0	0	0	0	0	0	0	0	0	0	0	0	0	0	2.362	1.925
C26	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1.914	1.813
C27	0	0	0	0	0	0	0	0	0	0	0	0	0	2.257	0	0
C28	0	0	0	0	0	0	0	0	0	0	0	0	0	2.821	0	0
C29	2.624	0	0	0	0	2.478	0	0	0	0	0	0	2.862	0	0	0
C30	2.961	0	0	0	0	0	0	0	0	0	0	0	0	2.412	2.572	2.641
C31	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C32	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
C33	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

, Appendix B), the triangular fuzzy numbers were converted into crisp values through the defuzzification process using Formulas (2)–(9), which accurately integrated the experts’ assessments. Through normalization (Formula (10)), the total influence matrix $T$ was obtained by using Formula (11). The degree of influential impact $r_i$ was calculated by using Formula (12), and the results are shown in

Table 5. Degree of the influential impact of the functional components.

Component	$\mathit{r}$	Rank	Weight	Category	Component	$\mathit{r}$	Rank	Weight	Category
C1	0.913	3	0.077	SD	C16	0.427	11	0.036	MM
C2	1.341	1	0.113	SD	C17	0.550	7	0.046	MM
C3	0.829	5	0.070	SD	C18	0.079	24	0.007	EI
C4	0.407	12	0.034	MM	C19	0.062	26	0.005	EI
C5	0.779	6	0.065	SD	C20	0.047	29	0.004	EI
C6	1.109	2	0.093	SD	C21	0.094	23	0.008	EI
C7	0.344	15	0.029	MM	C22	0.060	27	0.005	EI
C8	0.489	9	0.041	MM	C23	0.459	10	0.039	MM
C9	0.387	14	0.033	MM	C24	0.155	22	0.013	MM
C10	0.896	4	0.075	SD	C25	0.068	25	0.006	EI
C11	0.198	21	0.017	MM	C26	0.059	28	0.005	EI
C12	0.293	17	0.025	MM	C27	0.036	31	0.003	EI
C13	0.406	13	0.034	MM	C28	0.045	30	0.004	EI
C14	0.265	19	0.022	MM	C29	0.334	16	0.028	MM
C15	0.544	8	0.046	MM	C30	0.232	18	0.019	MM

Note: SD, source-driven factors; MM, major management factors; EI, end implementation factors.

. On the basis of these results, the influences among the functional components of the SMS in the wastewater treatment plant construction project could be illustrated by the complex network map shown in Figure 2, where the darker the color of a functional component, the greater its degree of influential impact $r_i$ in the SMS.

According to the ranking of the importance of the functional components and Figure 2, it can be seen that the degree of influential impact $r_i$ reflects the position of the functional components in the path of influence to some extent. The higher the degree of influential impact $r_i$, the closer the functional component is to the source of the path of influence, and the lower the degree of influential impact $r_i$, the closer the functional component is to the end of the path of influence. Therefore, according to the distribution of the degree of influential impact $r_i$, this study classified the functional components into three categories, namely source-driven factors, major management factors, and end implementation factors, as shown in Table 5.

The source-driven factors include C2, C6, C1, C10, C3, and C5, in that order. The corresponding degree of influential impact $r_i$ was found to have an interval of 0.779–1.341, and the overall importance was as high as 49.27%. This suggests that while the number of source-driven factors was small, their impact on the overall SMS was critical. Among them, C2 (safety management regulations) had the greatest degree of influence (1.341), reflecting its broad support for the whole SMS. C6 (leadership decisions and safety programs) was the next most important, with an influential impact of 1.109, reflecting its critical role in the operation of the SMS.

The major management factors included C17, C15, C8, C23, C16, C4, C13, C9, C7, C29, C12, C30, C14, C11, and C24, in that order, for a total of 15 factors. The corresponding degree of influential impact r_i was found to have an interval of 0.198–0.550, and the total importance was as high as 46.10%. This indicates that the major management factors played the main role in the safety management performance of the SMS.

The end implementation factors included C21, C18, C25, C19, C22, C26, C20, C28, and C27, in that order, for a total of nine factors. The corresponding degree of influential impact $r_i$ was found to have an interval of (0.045–0.155), and the total importance was 4.63%. It should be noted that these functional components were important for the SMS, but the end implementation factors are more influenced by the source-driven factors and major management factors in the complex network, as shown in Figure 2. In addition, most of these components are directly related to the safety of the personnel, environment, and equipment at the construction site, which is the basic barrier to ensuring the safety of frontline construction.

4.4. Inspecting the Safety Management Defects

Based on the previous records of the safety management defects of the wastewater treatment plant construction project, it was clear that most of the defects were concentrated in the end implementation factors and the major management factors. Overall, the records of safety management defects were scattered, and almost no source-driven factors were involved. In this study, the team of experts was invited to comprehensively identify one-quarter of the safety management defects in the construction process by tracing the root cause (Section 3.4), based on the path of influence within the complex network of the SMS (Figure 2). In total, 68 safety management defects were identified, which were mainly related to safety issues such as the erection of cables, the operation of the rebar fire, flood control in the foundation pit, the erection of scaffolds, stacking materials, covering bare soil, etc. Figure 3, Figure 4 and Figure 5 list the identified safety management defects of the prominent safety problems.

Based on the original record of the safety management defects (37 in total), the proposed model in this study identified 31 new safety management defects. Among the identified results, 19 defects were related to source-driven factors (27.94%), 38 defects were related to major management factors (55.88%), and 11 defects were related to end implementation factors (16.18%). Moreover, the significant increase in the proportion of source-driven factors and, to some extent, the proportion of major management factors, generally reflected the fact that identifying safety management defects based on the complex network in the SMS can significantly improve the comprehensiveness and depth of the identification process. In particular, it was possible to effectively identify some of the hidden defects, such as the fact that related procedures were not streamlined enough (C2), the inadequate timeliness of safety-related communication and coordination (C4), the lack of support for information on collaboration (C10), etc.

Regarding the source-driven factors, the functional components with notable safety management defects were ranked as C6, C10, C2, and C5. Defects in C6 (leadership decisions and safety programs) included inadequate detailing and quantification of special safety programs, the inability to meet inspection requirements due to having insufficient numbers of safety inspectors during peak construction periods, and the lack of attention by the management to reporting feedback and safety-related information management. Defects in C10 (management of safety-related information) included a lack of systematic and standardized processes for collection, recording, and sharing safety information, and inadequate updating of safety-related knowledge. C2 (safety management regulations) lacked normative requirements for special safety programs, a decentralized authority for checking practical qualifications, and insufficiently streamlined implementation procedures. Lastly, C5 (safety goals and their breakdown) had defects such as inadequate analysis of the peak construction requirements for quantifying the safety objectives and a lack of validation points for the implementation of safety objectives.

Regarding major management factors, the functional components with notable safety management defects were ranked as C4, C23, C17, C29, and C30. Defects in C4 (safety-related communication and coordination) were mainly due to the lack of convenient and efficient feedback channels, which, in turn, led to a lack of clarity about the management needs of frontline teams and the inadequate timeliness of safety-related communication and coordination. Defects in C23 (management of the frontline team) were confusion about the management of the frontline team leaders under the tight schedule of organizing the construction and the inability of team leaders to effectively balance workloads and stop unsafe behavior in a timely manner when communication and coordination were inadequate. Defects in C17 (safety inspections) were an inability to set adequate safety inspection items due to incomplete safety risk assessments, and inadequate implementation of safety inspections due to having insufficient safety staff, especially during peak construction periods. In addition, defects in C29 (safety incentives and penalties) and C30 (reporting unsafe incidents) occurred in pairs, reflecting the inadequate implementation of unsafe incident reports due to insufficient incentives and penalties.

Regarding the end implementation factors, the safety management defects manifested in piecemeal form as deviations in implementation or errors related to safety hazards, such as inadequate safety warning signs in the fire operation area (C22), inadequate standards of cable erection, and unadjusted flood control devices (C21), etc.

Overall, unlike the safety checklist method, the safety management defects identified by the complex network of the SMS were mostly presented in the basic form of a defect chain (safety issues → end implementation factors → major management factors → source-driven factors). Of these, the shortest defect chain contained three defects: “inadequate safety warning signs in the fire operation area (C22) → insufficient detail and quantification of special safety programs (C6) → not setting up the normative requirements of special safety programs (C2)”. The longest defect chain contained five defects: “inadequate standards of cable erection (C21) → confusion in the management of the frontline team (C23) → the tight schedule of organizing the construction (C9) → delays due to inefficient engineering changes (C24) → procedures not being streamlined (C2)”. The form of the defect chains clearly reflected the identification process from shallow to medium to deep.

4.5. Assessing the Degradation of Safety Management Performance

On the basis of identified safety management defects, the safety management performance of each functional component was assessed by the experts using the TFNs listed in Table 2. The initial fuzzy assessment $E^k$ was obtained. Then, the fuzzy assessment results were integrated by defuzzification using Formulas (2)–(9) to calculate the crisp assessment result $E$. The degree of degradation of the safety management performance of each functional component was determined by Formula (14), as shown in

Table 6. The degree of degradation of safety management performance.

Component	${\mathit{e}}_{\mathit{i}}$	${\mathit{d}}_{\mathit{i}}$	Component	${\mathit{e}}_{\mathit{i}}$	${\mathit{d}}_{\mathit{i}}$	Component	${\mathit{e}}_{\mathit{i}}$	${\mathit{d}}_{\mathit{i}}$
C1	3.091	22.73%	C11	3.147	21.33%	C21	2.328	41.80%
C2	2.814	29.65%	C12	2.626	34.35%	C22	2.672	33.20%
C3	3.147	21.33%	C13	3.154	21.15%	C23	2.542	36.45%
C4	2.632	34.20%	C14	3.219	19.53%	C24	2.727	31.83%
C5	2.749	31.28%	C15	3.147	21.33%	C25	2.714	32.15%
C6	2.676	33.10%	C16	2.854	28.65%	C26	2.418	39.55%
C7	3.103	22.43%	C17	2.513	37.18%	C27	2.827	29.33%
C8	3.114	22.15%	C18	2.573	35.68%	C28	3.262	18.45%
C9	2.764	30.90%	C19	3.191	20.23%	C29	2.714	32.15%
C10	2.457	38.58%	C20	2.549	36.28%	C30	2.542	36.45%

. The weight value for each functional component was obtained using Formula (15) according to the degree of influential impact $r_i$ (Table 5). Formula (16) was used to determine the assessment $P$ of the safety management performance of the SMS in the large-scale wastewater treatment plant construction project. Finally, Formula (17) was used to obtain the degree of degradation of the overall safety management performance. It was determined that the overall safety management performance of the SMS was assessed to be 2.821, achieving 70.52% of the expected performance level, which was between the moderate and good performance levels, with a corresponding degradation level of 29.48%.

In light of the assessments, the expert team determined that safety management performance should be at the level of “good” to be acceptable. According to Table 2, this indicates that the performance should be at least 75% of the expected performance. In other words, the degradation of safety management performance should not exceed 25%. To indicate the performance degradation of the functional components in a hierarchical manner and to provide an early warning, the functional component nodes that fell within the ranges of $[0, 25\%]$, $(25\%, 30\%)$, $(30\%, 35\%)$ and $[35\%, 100\%]$ were marked green, yellow, orange and red, respectively, as shown in Figure 6.

Figure 6 clearly shows the degree of performance degradation of the functional components in the SMS. Overall, the degradation of safety management performance represented a stepwise progression from source-driven factors, through to the major management factors, to the end implementation factors, visually reflecting the cumulative process leading to the degradation of safety management performance. It was clear that the most degraded areas (the red functional components) covered most of the end implementation factors and their adjacent major management factors. Obviously, this was not conducive to ensuring the integrated safety of the construction sites, thus creating an environment where safety-related incidents were more likely to occur. Therefore, it was crucial to implement corrective measures to contain the situation in a timely manner. Of note, the degree of degradation of the performance of C10 (safety-related information management), among the source-driven factors, was high, limiting the efficiency of safety-related collaboration by the management and reporting feedback at a fundamental level.

To ensure integrated safety at the frontline, it is imperative to develop short-term improvement strategies that promptly address the safety management defects in the proximal functional components, including C21, C18, C26, C20, C17, C23, C30, C25, C22, and C27. Long-term improvement strategies should be developed with due regard to the closer interactions between the source-driven factors and the major management factors, avoiding improvements to isolated functional components. Therefore, it was necessary to adopt a systemic mindset of collaborative improvement to address the safety management defects in the related functional components, including C10, C5, C6, C2, C4, C9, C29, C12, and C24. It should be noted that the selection of specific improvement measures requires further consideration of their economics and applicability, which is beyond the scope of this study and will not be discussed further. Finally, the expert team unanimously approved the improvement strategy, effectively avoiding blindness, fragmentation, and delays in decisions regarding improvement.

5. Discussion

Based on the functional components of the SMS in the illustrative example, it is evident that while there may be variations in the SMS from one construction project to another, the overall functional composition remains relatively consistent. The source-driven functional components, such as safety culture, safety management regulations, safety operating instructions, safety goals and their breakdown, leadership decisions, safety programs, and the management of safety-related information [58,59,60,61], serve as essential foundations for modern SMS. As for major management and end implementation, some differences in functional components arise due to variations in construction project types, scales, and regions [62]. Nonetheless, certain functional components, such as risk assessment, safety input, safety education and training, safety inspections, management of personal protection, fire management, and the management of equipment, facilities, and electricity, are prevalent across the board [63,64,65]. It is worth noting that some functional components, while not directly affiliated with the SMS, significantly impact the operation and performance of the SMS. Examples include planning for construction organization, management of the frontline team, engineering changes, etc. Therefore, it is necessary to incorporate these components into the complex network of the SMS.

The complex network of the SMS developed in the illustrative example effectively supports the basic idea that modern safety management is characterized by non-linearity and complexity [13,46]. It is evident that structured investigation methods (e.g., the safety checklist method) have significant limitations when dealing with complex non-linear systems, leading to safety management defects being considered locally or in isolation. In this regard, the traceability investigation method based on the influence paths between functional components proposed in this study aligns better with the objective reality of SMS in construction projects. It should be emphasized that the proposed investigation method does not conflict with the existing structured safety investigation method. This is because systematic investigations require a substantial amount of work and should not be conducted frequently as routine investigations; otherwise, it may seriously impact enterprise production. Therefore, the structured investigation method remains suitable for routine monitoring of the SMS, akin to routine maintenance. However, at specific intervals, adopting the proposed systematic investigation method, similar to major maintenance, becomes necessary. The relationship between these two approaches is complementary and supportive.

The identification results in the illustrative example were presented in the form of a chain of safety management defects, aligning with the philosophy of current non-linear safety management frameworks [14,15]. Kazaras pointed out that organizational flaws should not be seen in isolation but rather considered as a whole [13]. Therefore, the model proposed in this study is an extension of this perspective for specific applications in large construction projects. It can be seen that multiple safety management defects within the same functional component belong to different defect chains, enabling safety analysts to precisely pinpoint the location of safety management defects and understand their potential adverse effects. It is worth noting that some of the different safety management defects corresponded to the same deeper safety management defects. For instance, both “inadequate safety warning signs in the fire operation area” and “no clear space requirements and flow paths for the use of combustible materials” corresponded to the deeper defect of “insufficient detail and quantification of special safety programs”. Likewise, “insufficient clarity on the management needs of the frontline team” and “a lack of convenient and efficient feedback channels” both corresponded to the deeper defect of “lack of attention paid by the leadership to reporting feedback.” It is clear that if these deep-seated defects are not addressed, other new safety management problems may arise. This effectively supports the starting point of this study. In addition, the proposed method demonstrates promising results in identifying hidden safety management defects. For instance, the functional component C15 was assessed as having good performance, but the method identified a safety management defect within it (lack of education on safe behavior strategies in a complex environment).

Based on the visualization of the degradation of the functional components’ performance, it becomes evident that the deviations in the end implementation factors primarily originated from the larger number of inadequate safety management measures, which, in turn, stemmed from inadequate core drivers of the SMS. The visualization of the assessment results empowers safety analysts to grasp the state of degradation of safety management performance from a global perspective, facilitating a more systematic understanding of the process by which the accumulation of safety management defects leads to performance degradation. In addition, it is important to be alert to the muted state of affairs regarding the degradation of safety management performance, where good performance in terms of the end implementation factors masks the deep-seated safety management defects. In large construction projects, this deceptive state can lead to the erroneous assumption that there are few safety management issues. The failure to identify and address deep-seated defects in a timely manner can lead to the worsening of safety management performance. Therefore, comprehensive identification and visualization of the deep-seated defects by the method proposed in this study can provide a good early warning of the degradation of safety management performance.

6. Conclusions

Modern safety control theory suggests that the accumulation of safety management defects at the organizational level can lead to a degradation in the overall safety management performance, creating an environment that is conducive to safety-related incidents. This problem is exacerbated by the increasing complexity of managing safety in large construction projects. A literature review showed that grasping the complexity of safety management in large construction projects is crucial for a deeper identification of safety management defects and for an accurate assessment of safety management performance from a global perspective.

In this study, a new investigation and decision model was developed for assessing the degradation of the safety management performance of SMSs in large construction projects. The complex network of the SMS was constructed to visualize the interactions among the functional components, which was used to support deeper identification of the safety management defects and to reflect the degradation of safety management performance at the organizational level. The proposed model was verified using the example of a large-scale wastewater treatment plant construction project in Lanzhou City, China. According to the results, safety managers can obtain an accurate insight into the safety management defects of each functional component, as well as the degree of degradation of the safety management performance of the entire system. Timely short-term and systematic long-term improvement strategies were then developed to improve the performance of the functional components and the overall SMS.

A graphical representation of the functional components and interactions in an SMS helps to simplify the abstract understanding of complex management systems for safety practitioners, providing an index map for the deeper identification of safety management defects. The identification of the functional components should be performed by a team of experts in conjunction with the reality of specific construction projects, providing a more flexible description of the complex network of different SMSs and will thus have good applicability to different types and sizes of construction organizations. Meanwhile, the quantitative assessment of interactions among functional components provides a more accurate way to determine the importance and positioning of each functional component within the complex management system, effectively supporting the management philosophy of project complexity [17,66]. The case study indicated that process analysis, Delphi, and Fuzzy DEMATEL are reliable and accessible methods for capturing the interactions among the functional components in complex management systems. These methods can be applied in the future to investigate and assess the performance of complex SMS in other industries.

Compared with a list of safety management defects, this study proposes a new method of representing the defects as a chain, which can reflect the correlations between different defects. The network comprising defect chains enables a more systematic representation of the cumulative process of the degradation of safety management from the source-driven factors to the end implementation factors, which can provide sufficient support to help experts make an accurate assessment. Further, the degradation of each functional component can be presented in a complex visual network map to facilitate the understanding of the weak points or risk-sensitive areas throughout the SMS. Especially in the case of false safety perceptions, deep safety management defects can be identified in time to prevent a sudden collapse of the SMS by providing an early warning. Timely correction of poor safety management can lead to long-term sustainability and enhanced resilience.

Overall, this study was a new exploration of the specific application of non-linear safety control theory and complexity theory to the practice of safety management in large construction projects. The proposed investigation and decision model can provide a useful tool for safety analysts and safety managers who choose a systems theory approach to identifying safety management defects and providing assessment and early warning of declining safety management performance in the complex SMS. To achieve long-term stable safety management performance, it is recommended that construction companies, when applying the proposed model, should establish an information base on the safety management defects to provide reliable knowledge and information to the management. Given the randomness, repetitive nature, and concealment of safety management defects, it is necessary to conduct regular safety investigations and assessments of the complex SMS, in the same way that aircraft are regularly and thoroughly checked for faults. It should be noted that while the proposed model has been validated in a specific construction project, the appropriate period of its application has not yet been clarified. In this regard, the potential adverse impact of frequent, systematic investigations on enterprise production needs to be fully considered. Therefore, future research needs to focus on clarifying how to determine the appropriate investigation cycle for different construction organizations. Additionally, there is a need to further expand the application of the proposed model in different types of large construction projects in order to continuously improve the applicability of the proposed model.