Network Model Analysis of Quality Control Factors of Prefabricated Buildings Based on the Complex Network Theory

: Prefabricated buildings are gradually gaining popularity in China because of their lower costs, shorter construction periods, and environmental friendliness. However, compared with traditional buildings, prefabricated buildings require coordination and management of processes such as component production, transportation and storage, and on-site component assembly. Therefore, managing the quality of prefabricated buildings is complex. In order to manage the quality of prefabricated buildings better, it is necessary to study the quality systems of prefabricated buildings. Firstly, by analyzing the logical relationship of each stage of the prefabricated buildings, we identiﬁed the key stages. Then, the main quality control factors that affect the qualities and relationships of the main quality control factors were derived by combining relevant building codes, literature studies, and project experiences; a network model of quality control factors of prefabricated buildings (NQPB) was constructed. Secondly, the complex network theory was applied to analyze the node degree, betweenness centrality, clustering coefﬁcient, and other indicators of the NQPB to derive 17 key quality control factor nodes. The importance of the 17 key nodes in the quality management of prefabricated buildings was veriﬁed through a simulation. Next, the NQPB of Project A was constructed and analyzed, and ﬁve key nodes were identiﬁed. This demonstrates how the NQPB method can be applied to a speciﬁc prefabricated building project. Moreover, Project A was used as a case study to compare fault tree analysis (FTA), ﬁshbone diagram, and 4MIE methods with the NQPB method to derive the potential advantages of the NQPB method. Finally, further analysis led to recommendations for quality management of prefabricated building projects in general as well as for Project A. This study can be used as a reference for quality control and assurance managers in all stages of prefabricated buildings and provide new ideas and methods for the quality analysis and management of prefabricated buildings.


Introduction
Prefabricated buildings are buildings in which the main parts of their structural systems, peripheral protection systems, equipment and pipeline systems, and interior decoration systems are integrated with prefabricated parts [1].There are two main differences between prefabricated buildings and traditional buildings.First, the scope (in the broad sense of the construction sites in prefabricated buildings) is larger.In addition to the construction site, the component manufacturing plant is also considered part of the construction site.This is because some of the components of a prefabricated building are prefabricated in the component production factory rather than cast in place on the construction site.Second, the construction of prefabricated buildings also needs to consider the assembly technology of prefabricated components [2].
In recent years, with the development of China's economy, the construction industry has demanded faster construction schedules, higher construction quality, and more environmental friendliness.The construction of prefabricated buildings, compared with the construction of traditional buildings, has potential advantages.Including reduced construction times [3], building quality improvements [4], and lower resource waste [5], which can better meet the needs of the construction industry.Therefore, prefabricated buildings have been developed.However, the change in the production mode of prefabricated buildings has generated many quality problems [6].Furthermore, imperfect management mechanisms and fragmentation of the prefabricated building construction process make it difficult to effectively control the construction quality of prefabricated buildings [7].Yin et al. [8] argued that in prefabricated building projects, quality control and assurance managers need to enhance quality management in order to address prominent quality issues.Therefore, the quality systems of prefabricated buildings need to be studied to better manage the quality of prefabricated buildings.
At present, research on the quality analysis and management of prefabricated buildings has become a hot spot.Zhou [9] sorted out the main points of the whole process of prefabricated concrete residential building design, summarized possible design problems, and proposed solutions.Chang et al. [10] and Su et al. [11] analyzed the factors that lead to common quality problems in prefabricated buildings and proposed quality management measures.Qi et al. [12] classified the common quality problems in the construction process of assembled buildings, analyzed their causes, and made suggestions.Wenyi Cheng [13] analyzed the problems associated with construction quality in each stage of building industrialization and analyzed the factors of construction quality control in building industrialization construction using traditional quality management methods of construction projects.Duan et al. [14] analyzed the common quality problems in the construction of prefabricated buildings and proposed measures.Cao et al. [2] proposed a three-stage quality management system for the quality management of prefabricated buildings based on BIM and proposed quality control processes and management measures based on BIM according to the quality management requirements of prefabricated buildings.
Many scholars have also carried out research on the quality analysis and management of traditional buildings, providing theoretical bases as well as new ideas for the research on prefabricated building quality and its management.In [15][16][17], the authors analyzed the importance of the design phase, construction phase, and engineering survey on construction quality, and proposed corresponding measures to facilitate the improvement of construction quality.Zhang and Zhang [18] established a building quality control network system based on construction specifications and preventive measures.Moreover, del Solar Serrano et al. [19] applied the Plan, Do, Check, Act (PDCA) cycle, proposed a procedure based on a continuous improvement project, and applied this procedure to ceramic tiling execution.The results showed that the procedure was effective in reducing the number of defects and was suitable to control the execution of the construction units of a building.Hou et al. [20] analyzed the traversal relationship between the management objects in each stage of the project and obtained the logical order among the management objects.The above research reflects a trend that scholars are beginning to realize that the construction quality management system is a complex system with complex relationships among its internal factors; researchers are beginning to use systems science and complex network approaches in the study of construction quality and its management.
Barabás and Albert [21] and Watts and Strogatz [22] proposed scale-free networks and "small-world" networks, respectively.Since then, scholars have been studying the stability of complex networks.Albert et al. [23] studied the stability of scale-free networks after attacks through simulation experiments and found that scale-free networks are highly faulttolerant to random failures while being vulnerable to attacks.Bellingeria et al. [24] applied five attack strategies to simulate attacks on six different networks, and the results show that the stability of the network under different attack strategies depends on the topology of the network.These studies provide a method to study the overall nature of complex networks and lay the foundation for the application of complex networks in various fields.Some scholars have started to apply complex networks in quality management.Wan et al. [25] derived the important nodes of the supply chain quality network through a complex network analysis and proposed corresponding management strategies.Zhang et al. [26] established a quality management network for printed circuit board (PCB) production and obtained the focus on PCB quality improvement and management through a complex network analysis.
In the field of construction project management, Zhang et al. [27] constructed a complex network model of the causes of tower crane safety accidents and identified nine key causes, three groups of strongly correlated causes, and three key network links leading to tower crane safety accidents.Guo et al. [28] mapped and analyzed a network of behavioral risk chains of building construction accidents and derived the interactions between unsafe behaviors in building construction accidents.Kereri and Harper [29] analyzed the literature and found that the application of social network analysis in construction management research has a clear upward trend.Several authors have used social network analysis to construct a social network model, conducting quantitative analysis using Ucient software.They studied how social network analysis methods are applied in the organization and management of construction projects [30].Li et al. [31] applied a social network analysis to identify and investigate potential networks of risk factors associated with stakeholders in prefabricated residential construction projects, and the analysis yielded key risks in the network that affected the schedule and their interactions.
To summarize, the complex network theory has many applications in the research of construction project management, but less in the research on quality analysis and the management of prefabricated buildings and traditional buildings.A majority of the existing research only analyzes the quality influencing factors of prefabricated buildings, and does not analyze the relationship between the quality influencing factors.In the field of quality analysis and management of traditional buildings, scholars have begun to realize that the building quality system is complex, and they are using the network method to conduct research.However, there is no in-depth analysis of the relationship between the quality control factors.
Based on this, this paper is extended from the literature [32].This paper extends its abstract, introduction, network model analysis of quality control factors of prefabricated buildings, conclusions, and references sections.We added the case study, and suggestions for quality management of prefabricated buildings sections, as well as the simulation verification subsection.Firstly, we constructed an NQPB.Then, by calculating the topological indicators of the network, the network characteristics and the relationship between each quality control factor were analyzed in depth.Next, through the analysis of project A, the application of the NQPB method in a specific prefabricated building project was demonstrated.Using Project A as the object of analysis, we selected FTA, the fishbone diagram, and the 4MIE method to compare with the NQPB method; we conclude with the potential advantages of the NQPB method.Finally, we propose suggestions for the quality management of prefabricated buildings, accordingly.

Key Stages of Quality Management of Prefabricated Buildings
Studying the logical relationship of each stage of the prefabricated building project is conducive to finding out the key stages of quality management of prefabricated buildings, and laying the foundation for the following research.

The Relationship between the Stages of Prefabricated Buildings
The prefabricated building project generally has five stages; we analyzed the logical relationship between the stages, as shown in Figure 1.In the design-bid-build mode, the owners determine the design company through a bidding process.After the design company completes the engineering design, the owners determine the contractors and the component production factory, respectively, through bidding [20,33].Then, the construction stage and the component production stage begin.The contractors start to develop the construction plan, make the schedule plan, conduct site leveling, and other preliminary preparations [10,20].The component production factory starts to develop the production plan and studies the relevant drawings.After the relevant materials arrive, the fabrication of the components starts immediately.International procurement methods of construction materials and equipment for building projects include owner procurement, contractor procurement, etc. [34].If the owner is responsible for procurement, the owner may sign a procurement contract with the materials and equipment supplier.Then, the materials and equipment supplier will transport construction materials to the contractors and component production factory in a timely manner according to the project needs.If the contractor is responsible for procurement, the contractors and the component production factory will be responsible for the procurement of construction materials according to the project needs, which are carried out in the construction stage and the component production stage, respectively.In the engineering procurement construction (EPC) mode, the general contractor is responsible for the design, procurement, component production, and construction of the project [33].Therefore, in the EPC mode, the general contractor is responsible for the procurement of equipment and materials.
company completes the engineering design, the owners determine the contractors and the component production factory, respectively, through bidding [20,33].Then, the construction stage and the component production stage begin.The contractors start to develop the construction plan, make the schedule plan, conduct site leveling, and other preliminary preparations [10,20].The component production factory starts to develop the production plan and studies the relevant drawings.After the relevant materials arrive, the fabrication of the components starts immediately.International procurement methods of construction materials and equipment for building projects include owner procurement, contractor procurement, etc. [34].If the owner is responsible for procurement, the owner may sign a procurement contract with the materials and equipment supplier.Then, the materials and equipment supplier will transport construction materials to the contractors and component production factory in a timely manner according to the project needs.If the contractor is responsible for procurement, the contractors and the component production factory will be responsible for the procurement of construction materials according to the project needs, which are carried out in the construction stage and the component production stage, respectively.In the engineering procurement construction (EPC) mode, the general contractor is responsible for the design, procurement, component production, and construction of the project [33].Therefore, in the EPC mode, the general contractor is responsible for the procurement of equipment and materials.In the design-bid-build and EPC modes, the main construction process of a prefabricated building involves the following stages: design-component productionconstruction-operation [4,33,35].Since the component production stage and construction stage in the construction of a prefabricated building are not completely independent, the work between them may be carried out simultaneously [36].Therefore, the component production stage and the construction stage in Figure 1 are in a relatively parallel relationship.
As can be seen from Figure 1, process 1 means that owners send the project development requirements and description of the design task, etc., to the design company.Processes 2 and 3, respectively, refer to the design company sending the design drawings to the component production factory and the contractors.Generally, processes 2 and 3 are performed simultaneously.Process 4 refers to the transportation of the components to the construction site after the component production factory has completed the component production and quality inspection.Moreover, the quality of the components will be checked by the contractors before they enter the construction site.Process 5 means that in the construction stage if the contractors find the design drawings unreasonable, they will give feedback to owners, owners will send the information to the design company, and the design company will modify the design.Process 6 means that after the completion of In the design-bid-build and EPC modes, the main construction process of a prefabricated building involves the following stages: design-component production-constructionoperation [4,33,35].Since the component production stage and construction stage in the construction of a prefabricated building are not completely independent, the work between them may be carried out simultaneously [36].Therefore, the component production stage and the construction stage in Figure 1 are in a relatively parallel relationship.
As can be seen from Figure 1, process 1 means that owners send the project development requirements and description of the design task, etc., to the design company.Processes 2 and 3, respectively, refer to the design company sending the design drawings to the component production factory and the contractors.Generally, processes 2 and 3 are performed simultaneously.Process 4 refers to the transportation of the components to the construction site after the component production factory has completed the component production and quality inspection.Moreover, the quality of the components will be checked by the contractors before they enter the construction site.Process 5 means that in the construction stage if the contractors find the design drawings unreasonable, they will give feedback to owners, owners will send the information to the design company, and the design company will modify the design.Process 6 means that after the completion of the construction stage, the prefabricated building is officially delivered to owners, and owners entrust a property management company to manage the operation of the building.In addition, there is no clear sequence between the component production stage and the construction stage.However, in terms of completion time, the component production stage ends earlier than the construction stage.

Key Stages of Quality Management of Prefabricated Buildings
It can be seen from Figure 1 that the key stages affecting the quality of prefabricated buildings are the design, component production, and construction stage.To better classify and analyze each quality control factor, it is necessary to summarize and subdivide the three key stages.The following stage divisions are referenced to [10,34,36].
The construction stage has a relatively long duration and it contains a lot of work.In order to better analyze the quality control factors in the construction stage, this paper subdivides the construction stage into the construction preparation, construction, construction management, and completion acceptance stages.In addition, since the construction stage includes the acceptance, stacking, and maintenance of components, such work is highly related to the work in the component production stage, so this kind of work is combined with the work in the component production stage to form the component supply and management stage.Finally, six key stages of quality management of prefabricated buildings are obtained.They are design, component supply and management, construction preparation, construction, construction management, and completion acceptance stages.

Quality Control Factors of Prefabricated Buildings
First, the quality control factors of prefabricated buildings were extracted from the building codes [1] and literature [9][10][11][12][13][14]35].Then, duplicate factors and factors with little frequency of occurrence were removed.Moreover, factors with similar meanings were merged.Finally, these factors were categorized according to the six key stages, and the quality control factors of prefabricated buildings were obtained (see Table 1).In Table 1, numbers 1-10, 11-19, 20-24, 25-41, 42-47, and 48, 49 belong to the design, component supply and management, construction preparation, construction, construction management, and completion acceptance stages, respectively.Numbers 50-55 are six key stages and numbers 56-59 are four major quality defects.In addition, standard components refer to those with uniform parameters, such as size and reinforcement [9], which facilitate mass production by the component production factory.Non-standard components in number 12 refer to those with different parameters, such as size and reinforcement from standard components.

Construct a Network Model
According to the complex network theory, the quality control factors are regarded as "nodes", and the relationship between the quality control factors is regarded as "edges", and a complex network can be constructed.
Step 1, we construct the adjacency matrix.First, we draw an interrelationship digraph [26] containing the quality control factors in Table 1.Then, based on the literature [9][10][11][12][13][14] and project experience, we analyze the relationships among the quality control factors and complete the interrelationship digraph.Figure 2 shows the interrelationship digraph of some quality control factors.In Figure 2, the factor 'poor quality of component drawings' has arrows pointing to the factor 'components of poor quality', which indicates that the factor 'poor quality of component drawings' affects the factor 'components of poor quality'.Finally, the adjacency matrix is constructed according to the interrelationship digraph and the rules for constructing the adjacency matrix.
Buildings 2022, 12, x FOR PEER REVIEW Step 1, we construct the adjacency matrix.First, we draw an interrelationship [26] containing the quality control factors in Table 1.Then, based on the literatu and project experience, we analyze the relationships among the quality control fac complete the interrelationship digraph.Figure 2 shows the interrelationship di some quality control factors.In Figure 2, the factor 'poor quality of component d has arrows pointing to the factor 'components of poor quality', which indicates factor 'poor quality of component drawings' affects the factor 'components quality'.Finally, the adjacency matrix is constructed according to the interrela digraph and the rules for constructing the adjacency matrix.The establishment rule of the adjacency matrix is: if node 1 influences no relationship between node 1 and node 2 12 1 a = , otherwise it is 0. 12 1 a = is rep in the network as having a directed edge at node 1 pointing to node 2. For exam quality control factor 3 may have a negative impact on the quality of component d so 3,10 1 a = .Meanwhile, the quality control factor 10 may negatively affect com quality, so 10,11 1 a = .
Step 2, build the NQPB.First, write the adjacency matrix to an empty Exce save it.Then, open Gephi, click 'Import Spreadsheet' under the 'File' menu, and s Excel file above.Subsequently, under 'Import As', select 'Matrix', and click ne click 'Finish'.Next, in the 'Import Report' window, select 'Graph Type' as dire select 'New Workspace'.Finally, click 'OK' to generate an unweighted directed N The network model has 59 nodes (the node numbers are consistent with Tab 198 edges, as shown in Figure 3.The establishment rule of the adjacency matrix is: if node 1 influences node 2, the relationship between node 1 and node 2 a 12 = 1, otherwise it is 0. a 12 = 1 is represented in the network as having a directed edge at node 1 pointing to node 2. For example, the quality control factor 3 may have a negative impact on the quality of component drawings, so a 3,10 = 1.Meanwhile, the quality control factor 10 may negatively affect component quality, so a 10,11 = 1.
Step 2, build the NQPB.First, write the adjacency matrix to an empty Excel file and save it.Then, open Gephi, click 'Import Spreadsheet' under the 'File' menu, and select the Excel file above.Subsequently, under 'Import As', select 'Matrix', and click next.Then, click 'Finish'.Next, in the 'Import Report' window, select 'Graph Type' as directed and select 'New Workspace'.Finally, click 'OK' to generate an unweighted directed NQPB.
The network model has 59 nodes (the node numbers are consistent with Table 1) and 198 edges, as shown in Figure 3.

Key Nodes in the NQPB
In this paper, the method of a complex network is used to calculate the topological properties of the NQPB.The average path length, diameter, density, and clustering coefficient indicators of the network selected below are good measures of the overall topological properties of the network [23,37,38] and reflect the difficulty of quality management of NQPB.The following selected node degrees, clustering coefficient, betweenness centrality, and eigenvector centrality indicators are good measures of the importance of the nodes in the network [25,26,38,39], and help to find the important nodes in NQPB.The five nodes with larger node degrees, clustering coefficient, betweenness centrality, and eigenvector centrality derived below are used to identify the key nodes that lead to major quality defects in prefabricated buildings.Therefore, these nodes do not include the six key stage nodes and four quality defective nodes.The following definitions and formulas refer to [38].
The average path length and diameter.In [32], the authors used Gephi to calculate the average path length and diameter.The calculation of Gephi differs from the equations and definitions provided in [32], but does not affect the conclusions of literature [32].In this paper, this has been modified.In a directed network, the average path length refers to the average distance between any two unidirectionally connected nodes.The average path length measures the connection efficiency between the nodes in the network.The lower the node connection efficiency of NQPB, the slower the propagation of the quality control factor node problems in the network and the less likely to generate quality problems.Directed network diameter ( D ) refers to the maximum distance between any two unidirectionally connected nodes in the network.The smaller the network diameter, the closer the nodes of the network are to each other, and the more likely to generate quality problems.The formula of the network diameter is as follows: ,

Network Model Analysis of Quality Control Factors of Prefabricated Buildings 4.1. Key Nodes in the NQPB
In this paper, the method of a complex network is used to calculate the topological properties of the NQPB.The average path length, diameter, density, and clustering coefficient indicators of the network selected below are good measures of the overall topological properties of the network [23,37,38] and reflect the difficulty of quality management of NQPB.The following selected node degrees, clustering coefficient, betweenness centrality, and eigenvector centrality indicators are good measures of the importance of the nodes in the network [25,26,38,39], and help to find the important nodes in NQPB.The five nodes with larger node degrees, clustering coefficient, betweenness centrality, and eigenvector centrality derived below are used to identify the key nodes that lead to major quality defects in prefabricated buildings.Therefore, these nodes do not include the six key stage nodes and four quality defective nodes.The following definitions and formulas refer to [38].
The average path length and diameter.In [32], the authors used Gephi to calculate the average path length and diameter.The calculation of Gephi differs from the equations and definitions provided in [32], but does not affect the conclusions of literature [32].In this paper, this has been modified.In a directed network, the average path length refers to the average distance between any two unidirectionally connected nodes.The average path length measures the connection efficiency between the nodes in the network.The lower the node connection efficiency of NQPB, the slower the propagation of the quality control factor node problems in the network and the less likely to generate quality problems.Directed network diameter (D) refers to the maximum distance between any two unidirectionally connected nodes in the network.The smaller the network diameter, the closer the nodes of the network are to each other, and the more likely to generate quality problems.The formula of the network diameter is as follows: where d ij is the distance from node i to node j.After the Gephi calculation, we know that the average path length of the network is 1.929, indicating that any two unidirectionally connected nodes only need one node on average to contact.The diameter of the network is 4, indicating that any two unidirectionally connected nodes need at most three nodes to contact.The above data show that the quality control factors are closely related.Network density (ρ) refers to the ratio of the number of edges actually present in the network to the maximum possible number of edges in the network.The formula is as follows: where M is the actual number of edges in the network, N is the number of nodes in the network.The network density can measure the closeness of the connection between the nodes in the network.The greater the density of the NQPB, the more closely connected the nodes of quality control factors are, the more difficult the quality management is, and the more likely to cause quality problems in prefabricated buildings.Node degree.Node degree (k i ) in directed networks includes out-degree and in-degree.Out-degree (k out i ) refers to the number of edges from node i to other nodes, in-degree (k in i ) refers to the number of edges pointing from other nodes to node i.The out-degree, in-degree and degree of node i can be expressed as: where N is the number of nodes in the network, a ij denote the edge from node i to node j.The in-degree, out-degree, and degree of a node measure how much the node is connected to other nodes.The more node i is connected to other nodes, the more influence node i has on the network and the more important the node i is in the network.Through calculations, five nodes with larger in-degrees, out-degrees, and degrees are obtained, respectively, as shown in Table 2.The findings in Table 2   Clustering coefficient.The clustering coefficient of the network (C) refers to the average of the clustering coefficients of all nodes in the network.The formula is as follows: The larger the clustering coefficient of the NQPB, the stronger the connection between the nodes in the network and the more likely to cause quality problems in prefabricated buildings.Using Gephi for calculation, the clustering coefficient of the NQPB is 0.187, which is relatively high.
The clustering coefficient (C i ) refers to the probability of the connection between any two neighbor nodes of node i. C i is defined as: where E i refers to the number of edges between the k i neighboring nodes of node i.Combined with the node degree, it is concluded that the five nodes with larger clustering coefficients are: 8, 30, 3, 6, and 34.The higher the clustering coefficient of a node, the closer the relationship between the neighbor nodes of the node.In quality management, if there is a problem with these five nodes, it is very easy to have a chain reaction and affect its neighbor nodes.Therefore, we should focus on controlling the five nodes with larger clustering coefficients.Betweenness centrality.Betweenness centrality (BC i ) describes the shortest paths passing through a node; the formula is as follows: where g st denotes the shortest paths between nodes s and t, n i st denotes the shortest paths passing through node i among the g st shortest paths from node s to node t.The betweenness centrality of a node measures the role of the node in propagating among the nodes in the network.Through calculation, it is concluded that the top 5 nodes in betweenness centrality are 11, 4, 29, 36, and 27, indicating that these nodes have a significant role in the network connection.Therefore, we should focus on controlling the above five nodes.
Eigenvector centrality.The basic idea of eigenvector centrality is that the importance of a node depends on the number of its neighbor nodes and also on the importance of its neighbor nodes.The greater the eigenvector centrality of a node, the more important the node is.Through calculations, it is concluded that the five nodes with the larger eigenvector centralities are: 35, 36, 39, 40, and 38, indicating that the nodes connected to them are relatively important.Therefore, managing these five nodes well can improve the quality of prefabricated buildings.

Simulation Verification
In the NQPB, 17 key nodes play an important role and can directly affect the quality of prefabricated buildings.If project parties in each stage of the prefabricated buildings can correct and avoid the problems of these 17 key nodes in their work, they can effectively disintegrate the NQPB and improve the quality of prefabricated buildings.To quantitatively and qualitatively demonstrate this, this paper conducted simulations via Python, attacking key nodes sequentially, one node at a time, according to their serial numbers, from smallest to largest.Moreover, after each attack, the number of nodes, number of edges, average path length, clustering coefficient, and network density of the NQPB were calculated.The simulation results are shown in Figures 4-6.Among them, the average path length, clustering coefficient, and network density were normalized (by maximum-minimum) for the purpose of analysis and comparison.
quantitatively and qualitatively demonstrate this, this paper conducted simulations via Python, attacking key nodes sequentially, one node at a time, according to their serial numbers, from smallest to largest.Moreover, after each attack, the number of nodes, number of edges, average path length, clustering coefficient, and network density of the NQPB were calculated.The simulation results are shown in Figures 4-6.Among them, the average path length, clustering coefficient, and network density were normalized (by maximum-minimum) for the purpose of analysis and comparison.quantitatively and qualitatively demonstrate this, this paper conducted simulations via Python, attacking key nodes sequentially, one node at a time, according to their serial numbers, from smallest to largest.Moreover, after each attack, the number of nodes, number of edges, average path length, clustering coefficient, and network density of the NQPB were calculated.The simulation results are shown in Figures 4-6.Among them, the average path length, clustering coefficient, and network density were normalized (by maximum-minimum) for the purpose of analysis and comparison.According to Figures 4 and 5, it can be seen that the number of nodes and the number of edges of the NQPB decreased after the key nodes were attacked.Among them, the number of edges decreases faster, from 198 to 70.This is due to the fact that the key nodes affected many nodes with high node degrees, and the edges connected to them dissipated According to Figures 4 and 5, it can be seen that the number of nodes and the number of edges of the NQPB decreased after the key nodes were attacked.Among them, the number of edges decreases faster, from 198 to 70.This is due to the fact that the key nodes affected many nodes with high node degrees, and the edges connected to them dissipated after the key nodes were attacked.The decrease in the number of nodes and edges indicates that the integrity of the network structure decreases and is less likely to cause quality problems in the prefabricated building.
According to Figure 6, it can be seen that the network density and clustering coefficient of the NQPB decreased after the key nodes were attacked, while the average path length increased.The decrease in network density and clustering coefficient indicates that the connections between the nodes of the NQPB become sparse and do not easily lead to the quality problems of the prefabricated buildings.The rise in the average path length indicates that the average distance of unidirectionally connected node pairs of the NQPB rises, the average connection efficiency of the unidirectionally connected node pairs of the NQPB decreases, and the problems of individual nodes do not easily cause the quality problems of the prefabricated buildings.
After attacking the 17 key nodes, the NQPB becomes sparse and the number of edges pointing to the four quality defective nodes decreases, as shown in Figure 7.This indicates that the network in Figure 7 circumvents some of the situations that lead to quality defects in prefabricated buildings.Based on the analysis of the above simulation results, it can be seen that after the 17 key nodes of the NQPB were attacked, the NQPB was disintegrated, the connections between the nodes became sparse, the efficiency of the connections between the nodes decreased, and the number of edges pointing to the four quality defective nodes decreased.This makes it difficult to form links to the quality defective nodes in the NQPB and enables managers to better control the quality of prefabricated buildings.This fully illustrates that the 17 key nodes play an important role in the quality management of prefabricated buildings.Based on the analysis of the above simulation results, it can be seen that after the 17 key nodes of the NQPB were attacked, the NQPB was disintegrated, the connections between the nodes became sparse, the efficiency of the connections between the nodes decreased, and the number of edges pointing to the four quality defective nodes decreased.This makes it difficult to form links to the quality defective nodes in the NQPB and enables managers to better control the quality of prefabricated buildings.This fully illustrates that the 17 key nodes play an important role in the quality management of prefabricated buildings.

Case Study
The NQPB analyzed above contains common quality control factor nodes, but in a specific prefabricated building project, all of the problems regarding quality control factor nodes in the NQPB may not exist.Therefore, the NQPB needs to be adjusted in some way when applied to a specific prefabricated building project.The following project example is referenced in the literature [36].

Analysis Process
The quality management analysis process for a specific prefabricated building project using the NQPB method is shown in Figure 8. First, information about the project was collected and analyzed to identify the quality management issues that exist in the project.
Then, the quality control factors in Table 1, corresponding to each quality management problem present in the project, were identified and the next level nodes that may result from these quality control factor nodes were identified.The unidentified quality control factor nodes represent the quality management issues that do not exist in the project.The more nodes unidentified, the fewer quality management problems of the project, the sparser the NQPB of the project, and the less likely to generate quality problems.Therefore, in the NQPB constructed above, the unidentified nodes were deleted to obtain the NQPB of the project.
Next, several topological indicators of the NQPB of the project were calculated, and the key nodes and stages of the project were derived.
Finally, based on the results of the above analysis, quality management recommendations are proposed for the project.

Basic Information of Project A
Project A is located in the easternmost part of the economic development zone of Laiwu District, Jinan City, near Cheng Story Industrial Park, and near the coach terminal of Laiwu District, with convenient transportation.
Project A is the first assembled concrete public building in the Laiwu District, including a comprehensive teaching building, practical training building, gymnasium, and two closed corridors connecting the buildings, with an assembly rate of 80%.The construction area of the comprehensive teaching building is 30,264.88square meters, the construction area of the practical training building is 34,216.96square meters with a height of 31.997m, and the gymnasium has an above-ground construction area of 7537.1 square meters and an underground construction area of 3564.7 square meters with an overall height of 32.1 m.The contract period was 300 days.First, information about the project was collected and analyzed to identify the quality management issues that exist in the project.
Then, the quality control factors in Table 1, corresponding to each quality management problem present in the project, were identified and the next level nodes that may result from these quality control factor nodes were identified.The unidentified quality control factor nodes represent the quality management issues that do not exist in the project.The more nodes unidentified, the fewer quality management problems of the project, the sparser the NQPB of the project, and the less likely to generate quality problems.Therefore, in the NQPB constructed above, the unidentified nodes were deleted to obtain the NQPB of the project.
Next, several topological indicators of the NQPB of the project were calculated, and the key nodes and stages of the project were derived.
Finally, based on the results of the above analysis, quality management recommendations are proposed for the project.

Basic Information of Project A
Project A is located in the easternmost part of the economic development zone of Laiwu District, Jinan City, near Cheng Story Industrial Park, and near the coach terminal of Laiwu District, with convenient transportation.
Project A is the first assembled concrete public building in the Laiwu District, including a comprehensive teaching building, practical training building, gymnasium, and two closed corridors connecting the buildings, with an assembly rate of 80%.The construction area of the comprehensive teaching building is 30,264.88square meters, the construction area of the practical training building is 34,216.96square meters with a height of 31.997m, and the gymnasium has an above-ground construction area of 7537.1 square meters and an underground construction area of 3564.7 square meters with an overall height of 32.1 m.The contract period was 300 days.

Construct and Analyze the NQPB of Project A
This paper combines the quality management problems of Project A summarized in the literature [36] and the quality control factors in Table 1, and finds that many of the quality management problems of Project A can correspond exactly to the quality control factors in Table 1.Table 3 summarizes the quality management problems and quality control factor nodes of Project A, which can help us to construct an NQPB belonging to Project A. The NQPB of Project A should include the quality control factor nodes in Table 3 and the nodes directly caused by them.This is because some quality management problems that occur when conducting quality management of prefabricated buildings may cause other problems and even chain reactions.Therefore, when conducting a quality management analysis of prefabricated buildings, the current problems, as well as the potential problems, need to be taken into account.
The NQPB of Project A is shown in Figure 9.
After the Gephi calculation, the number of nodes in the network was 33, the number of edges was 102, the diameter of the network was 3, the network density was 0.097, the clustering coefficient of the network was 0.23, and the average path length was 1.769.Accordingly, it can be seen that the NQPB of Project A was a connected graph, the network size was small, the connection between nodes was tight, and the diameter of the network was small.This indicates that in the quality management of Project A, the key nodes should be controlled in time to reduce the spread of problems.Moreover, by observing Figure 9 and Table 3, it can be seen that only quality defective node 56 occurred in Project A and could lead to quality defective node 57.Therefore, the quality problem of Project A was relatively minor.
The NQPB of Project A should include the quality control factor nodes in Table 3 and the nodes directly caused by them.This is because some quality management problems that occur when conducting quality management of prefabricated buildings may cause other problems and even chain reactions.Therefore, when conducting a quality management analysis of prefabricated buildings, the current problems, as well as the potential problems, need to be taken into account.
The NQPB of Project A is shown in Figure 9.  Through the Gephi calculation, important nodes with larger out-degrees, in-degrees, degrees, clustering coefficients, and eigenvector centralities were derived, respectively, as shown in Table 4.According to Table 4, nodes 36, 35, 29, 39, and 11 appeared more than once, which indicates that these nodes play an important role in the network and are the key nodes in the quality management of Project A. From the distribution of key nodes, Project A has more problems in the construction stage, followed by the component supply and management stage.Therefore, the construction stage and the component supply and management stage are important stages of quality management of Project A. Moreover, it is important to focus on managing the nodes of quality control factors that already exist in Project A in Table 3.

Potential Advantages of the NQPB Method
The NQPB method aims to analyze the whole process management of prefabricated buildings from a systematic perspective and identify the problems and potential problems comprehensively, thus helping prefabricated building quality control and assurance managers to better manage the quality of prefabricated buildings.
In quality management, the FTA, fishbone diagram, and 4MIE methods can all identify the quality control factors of a project.Among them, FTA identifies the causes of construction quality problems in a project and establishes logical relationships between the causes of every specific quality problem [40].The fishbone diagram aims to use a step-by-step inductive approach to find the causes of project quality problems [41].Moreover, 4M1E classifies the factors that measure the level of quality into humans, materials, machines, methods, and the environment [42], which can identify the causes of project quality problems in a comprehensive way.
In this paper, Project A was used as an example, the above three methods were selected to compare with the NQPB method, and the potential advantages of the NQPB quality management analysis method were derived.

Faster and More Comprehensive Identification of Quality Control Factors
The quick and comprehensive identification of quality control factors was the key to performing quality management in Project A. Here, the above four methods were used to identify the quality control factors of Project A separately.
The process of identifying the quality control factors of Project A differed among the four methods, and the time required to identify them also differed.When using the four methods, quality control and assurance managers needed to collect and analyze Project A's information comprehensively to identify the quality control factor nodes that already existed.Therefore, using any of the four methods can comprehensively identify the existing quality control factor nodes.The following describes the process of using the four methods to identify the quality control factors of Project A.
Using the FTA method, a fault tree needs to be constructed first.Building a fault tree requires identifying all possible quality issues of Project A and designating these quality issues as top events.Then, the fault tree is drawn by analyzing the possible causes of each top event until the root causes of each top event are found.After mapping the fault trees, the relevant managers identify the upper-level events of the already existing quality control factor nodes in each fault tree.These upper-level events are the potential quality control factor nodes that may result from the already existing quality control factor nodes.Finally, since the FTA method generally considers the bottom event of the fault tree to be the root cause of the top event, the FTA method will consider the already existing quality control factor nodes of Project A as the critical quality control factor nodes.
Using the fishbone diagram method, a fishbone diagram needs to be drawn first.First, take the quality problem of Project A as the main arrow.Then, identify the big bone (big cause) that leads to the quality problem, then identify the medium bone (medium cause) that leads to the big bone, and the small bone (small cause) that leads to the medium bone.Finally, a fishbone diagram is drawn.Figure 10  The process of identifying the quality control factors of Project A differed among the four methods, and the time required to identify them also differed.When using the four methods, quality control and assurance managers needed to collect and analyze Project A's information comprehensively to identify the quality control factor nodes that already existed.Therefore, using any of the four methods can comprehensively identify the existing quality control factor nodes.The following describes the process of using the four methods to identify the quality control factors of Project A.
Using the FTA method, a fault tree needs to be constructed first.Building a fault tree requires identifying all possible quality issues of Project A and designating these quality issues as top events.Then, the fault tree is drawn by analyzing the possible causes of each top event until the root causes of each top event are found.After mapping the fault trees, the relevant managers identify the upper-level events of the already existing quality control factor nodes in each fault tree.These upper-level events are the potential quality control factor nodes that may result from the already existing quality control factor nodes.Finally, since the FTA method generally considers the bottom event of the fault tree to be the root cause of the top event, the FTA method will consider the already existing quality control factor nodes of Project A as the critical quality control factor nodes.
Using the fishbone diagram method, a fishbone diagram needs to be drawn first.First, take the quality problem of Project A as the main arrow.Then, identify the big bone (big cause) that leads to the quality problem, then identify the medium bone (medium cause) that leads to the big bone, and the small bone (small cause) that leads to the medium bone.Finally, a fishbone diagram is drawn.Figure 10   According to the characteristics of the fishbone diagram, the small bones, medium bones, and big bones in the fishbone diagram generally cannot be repeated.Moreover, each big bone of the fishbone diagram is generally parallel and causal analysis will be performed for each big bone separately.Therefore, the fishbone diagram cannot explore According to the characteristics of the fishbone diagram, the small bones, medium bones, and big bones in the fishbone diagram generally cannot be repeated.Moreover, each big bone of the fishbone diagram is generally parallel and causal analysis will be performed for each big bone separately.Therefore, the fishbone diagram cannot explore the relationship between small and medium bones belonging to different big bones, or the same big bone.Most of the quality control factor nodes that already exist in Project A are the small and medium bones in the fishbone diagram.Using the fishbone diagram to find the potential quality control factor nodes, the medium bones caused by the small bones (8, 11, 29, and 36) and the big bones caused by the medium bones (50, 51, 52, 53, and 55) can be identified.Moreover, when the fishbone diagram method is used, managers generally give priority to resolving the small bones.Therefore, the critical quality control factor nodes obtained by using the fishbone diagram method are the small bones of the already existing quality control factor nodes.
When using the 4M1E method, managers need to list the possible quality control factors of Project A based on five aspects: humans, materials, machines, methods, and the environment.Using the 4M1E method can help managers identify the nodes of quality control factors that already exist in Project A faster.However, the quality control factors listed in the 4M1E method are listed in parallel according to the five aspects.Therefore, it is difficult to identify the potential quality control nodes and critical quality control nodes of Project A.
When using the NQPB method, managers can quickly find the potential quality control factor nodes and critical quality control factor nodes of Project A. The specific steps can be found in Section 5.3.
In summary, in terms of the complexity of the process of identifying the quality control factor nodes of Project A by the four methods, the NQPB method may be the fastest, followed by the 4M1E, and then the fishbone diagram method.The slowest may be the FTA method.This indicates that by using the NQPB method, managers can identify the quality control factor nodes of Project A as fast as possible and implement the corresponding quality management measures quickly to ensure the construction schedule and the construction quality of Project A.
Table 5 lists the quality control factors of Project A identified by the four methods.According to Table 5, it can be seen that from the perspective of comprehensiveness in identifying quality control factors, all four methods can comprehensively identify the already existing quality control factor nodes of Project A. FTA and NQPB methods can comprehensively identify the potential quality control factor nodes, the fishbone diagram method is the second most effective, the 4M1E method is the least effective.The effectiveness of the four methods in identifying the key quality control factor nodes will be discussed in the next subsection.Thus, the FTA and NQPB methods were the most effective in fully identifying the quality control factor nodes of Project A. The fishbone diagram method was the second most effective.The least effective was the 4M1E method.In addition, the process of identifying quality control factors using the FTA method is more complex, requiring an accurate and comprehensive mapping of each fault tree and the extraction of quality control factors from multiple fault trees.Therefore, when using the FTA method, it is relatively easy to miss some quality control factors.Therefore, this paper recommends using the NQPB method to identify quality control factor nodes.
The NQPB method can comprehensively identify the potential quality control factor nodes.This facilitates the relevant managers to observe and solve the potential quality control factor nodes in a timely manner and avoid the proliferation of existing quality control factor node problems.This can save the time and cost of rework when potential quality control factor nodes appear.

It Is Better to Avoid Quality Problems in Prefabricated Buildings
When using the four methods for quality management of Project A, managers prioritize addressing key quality control factor nodes.Due to human resources, materials, and time constraints, it is assumed that managers address up to five critical quality control factor nodes first.In order to quantitatively and qualitatively demonstrate that the NQPB method can be used for better quality management, in this paper, the simulation was performed by Gephi, using the network in Figure 9 as the simulation object.The first five pre-existing quality control nodes of 4M1E in Table 5 were selected, and the remaining three methods selected the first five key quality control factor nodes for attacking, one node at a time.Meanwhile, after the attack, the number of edges, average path length, clustering coefficient, and network density of the attacked Figure 9 network were calculated.The simulation results are shown in Table 6.As can be seen from Table 6, after attacking the key nodes of the NQPB method, the attacked Figure 9 network has the least number of edges.The fewer edges in the network indicate that the fewer the connections between the nodes in the network, the less likely it will be to generate quality problems in the prefabricated building.Therefore, using the NQPB method for quality management can minimize the number of edges in the network, and the effect may be the best.
As can be seen from Table 6, the average path length of the network is the largest and the network density is the smallest after attacking the key nodes of the NQPB method.The larger the average path length, the lower the average efficiency of the connection of any two unidirectionally connected nodes of the network, and the problems of individual nodes are not likely to cause quality problems in the prefabricated building.The smaller the network density, the sparser the connections between the nodes of the network and the easier the network is to be disintegrated.Therefore, quality management using the NQPB method can minimize the average path length and network density characteristics of the network, and the effect may be the best.
From Table 6, it can be seen that by using FTA and 4M1E methods for quality management, the network has the lowest clustering coefficient, and the effects are probably the best.The lower the clustering coefficient of the network, the lower the probability that the neighboring nodes (of the nodes) are connected, and the lower the aggregation of the network nodes.
In summary, the NQPB method is used for quality management, which can better reduce the number of edges, average path length, and network density characteristics of the network.The NQPB method performs poorly in reducing the clustering coefficient of the network; however, combining the four network topology metrics in Table 6, after attacking the key nodes of the NQPB method, the network becomes sparser overall and the average distance of any two unidirectionally connected nodes of the network rises.Therefore, the NQPB method can disintegrate the Figure 9 network more quickly relative to the FTA, fishbone diagram, and 4M1E methods, and can better avoid generating quality problems in prefabricated buildings.

Potential Savings in Construction Time and Cost
From Table 5, it can be seen that when the fishbone diagram method was used to identify the quality control factor nodes of Project A, the potential quality control factor nodes 2, 4, 5, 6, 10, 18, 26, 30, 35, 37, 38, 39, 40, and 57 could not be identified.When the 4M1E method was used, the potential quality control factor nodes could not be identified.Among these unidentified potential quality control factor nodes, nodes 35,36,37,38,39, and 40 can directly lead to quality problems in the prefabricated building.If these six potential quality control factor nodes can be identified during the quality management of Project A, it is likely that the corresponding quality management will be carried out in a timely manner, thus effectively avoiding quality problems.If these six potential quality control factor nodes are not identified, it may not be possible to prevent the quality problems of the six nodes, and thus rework may be required.This would require additional time and costs.
The time and cost involved in potential rework lifting caused by quality problems in nodes 35 and 36 were analyzed to demonstrate the potential benefits of the NQPB approach in terms of time and cost savings.The quality problems of nodes 35 and 36 are related to the construction of the components; therefore, data on the components of Project A from the literature [36] were extracted and summarized in Table 7.The quality problem of node 35 is that the construction quality of key parts is poor.The key parts refer to the construction of load-bearing elements, which are the prefabricated load-bearing walls, prefabricated concealed columns, and prefabricated laminated slabs in Table 7.Among them, the construction problems of prefabricated laminated slabs have been identified (see Table 3).Therefore, it is assumed that there is a quality problem in node 35 that may not be prevented when using the fishbone diagram method and the 4M1E method.This problem is the poor construction quality of 35 m 3 of prefabricated load-bearing walls and 20 m 3 of prefabricated concealed columns.
The quality problem of node 36 involves the poor hoisting quality of components.The poor hoisting quality of any component type in Table 7 belongs to the quality problem of node 36.It is assumed that there is a quality problem in node 36 that may not be prevented when using the 4M1E method.This problem is the poor hoisting quality of 50 m 3 of prefabricated facades.
In order to estimate the time and cost of rework caused by the quality problems of nodes 35 and 36, in this paper, we refer to the comprehensive quotas for housing construction and decoration engineering [43,44], and estimate the possible rework lifting costs and man-days for the 35 m 3 of prefabricated load-bearing walls, 20 m 3 of prefabricated concealed columns, and 50 m 3 of prefabricated facades, as shown in Table 8.Among them, the mechanical cost of the rework lifting cost is not calculated.Man-days is 10, which means a worker works for 10 days, 8 h per day [44].Man-day can reflect the time required for the rework.From Table 9, it can be seen that using NQPB and FTA methods can prevent the quality problems of nodes 35 and 36 well, thus saving unnecessary rework costs and time.Using the fishbone diagram method caused RMB 8481.555 of rework costs and 65.95 rework man-days due to the inability to prevent the quality problem of node 35.Using the 4M1E method caused RMB 18,305.305 of rework costs and 147.9 rework man-days due to the inability to prevent the quality problem of nodes 35 and 36.It can be concluded that the NQPB and FTA methods can comprehensively identify the potential quality control factor nodes of Project A. They can prevent the quality problems of quality control factor nodes in time and save the cost and time of the rework.

Provide a Macro-Quantitative Analysis Method
The FTA method, by constructing fault trees, is able to estimate the probability of occurrence of each prefabricated building quality problem.During the implementation of a prefabricated building project, it can update the probability of occurrence of relevant quality problems in real-time, thus assisting managers to develop appropriate quality management strategies.However, the fault tree is solely drawn based on each prefabricated building quality problem; therefore, it is difficult for the FTA method to explore the relationship between each quality control factor of the prefabricated building project and to quantitatively analyze the overall quality management of the prefabricated building project.
Both the fishbone diagram method and the 4M1E method are qualitative analysis methods that aim to identify the causes of quality problems in prefabricated buildings.Neither of these methods allows for quantitative analysis.
The NQPB method involves constructing an adjacency matrix to generate an NQPB.The network can be updated in real-time during the implementation of the prefabricated building project.Meanwhile, the complex network method can be used to calculate each topological indicator of the network, so as to quantify the overall quality management situation of the prefabricated building project.
Therefore, the NQPB method is better for a macroscopic quantitative analysis than the above three methods, so as to quantitatively derive the overall quality management situation of the prefabricated building project.This helps managers to develop quality management plans.

Suggestions for Quality Management of Prefabricated Buildings 6.1. Important Stages of Quality Management of Prefabricated Buildings
The 17 key nodes of NQPB were obtained above.From the distribution of key nodes in key stages, there are four key nodes in the design stage, one key node in the component supply and management stages, two key nodes in the construction preparation stage, and 10 key nodes in the construction stage.There are no key nodes in the construction management and completion acceptance stage.Therefore, in the quality management of prefabricated buildings, we should focus on design, component supply and management, construction preparation, and construction stages.Specifically, in the design stage, the design company needs to focus on four issues: (1) whether the designers have experience in the design of prefabricated buildings; (2) whether the drawings are construction-friendly; (3) whether the division of prefabricated components is reasonable; (4) whether the design takes into account the characteristics of prefabricated buildings.In the component supply and management stage, the component production factory should pay more attention to the production quality of the components, and the stacking, maintenance, and transportation of the components.In the construction preparation stage, contractors need to focus on the construction drawing review and develop a detailed construction plan.During the construction stage, contractors need to focus on the construction survey, the construction of key parts, hoisting components, grouting work after hoisting components, the connection of the steel bar and prefabricated sleeve, and the assembly of the components and pipeline.Moreover, contractors need to focus on the quality concept and construction techniques of workers.
In addition, six key stages of the network model are extracted from the network model (see Figure 11).According to Figure 11, the design, component supply and management, construction preparation, and construction management stages will affect the quality of the construction stage, of which the design stage affects more stages.The construction stage has the largest degree, which is the core stage in the network.Therefore, in quality management, we should focus on the construction and design stages, and take into account the other four stages.In addition, six key stages of the network model are extracted from the network model (see Figure 11).According to Figure 11, the design, component supply and management, construction preparation, and construction management stages will affect the quality of the construction stage, of which the design stage affects more stages.The construction stage has the largest degree, which is the core stage in the network.Therefore, in quality management, we should focus on the construction and design stages, and take into account the other four stages.workers, including the operation of construction machinery.Moreover, contractors should educate their workers about quality and establish correct quality awareness.In addition, contractors should strengthen the inspection of each construction process to detect quality problems in time.

Suggestions for the Whole Process Management of Prefabricated Buildings
Finding the links to the four quality defective nodes helps quality control and assurance managers to carry out the whole process management of prefabricated buildings.By identifying the paths to the quality defective nodes, the links leading to the quality defective nodes can be found.Quality defective node 56 is used as an example for the analysis.The 1-3 level nodes leading to node 56 are found according to the NQPB.The level 3 nodes represent nodes that need two nodes to reach node 56.Accordingly, node 56 (and its level 1-3 node network diagram) is drawn (see Figure 12).Level 1 nodes can directly lead to the generation of node 56, and level 3 nodes ar basically the source nodes leading to node 56.In the prevention of node 56, the control o level 1 and 3 nodes is really important.In addition, level 2 nodes can connect the level and 3 nodes, and they need to be controlled.The level 1-3 nodes of quality defective node 56, 57, 58, and 59, are shown in Table 10.Level 1 nodes can directly lead to the generation of node 56, and level 3 nodes are basically the source nodes leading to node 56.In the prevention of node 56, the control of level 1 and 3 nodes is really important.In addition, level 2 nodes can connect the level 1 and 3 nodes, and they need to be controlled.The level 1-3 nodes of quality defective nodes 56, 57, 58, and 59, are shown in Table 10.
It can be seen from Table 10 that the level 1 nodes of the four quality defective nodes are mainly distributed in the construction stage, including nodes 34-40.These nodes are the defect factors of specific construction procedures, which can directly lead to quality problems in prefabricated buildings.Node 46 in the construction management stage is the level 1 node of the four quality defective nodes, which can negatively affect the quality of prefabricated buildings.Node 1 in the design stage is the level 1 node of the quality defective node 58, which has an impact on the overall structural behavior of the prefabricated building.Therefore, in the quality management of level 1 nodes, the contractors should improve the construction technology, strengthen the management of subcontractors, and control the construction quality of subcontractors.Specifically, in the construction survey, contractors should arrange for experienced workers to carry out the construction survey and inspect the completed construction survey work in a timely manner.In the construction of key parts and the grouting of some component connection parts, contractors should focus on the laps of key parts, such as beams, slabs, and columns [10].Construction managers should supervise the process of workers stirring the grouting material, including the ratio of materials.Moreover, construction managers should supervise the process of grouting to ensure that the workers have operated according to the specifications [11].Before the hoisting of components, construction managers should check the quality of hoisting equipment [10] and the components to be hoisted.After each concrete pouring, construction managers should arrange for workers to cover and maintain the concrete in time.Before the connection of steel bars and prefabricated sleeves, construction managers should carefully check their positions [12].If the position of the prefabricated sleeve is misaligned with the position of the steel bar, it may be necessary to have the component production factory re-produce the corresponding component in strict accordance with the drawings.In the process of assembling the components and the pipeline, if the quality of the components is found to make the site threading difficult [12], the component production factory should be asked to reproduce the corresponding components.The design company should pay attention to the structural form selection of prefabricated buildings.
Level 2 nodes of the four quality defective nodes, mainly distributed in the construction stage, include nodes 25, 26, 27, 29, 30, 31, 33, and 34; these nodes are mainly the personnel factors of the construction team, construction materials, mechanical factors, and the inspective factors of the construction process.These factors may lead to specific construction process defects.Nodes 21 and 24 in the construction preparation stage and node 11 in the component supply and management stage are the level 2 nodes of the four quality defective nodes, which can directly affect the construction quality.Nodes 4 and 9 in the design stage are also level 2 nodes.Therefore, in the quality management of level 2 nodes, the contractors should hire managers with experience in prefabricated building construction and conduct construction training for workers, as well as strictly control the quality of construction materials and machinery, and strengthen the inspection of construction procedures.Moreover, the contractors should formulate detailed and reasonable construction plans during the construction preparation stage, and examine construction drawings well.In addition, the management of level 2 nodes in the design and component supply and management stages should be strengthened.
Level 3 nodes of four quality defective nodes, mainly distributed in the design and component supply and management stages, include nodes 1, 2, 3, 6, 7, 8, 10, and 13-19.Node 20 in the construction preparation stage, nodes 28 and 32 in the construction stage, and node 43 in the construction management stage are also level 3 nodes.Therefore, in the quality management of level 3 nodes, the design company should fully consider the structure and construction characteristics of the prefabricated building, and coordinate the design conflicts of various specialties.The component production factory should strengthen the component production capacity and pay attention to the component transportation to prevent the components from being worn during transportation.The contractors should strengthen the inspection of the components, and carry out reasonable stacking and maintenance of the components.In addition, it is necessary to strengthen the management of the level 3 nodes in the construction preparation, construction, and construction management stages.

Suggestions for Quality Management of Project A
Walter A. Shewhart, an American quality management expert, proposed the PDCA cycle, which divides quality management into the plan, do, check, and act stages [19].This theory is widely used in the quality management of construction projects.
This paper proposes the management recommendations of Project A, incorporating the PDCA cycle.First, each stage of the project should be planned in advance for each quality control factor before taking action.Then, it acts according to the plan.In the process of action, one should check (in time) to find the problems.If one finds problems, one can find the quality control nodes corresponding to those problems, and then find the nodes that are directly caused by those problems in NQPB of Project A.
Next, one should communicate with the relevant staff in a timely manner to prevent problems.For example, in the case study above, we found that in the component supply and management stage, some of the transport vehicles in Project A did not meet the component size requirements, and this problem corresponded to node 16.It is known from the NQPB that node 16 may lead to poor quality of components (node 11).Therefore, the quality control and assurance managers at the construction site need to organize personnel to carefully inspect the components and eliminate those that are badly worn.Moreover, the quality control and assurance managers at the construction site should also check the already assembled components and consider removing and replacing them if there are more severely worn components.
Finally, after the entire project is completed, a review should be conducted to form a standard for the parts that were done well.Moreover, the quality control and assurance managers need to summarize the parts that did not perform well and wait until the next PDCA cycle to solve them.

Conclusions
This paper reviews the quality system of prefabricated buildings as complex systems and identifies the key stages that affect the quality of prefabricated buildings.Each quality control factor, key stage, and quality defect was regarded as a node, the relationship between nodes was regarded as an edge, and the NQPB was constructed.Through the analysis of the NQPB, 17 key nodes were obtained.Then, a simulation was performed by Python, and the number of nodes, edges, network density, and clustering coefficient of the network decreased, and the average path length increased by attacking the 17 key nodes in turn.This caused the NQPB to be disintegrated, and it was difficult to form links to the four quality defective nodes.This indicates that these 17 key nodes play an important role in the quality management of prefabricated buildings.
Next, this paper applies the analysis method of the NQPB to Project A. The key nodes of Project A were identified.Meanwhile, by comparing the results of the FTA, fishbone diagram, 4M1E, and NQPB methods in identifying quality control factors for Project A, it was concluded that the NQPB method can identify quality control factors more quickly and comprehensively.Through simulation, it was found that the NQPB method may be better at avoiding quality problems in prefabricated buildings compared to the other three methods.Furthermore, we found that the NQPB method has potential advantages in saving construction time and costs.It was also found that the NQPB method could better quantify the overall quality management of the prefabricated building project.This

Figure 1 .
Figure 1.The logical relationship of each stage of prefabricated building.

Figure 1 .
Figure 1.The logical relationship of each stage of prefabricated building.

Figure 2 .
Figure 2. Interrelationship digraph of some quality control factors.

Figure 2 .
Figure 2. Interrelationship digraph of some quality control factors.

Figure 3 .
Figure 3. Network model of quality control factors of prefabricated buildings.

Figure 3 .
Figure 3. Network model of quality control factors of prefabricated buildings.

Figure 4 .
Figure 4. Number of nodes of the attacked NQPB.

Figure 5 .
Figure 5. Number of edges of the attacked NQPB.

Figure 4 .
Figure 4. Number of nodes of the attacked NQPB.

Figure 4 .
Figure 4. Number of nodes of the attacked NQPB.

Figure 5 .
Figure 5. Number of edges of the attacked NQPB.Figure 5. Number of edges of the attacked NQPB.

Figure 5 . 27 Figure 6 .
Figure 5. Number of edges of the attacked NQPB.Figure 5. Number of edges of the attacked NQPB.Buildings 2022, 12, x FOR PEER REVIEW 12 of 27

Buildings 2022 , 27 Figure 8 .
Figure 8. Process of the quality management analysis using the NQPB method.

Figure 8 .
Figure 8. Process of the quality management analysis using the NQPB method.

Figure 9 .
Figure 9.The NQPB of Project A.

Figure 9 .
Figure 9.The NQPB of Project A.
is a schematic diagram of a fishbone diagram.Buildings 2022, 12, x FOR PEER REVIEW 17 of 27 is a schematic diagram of a fishbone diagram.

Figure 10 .
Figure 10.A schematic diagram of a fishbone diagram.

Figure 10 .
Figure 10.A schematic diagram of a fishbone diagram.

Buildings 2022 ,
12, x FOR PEER REVIEW 22 of 27supply and management stages, two key nodes in the construction preparation stage, and 10 key nodes in the construction stage.There are no key nodes in the construction management and completion acceptance stage.Therefore, in the quality management of prefabricated buildings, we should focus on design, component supply and management, construction preparation, and construction stages.Specifically, in the design stage, the design company needs to focus on four issues: (1) whether the designers have experience in the design of prefabricated buildings; (2) whether the drawings are constructionfriendly; (3) whether the division of prefabricated components is reasonable; 4) whether the design takes into account the characteristics of prefabricated buildings.In the component supply and management stage, the component production factory should pay more attention to the production quality of the components, and the stacking, maintenance, and transportation of the components.In the construction preparation stage, contractors need to focus on the construction drawing review and develop a detailed construction plan.During the construction stage, contractors need to focus on the construction survey, the construction of key parts, hoisting components, grouting work after hoisting components, the connection of the steel bar and prefabricated sleeve, and the assembly of the components and pipeline.Moreover, contractors need to focus on the quality concept and construction techniques of workers.

Figure 11 .
Figure 11.Six key stages of the network model.To summarize, the construction stage is the most critical stage of the quality management of prefabricated buildings.From the relationship between key nodes in the construction stage, key nodes 25, 27, 29, and 30 will lead to key nodes 34, 35, 36, 38, 39, and 40.Therefore, it is crucial to solving the problems of key nodes 25, 27, 29, and 30.During the construction stage, contractors should strengthen the construction technology training of workers, including the operation of construction machinery.Moreover, contractors should educate their workers about quality and establish correct quality awareness.In addition, contractors should strengthen the inspection of each construction process to detect quality problems in time.

Figure 11 .
Figure 11.Six key stages of the network model.To summarize, the construction stage is the most critical stage of the quality management of prefabricated buildings.From the relationship between key nodes in the construction stage, key nodes 25, 27, 29, and 30 will lead to key nodes 34, 35, 36, 38, 39, and 40.Therefore, it is crucial to solving the problems of key nodes 25, 27, 29, and 30.During the construction stage, contractors should strengthen the construction technology training of

Table 1 .
Quality control factors.

Table 2 .
Nodes with larger in-degrees, out-degrees, and degrees.

Table 3 .
Quality management problems and quality control factor nodes of Project A.

Table 4 .
Nodes with larger node indicators in the NQPB of Project A.

Table 5 .
Quality control factors of Project A identified by the four methods.

Table 7 .
Types of components and their numbers for each standard layer.

Table 8 .
Possible rework lifting costs and man-days for 35 m 3 of prefabricated load-bearing walls, 15 m 3 of prefabricated concealed columns, and 50 m 3 of prefabricated facades.

Table 8
refers to the legal tender of the People's Republic of China.Based on Table8, the possible rework lifting costs and man-days for nodes 35 and 36 of the four methods are summarized, as shown in Table9.

Table 9 .
Possible rework lifting costs and man-days for nodes 35 and 36 of the four methods.