Analysis of Factors Affecting Prefabricated Building Quality Based on ISM-BN

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Citation: Zhang, J.; Wang, M.; Zhao, L.; Chen, M. Analysis of Factors Affecting Prefabricated Building Quality Based on ISM-BN Sustainability 2023 , 15 , 9682. https:// doi.org/10.3390/su 15129682 Academic Editors: Payam Rahnamayiezekavat, Olivia Mirza and Md Kamrul Hassan Received: 16 May 2023 Revised: 7 June 2023 Accepted: 13 June 2023 Published: 16 June 2023 Copyright: © 2023 by the authors Licensee MDPI, Basel, Switzerland This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/) sustainability Article Analysis of Factors Affecting Prefabricated Building Quality Based on ISM-BN Jun Zhang, Mengtong Wang, Lilin Zhao * and Min Chen * School of Transportation and Civil Engineering, Nantong University, Nantong 226019, China; 13951411616@139.com (J.Z.); wangmengtongsandy@hotmail.com (M.W.) * Correspondence: lilinz 0919@163.com (L.Z.); chen.min@ntu.edu.cn (M.C.) Abstract: In recent years, the rise of the domestic industry has boosted the use and popularity of prefabricated buildings. Prefabricated buildings differ significantly from traditional design, construction, and production models. However, due to the short development period of prefabricated buildings in China, the quality management of these new structures is still not mature, resulting in frequent project delays and failure. To improve quality management, this paper aims to establish an evaluation model of factors affecting prefabricated building quality. The 4 M 1 E framework was used to categorize and generalize related quality factors. Then, GeNIe software was used to establish a visual Bayesian network quality factor evaluation model. The factors that need to be managed and given attention to in the prefabricated construction project were discovered using reverse reasoning, sensitivity, and critical factor analysis. The results indicated that among the multiple stages of prefabricated buildings, the construction stage has the greatest impact on the quality of buildings. C 2(Insufficient sense of responsibility of construction personnel) is the most significant factor that needs to be controlled. In addition, this paper combined the ISM-BN model with actual engineering projects to identify key factors affecting the project’s quality, demonstrating the model’s applicability. The evaluation model of quality factors in prefabricated buildings was established. It can identify the underlying causes of quality issues in prefabricated buildings and control engineering quality at the source, acting as an effective guide for practitioners and enterprises Keywords: ISM-BN method; risk matrix method; quality management; 4 M 1 E 1. Introduction Prefabricated buildings are formed by producing prefabricated components in factories and then assembling them on-site [ 1 ]. Compared to the traditional cast-in-place concrete building production mode, prefabricated buildings are more conducive to improving labor efficiency, have a higher degree of standardization, and require less on-site wet work. At the beginning of the 20 th century, industrialized countries such as the United States and the United Kingdom were desperate to solve their housing needs, and the construction of prefabricated buildings was found to be one of the effective solutions [ 2 ]. The construction method of prefabricated buildings has significantly reduced construction time and cost, which has proven to deal with various housing problems. For instance, energy-efficient materials such as recycled steel can promote environmental sustainability for prefabricated buildings in many industrialized countries [ 3 ]. As a result, there has been a large growth in prefabricated buildings globally since World War II. Recently, prefabricated buildings have received significant attention from the Chinese government. On 27 September 2016, the State Council issued “Guiding Opinions on Vigorously Developing Prefabricated Buildings”, aiming to continuously increase the proportion of prefabricated buildings and establish a quality supervision system [ 4 ]. Under the government’s vigorous promotion, several provinces issued implementation opinions to promote the development of prefabricated buildings. In 2021, the market size of China’s prefabricated construction Sustainability 2023 , 15 , 9682. https://doi.org/10.3390/su 15129682 https://www.mdpi.com/journal/sustainability

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Sustainability 2023 , 15 , 9682 2 of 31 industry reached RMB 1325.7 billion, and the newly started prefabricated building area totaled 740 million square meters, accounting for 24.5% of the newly built construction area (according to data from China Industrial Research Institute). In general, the positive development trend of prefabricated buildings has played a critical role in promoting the upgradation of the Chinese construction industry Quality management is one of the three primary objectives of project management, and the “assembly” feature of prefabricated buildings sets higher standards for quality. The construction process of prefabricated buildings involves activities not present in traditional construction projects. Therefore, the practice and assessment of the quality management of prefabricated buildings cannot follow the traditional model [ 5 ]. Firstly, the design of prefabricated buildings requires more experience and knowledge than traditional building projects. A lack of design experience and knowledge can lead to poor buildability and multiple design changes [ 6 , 7 ]. Secondly, producing prefabricated components requires industrialization, necessitating mature technology and a sound management mechanism [ 8 ]. Thirdly, prefabricated building projects have an additional transportation link. Unreasonable transportation plans, a lack of protection measures, unreasonable loading and unloading, etc., can all compromise the quality of prefabricated buildings [ 9 ]. Fourthly, the on-site construction of prefabricated buildings is more complex than traditional buildings. Poorly defined specifications, inadequate construction processes, and suboptimal personnel management can all negatively impact the quality of prefabricated buildings [ 10 ]. Therefore, in every link of a prefabricated building, high-level quality management is essential for the project to meet the required quality standards within a certain deadline. Currently, some shortcomings are present in the quality management of prefabricated buildings: (1) Inspection and testing are vital links. Some enterprises have not fully carried out inspection and testing. Prefabricated components cannot be guaranteed to meet the requirements [ 11 ]. (2) Prefabricated building projects involve multiple stakeholders These stakeholders cannot achieve effective communication, resulting in the failure of the prefabricated building to progress smoothly, which affects the quality of prefabricated buildings [ 5 ]. (3) The lack of effective record files during the construction of prefabricated buildings makes it impossible to effectively track the quality of prefabricated buildings [ 12 ]. Prefabricated buildings are in a high growth stage, and many regional markets have huge demand. Some methods are used to evaluate the quality management level of assembled concrete buildings, generally identifying performance evaluation factors from different angles. For example, assessment models are established to provide data information on the design, off-site manufacturing, on-site construction, and transportation stages of prefabricated buildings, and to identify quality defects during the industrialization of prefabricated buildings [ 13 ]; Industry surveys of prefabricated construction companies are conducted, identifying quality-related factors from multiple dimensions, and posing the challenges facing prefabricated construction companies [ 14 ]; To systematically identify the factors that affect the quality of prefabricated buildings, structural equation modeling was used to develop an assessment method to measure the impact of these factors on assembled buildings [ 9 ]. Compared with traditional buildings, the construction environment and logistics management of prefabricated buildings are becoming increasingly complex, and traditional quality control methods cannot meet the advancement of projects. Scholars are currently researching quality management systems in the following general areas, for example, the development of automatic aggregate quality inspection techniques to improve inspection efficiency, which are used to inspect component geometric quality [ 15 ]; Prefabricated component information tracking and coordination system is established, basing on radio frequency identification (RFID) technology to realize the possibility of information interaction between prefabricated component supply chain and construction site [ 16 ]; The data of prefabricated component supply chain are often distributed on design, production, transportation, and other stages, proposing ontology-based and multi-intelligence decision support framework to achieve integration of multi-layer information to optimize multiparty coordination [ 17 ]. Scholars’ research has some shortcomings in the quality management of

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Sustainability 2023 , 15 , 9682 3 of 31 prefabricated buildings. Scholars have used simpler mathematical models to explore the quality influencing factors, but have not explored the quality management of prefabricated buildings deeply enough By combining ISM and Bayesian methods, this paper aims to quantify the importance of the related factors. American scholar Warfield proposed the establishment method of interpretive structural model (ISM) to establish the relationship between the factors. ISM method can transform fuzzy or undefined models into clearly defined models so that complex systems had a fundamental factor layer, indirect factor layer, and direct factor layer after constructing the matrix [ 18 ]. Therefore, the ISM has been widely applied in influencing factor analysis, strategy research, and risk management. Another model used in this study was the Bayesian network (BN), also known as the belief network. It was a directed acyclic probabilistic model. The Bayesian network was created by Judea Pearl in 1985 to describe the causal relationship between variables and the exact impact probability. It is a quantitative and qualitative model [ 19 ]. The Bayesian network model has been proven capable of reliability, risk, and quality analyses. Judea Pearl and P. W. Jones summarized the inference mechanism of the Bayesian network, so the Bayesian network model gradually became a research field [ 20 ]. The ISM model requires manual construction of relationship graphs between variables and thus requires expertise and experience to guide it. The Bayesian model is only based on conditional probabilistic relationships and thus cannot handle complex causal relationships. Combining structural models and Bayesian network models can overcome their respective limitations. The ISM-BN model can infer both complex causal and probabilistic relationships The remaining sections were as follows: Section 2 explains the framework of methodology and the methods and steps of building the quality factor model. Section 3 explains the identification of quality factors, the collection of questionnaire data, and the establishment of a four-stage Bayesian network model. Section 4 includes the data analysis process, namely the reverse reasoning analysis, sensitivity analysis, and key factor analysis of the Bayesian network model, to ascertain the most significant quality factors that must be addressed. Section 5 discusses the measures to improve the level of prefabricated quality and the prospects for the future. Section 6 concludes the paper, by providing practical implications and suggestions for future research 2. Research Method 2.1. Framework of Methodology This study was conducted in three steps. First, quality factors affecting prefabricated buildings were identified and determined. By compiling and studying domestic and foreign literature on the quality management of prefabricated concrete buildings, the preliminary quality factors were identified, which were further revised and validated through six individual interviews with experts in the construction management field. Second, the interpretive structural model was used to present the quality factors in each of the four stages of a typical construction lifecycle, which determined the basic level of the Bayesian network. Individual interviews with another six experts were conducted to determine the relationship between each factor and the quality of prefabricated buildings. In the interviews, the experts were asked to rate their perceived degree of connections between the factors and quality, in which 0 represents no direct connection and 1 means that there is a direct connection between them. The average score of each factor was calculated, and factors with values equal to or greater than 0.5 were considered highly related factors Table A 2 in Appendix A shows the questionnaire used in the design stage Third, a Bayesian network model is established for the quality evaluation of prefabricated concrete buildings. The parameters of each node in the Bayesian network are obtained from online questionnaires (Tables A 4 – A 7 ). The methodological framework of this paper is shown in Figure 1 .

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Sustainability 2023 , 15 , 9682 4 of 31 Sustainability 2023 , 15 , x FOR PEER REVIEW 4 of 33 obtained from online questionnaires (Tables A 4–A 7). The methodological framework of this paper is shown in Figure 1. Figure 1. The method flow chart in the research. 2.2. ISM-BN Model Warfield, an American scholar, proposed establishing an interpretive structural mode, referred to as the ISM method. It aims to convert a vague or undefined model into a clearly defined model so that a more complex system includes a fundamental factor layer, an indirect factor layer, and a direct factor layer that can be constructed [18]. Bayesian network, abbreviated as BN, was proposed by American scholar Pearl in 1988 as a directed acyclic graph consisting of arcs and nodes [20]. Since the combination of the two models can infer complex causal and probabilistic relationships, researchers started to establish integrated ISM-BN models in construction management [21]. In this research, the ISM-BN model of the quality factors of PC buildings was developed in five steps. Step 1. The relationship between the quality factors of PC buildings and the impact matrixes was identified. The influence matrixes reflected the direct relationship between quality factors, transforming complex thoughts into clear and intuitive models. After determining the factor index system of PC building quality in the framework of 4 M 1 E, the adjacency matrixes of the quality factors in the four stages were determined according to the expert score The rules were as follows: {?} = 0 1 {?} {?} (1) i was the row, j was the column. Step 2. The accessible matrixes of the quality factors of PC buildings were determined. Figure 1. The method flow chart in the research 2.2. ISM-BN Model Warfield, an American scholar, proposed establishing an interpretive structural mode, referred to as the ISM method. It aims to convert a vague or undefined model into a clearly defined model so that a more complex system includes a fundamental factor layer, an indirect factor layer, and a direct factor layer that can be constructed [ 18 ]. Bayesian network, abbreviated as BN, was proposed by American scholar Pearl in 1988 as a directed acyclic graph consisting of arcs and nodes [ 20 ]. Since the combination of the two models can infer complex causal and probabilistic relationships, researchers started to establish integrated ISM-BN models in construction management [ 21 ]. In this research, the ISM-BN model of the quality factors of PC buildings was developed in five steps Step 1. The relationship between the quality factors of PC buildings and the impact matrixes was identified The influence matrixes reflected the direct relationship between quality factors, transforming complex thoughts into clear and intuitive models. After determining the factor index system of PC building quality in the framework of 4 M 1 E, the adjacency matrixes of the quality factors in the four stages were determined according to the expert score The rules were as follows: a ij = 0 1 Factor a i has no e f f ect on a j Factor a i has e f f ect on a j i 6 = j (1) i was the row, j was the column Step 2. The accessible matrixes of the quality factors of PC buildings were determined The accessible matrixes represented whether there was a direct or indirect relationship among the quality factors of PC buildings. According to the rank of the adjacency matrix A

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Sustainability 2023 , 15 , 9682 5 of 31 of the quality factors, the unit matrix of the same order was added to A. Then, the reachable matrix R was obtained by power square operations. The calculation formula was as follows: R = (A + I) k+1 = (A + I) k 6 = (A + I) k − 1 6 = (A + I) k − 2 6 = . . 6 = (A + I) (2) k = 1, 2, 3 . . . , I was the same order unit matrix of A Step 3. According to the reachability matrix results of each stage (design, production, transportation, and construction), the leading sets, reachable sets, and common sets were obtained. Levels and ranks were divided based on common sets According to each iteration’s common sets, each level’s quality factors were determined. The leading set P( B i ) represented the set of all indexes whose element value was 1 in the jth column of the reachable matrix R. The expression was: P ( B i ) = B j ∈ B b ij = 1 (3) The reachable set N( B i ) represented the set of all indexes whose element value was 1 in the ith row of the reachable matrix R. The expression was: N ( B i ) = B i ∈ B b ij = 1 (4) The common set M( B i ) represented the intersection of the leading set and the reachable set. The expression was: M ( B i ) = P ( B i ) ∩ N ( B i ) (5) Step 4. The BN model of PC buildings’ quality factors was drawn in four stages in design, production, transportation, and construction, respectively, based on the hierarchical relationship of the quality factors divided by ISM The GeNIe 3.0 software was employed to draw the BN model in order to fully quantify the hierarchical relationship model of quality factors obtained by ISM. The variable nodes of the BN were divided into parent and child nodes. The variables without parent nodes were root nodes, and the variables without child nodes were leaf nodes P ( A = ST 1 | B = ST 0, C = ST 0 ) = P ( A = ST 1, B = ST 0, C = ST 0 ) P ( B = ST 0, C = ST 0 ) (6) Step 5. Four stages’ of Bayesian networks of PC buildings were analyzed The posteriori probability analysis, sensitivity analysis, and key factor analysis were carried out for BN in the design, production, transportation, and construction stages, respectively. By comparing the three kinds of analysis results, the corresponding measures for improving the quality management of prefabricated buildings were provided 3. Model Building 3.1. Selection of Quality Influencing Factors Many scholars have conducted several practical investigations on the quality management of prefabricated buildings [ 22 , 23 ]. Most of the research on the quality management of prefabricated buildings focused on a single stage, multiple stages, and stakeholders The following scholars mainly explored the quality management level of prefabricated buildings at a single stage. Li et al. analyzed the development status of prefabricated building production in Hong Kong, highlighting information gaps and insufficient communication between designers and construction stages as weaknesses [ 24 ]. Chen analyzed the prefabricated component production process and found issues such as insufficient use of technology, lack of skilled personnel, and poor storage environments affecting the quality [ 25 ]. Li et al. pointed out that in the construction management stage, attention should be paid to recruiting experienced technical personnel and the particularity of the connection of prefabricated components [ 26 ]. Ren identified quality risk factors of the construction stage, emphasized construction personnel’s awareness, and highlighted the

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Sustainability 2023 , 15 , 9682 6 of 31 importance of a reasonable plan for project success [ 27 ]. Guo built an SD quality risk model and analyzed that the factors that had the greatest impact on the quality of prefabricated construction were management and implementation factors, followed by environmental factors [ 28 ]. Deng et al. established a quality risk assessment model, highlighting the professionalism of production personnel, production equipment quality, and standard system integrity as key factors affecting component quality [ 8 ]. Some scholars had considered the whole construction process and sorted out the quality factor indicators from the design to the construction stages. Su et al. identified the factors that impact prefabricated building quality, including industrial workers’ technology lack and environmental factors affecting the component strength (pH) [ 29 ]. Wang established a risk quality evaluation model encompassing design, production, transportation, and construction stages, then proposed measures to deal with quality risks: pay attention to the skills of professionals, strengthen the quality inspection of components entering the site, and enhance the awareness of quality supervision [ 21 ]. Qu summarized quality factors through expert discussion and questionnaires, identifying issues such as inconsistent standards and specifications, lack of professional cooperation, and low construction employee quality [ 30 ]. Chen et al. used system dynamics to establish a quality chain control model, highlighting the impact of design scheme rationality, transport personnel professionalism, and construction scheme rationality on the prefabricated building quality [ 31 ]. Wen established a production and construction evaluation system, identifying issues such as prefabricated buildings’ lack of design standardization, unsatisfactory component production technology, unreasonable transportation plan, and insufficient professional practitioners [ 32 ]. Gan et al. identified quality as a key issue affecting the promotion of prefabricated buildings, highlighting the lack of component production standards and specifications, quality management systems, and technical guidelines for the project construction [ 7 ]. Dong identified construction quality factors from the aspects of components, construction preparation, equipment, and management coordination. Key factors were a lack of component production experience and rationality, as well as insufficient coordination between the construction party, manufacturer, and designer [ 33 ]. Xia et al identified 25 quality factors based on prefabricated component production, transportation, storage, and hoisting stages, with transportation and storage having the greatest impact on component quality [ 9 ]. Wang et al. explored key risk factors of prefabricated buildings in China, including factory management, transportation planning, component strength, and housing quality monitoring technology [ 23 ]. In addition, some scholars evaluated the quality management level of prefabricated buildings from the stakeholders’ perspective. Tao et al. evaluated stakeholders’ impact on prefabricated building quality defects, finding that unreasonable construction personnel operation and ineffective quality inspections during construction were major factors [ 5 ]. Peter et al. interviewed contractors and identified obstacles to quality management implementation, including the lack of skilled workers, unreasonable project deadlines, and the lack of supervision [ 34 ]. The screening of factors through the literature revealed that most of the literature is lacking in the breadth of research on the quality of prefabricated buildings and uses simpler models in the quantification of factors An extensive literature review has resulted in the identification of a total of 36 quality factors, which can be matched into four stages of a typical construction project, namely design stage, prefabricated component production stage, transport stage, and construction stage. The factors were further classified into five dimensions according to the 4 M 1 E framework, which includes man, material, machine, method, and environment. 4 M 1 E method is an important analytical tool to study quality-related problems, and it is widely used to summarize and correct significant influencing quality factors in the field of quality management [ 35 ]. After that, six individual interviews were conducted with experts in the construction management field to verify and supplement the identified quality factors. All six experts have rich professional knowledge and hands-on experience in prefabricated concrete buildings, with four academics and two industrial practitioners. All

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Sustainability 2023 , 15 , 9682 7 of 31 six experts have master’s degrees and above. Among them, four academics are engaged in research related to assembled buildings and have an excellent understanding of the local development of assembled buildings. Two industry practitioners are engaged in the structural technology of prefabricated buildings and have published several patents, who comprehensively understand the existing problems of prefabricated buildings. As shown in Table 1 , the factor indexes affecting building quality under the framework of 4 M 1 E were obtained after expert interviews. After modification and supplement, 43 quality factors were finally obtained Table 1. Factors affecting prefabricated building quality Stage 4 M 1 E Quality Factors Serial Number Source Design stage Man Lack of precast design skills or experience D 1 [ 5 , 21 ] Insufficient responsibility of designers D 2 [ 30 , 36 ] Inadequate communication and coordination among professional designers D 3 [ 21 , 31 ] Insufficient communication between designers and other stakeholders D 4 [ 7 , 24 ] Method Split design is unreasonable or not in place D 5 Expert interview Design standardization is not high D 6 [ 5 , 30 , 32 ] Lack of coordination between traditional design and prefabricated design D 7 Expert interview Lack of coordination between prefabricated design and construction plan D 8 [ 24 , 32 ] Environment Design time is tight D 9 [ 7 , 34 ] Prefabricated component production stage Man Relevant staff have weak quality awareness P 1 [ 32 , 36 ] Insufficient professional competence of production personnel P 2 [ 8 , 25 , 29 ] Material Insufficient quantity of raw materials (such as steel bars, cement not in the prescribed quantity) P 3 Expert interview Machine Production equipment does not meet the standard P 4 [ 8 , 21 ] Method The curing conditions do not meet the requirements (standard curing room conditions) P 5 [ 5 , 8 ] Unreasonable ratio of raw materials P 6 Expert interview Lack of technical specifications and standards for component production P 7 [ 7 , 8 , 33 ] Lack of production quality management information system P 8 [ 24 , 25 ] The production process cannot meet the quality requirements P 9 [ 5 , 31 ] Components not stored according to standard (industry standard) P 10 [ 25 , 33 ] Environment Workshop temperature and humidity do not meet the requirements P 11 [ 5 , 29 ] Production time is tight P 12 [ 21 , 34 ] Transport stage Man Transport personnel are not professional enough T 1 [ 23 , 31 ] Insufficient sense of responsibility of transport personnel T 2 [ 26 , 36 ] Machine Unreasonable selection of transport tools T 3 [ 9 , 32 ] Unreasonable selection of hoisting tools T 4 [ 9 , 32 ] Method Unreasonable shipping sequence of prefabricated components T 5 Expert interview Unreasonable transportation route planning T 6 [ 5 , 8 , 37 ] Improper loading and unloading of prefabricated components T 7 [ 5 , 9 , 32 ] Prefabricated components transportation protection measures are not in place T 8 [ 23 , 31 ] Environment The transportation distance is too long T 9 [ 23 , 31 ]

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Sustainability 2023 , 15 , 9682 8 of 31 Table 1. Cont Stage 4 M 1 E Quality Factors Serial Number Source Construction stage Man Insufficient practical experience of construction workers and managers C 1 [ 28 , 29 , 34 ] Insufficient sense of responsibility of construction personnel C 2 [ 26 , 27 , 36 ] Inadequate communication between various units and on-site construction personnel C 3 Expert interview Insufficient quality and level of supervisors C 4 [ 21 , 30 ] Prefabricated components are checked careless C 5 [ 21 , 30 ] Material Insufficient connection strength of prefabricated components (e.g., insufficient grouting strength, insufficient bolt strength) C 6 [ 23 , 26 ] Machine Lack of construction quality inspection tools C 7 [ 21 , 23 ] Method Instructions for on-site assembly and construction are not detailed or accurate C 8 [ 7 , 21 ] Unreasonable construction schedule C 9 [ 5 , 30 ] Improper construction practices C 10 [ 5 , 27 , 29 ] Component installation accuracy is not enough C 11 Expert interview Improper stacking of prefabricated components C 12 [ 9 , 21 ] Environment Construction workers lack reasonable working surfaces C 13 [ 28 , 31 ] 3.2. Data Collection Based on the principle of risk matrix method, the questionnaire (Tables A 4 – A 7 in Appendix A ) was designed to classify the risk level of each quality factor. Then, the conditional probability of the nodes of the Bayesian network model was evaluated. Questionnaires were distributed to professionals who work as designers, contractors, and clients in prefabricated building projects. The questionnaire survey was conducted over 14 days, obtaining 136 valid questionnaires (160 total questionnaires distributed). The questionnaires with extreme response bias (i.e., participants repeatedly choose an extreme answer value to answer a question in a questionnaire) were considered invalid and thus excluded from the data collected. The criteria for the selection of the samples include: (1) they must be academics, engineers, or managers who have hands-on working experience in prefabricated construction projects; and (2) they must have experienced at least one prefabricated building project within the last three years and be familiar with the recent development of prefabricated buildings. Table 2 showed participants’ background information (professional title, years of working, educational background). The results showed that most respondents (71.3%) have intermediate or higher professional titles, and more than half (61.8%) have at least 8 years of work experience, suggesting that the sample statistics in this paper are reliable Table 2. Background information of the questionnaire Constitution Classification Number Professional title Primary 23 Intermediate 43 Sub-senior 31 Senior 10 Years of working Less than 3 years 29 3 to 7 years 23 8 to 12 years 31 13 to 17 years 24 More than 18 years 29 Educational background Junior college 17 Undergraduate course 95 Master’s degree 19 Doctor 3

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Sustainability 2023 , 15 , 9682 9 of 31 As shown in Tables A 3 – A 7 in Appendix A , respondents scored the indicators according to the score table of factors affecting prefabricated building quality. This questionnaire was administered on a 5-point Likert scale. As shown in Table 3 , scores 1–5 represent hardly happens (virtually no impact), less frequent (less impact), general, more frequent (less impact), and most frequent occurrences (serious impact). This paper obtained the scores of factors affecting quality in the degree of loss and probability of occurrence. As shown in Figure 2 , the statistics were transformed by the risk matrix method and classified into three levels: low risk, medium risk, and high risk Table 3. Levels of score table Score 1 2 3 4 5 Probability of occurrence Hardly happens Less frequent General More frequently Most frequently occurrences Degree of influence Virtually no impact Less impact General Less impact Serious impact Sustainability 2023 , 15 , x FOR PEER REVIEW 10 of 33 1 R 2 R 2 R 3 R 3 R 3 2 R 2 R 2 R 2 R 3 R 3 3 R 1 R 2 R 2 R 2 R 3 4 R 1 R 1 R 2 R 2 R 2 5 R 1 R 1 R 1 R 2 R 2 1 2 3 4 5 Figure 2. Risk matrix chart 3.3. Establishment of ISM-BN Model 3.3.1. Calculating Reachable Matrix The reachable matrix was the basis for determining the relationship between quality factors. Before calculating the reachable matrix, it was necessary to establish the adjacency matrix. Due to it being difficult determining the direct or indirect relationships between quality factors based on one’s own experience and intuitive judgment, the expert score method was used in this research. In this interview, six experts were found to judge the relationship between factors. The basic information of these six experts is as follows: one of them is an associate professor (who has published many papers and presided over many city and hall level projects), two senior engineers (who are both chief engineers of their respective units and have published many patents), one intermediate engineer (who has participated in the construction of many assembled concrete building projects and has been on the front line for a long time), and two lecturers (who are both PhD graduates and have published more than ten academic papers). These experts are all engaged in project management and have a good understanding of prefabricated construction quality problems. Specifically, experts were required to evaluate the relationship between quality factors {?} and {?} . The evaluation standard was as follows: when there is a direct relationship between {?} and {?} , the evaluation is divided into 1. When there is no direct relationship between {?} and {?} , the evaluation is divided into 0 (according to the scores of each expert, the average score of each relationship was calculated, and the relationship equal to or greater than 0.5 was judged to be relevant). According to the comprehensive evaluation of experts, the adjacency matrixes of design, production, transportation, and construction stages were determined. Taking the design stage as an example, Table 3 showed the adjacency matrix of the quality factor in this stage. Based on the results of the adjacency matrix in the design stage shown in Table 3, the adjacency matrix was adjusted and iterated according to the steps in Section 2.2 The reachability matrix of the design stage was shown in Table 4. The adjacency matrix in Table 4 and the reachable matrix in Table 5 corresponded to the factors affecting the quality of the design stage in Table 1. Therefore, the structural model of this stage was established by dividing the reachable matrix of the design stage. The steps of building the structural models in the production, transportation, and construction stages were similar to those in the design stage. The reachability matrixes of the remaining three stages were shown in Appendix A (Tables A 8–A 10). Figure 2. Risk matrix chart 3.3. Establishment of ISM-BN Model 3.3.1. Calculating Reachable Matrix The reachable matrix was the basis for determining the relationship between quality factors. Before calculating the reachable matrix, it was necessary to establish the adjacency matrix. Due to it being difficult determining the direct or indirect relationships between quality factors based on one’s own experience and intuitive judgment, the expert score method was used in this research. In this interview, six experts were found to judge the relationship between factors. The basic information of these six experts is as follows: one of them is an associate professor (who has published many papers and presided over many city and hall level projects), two senior engineers (who are both chief engineers of their respective units and have published many patents), one intermediate engineer (who has participated in the construction of many assembled concrete building projects and has been on the front line for a long time), and two lecturers (who are both PhD graduates and have published more than ten academic papers). These experts are all engaged in project management and have a good understanding of prefabricated construction quality problems. Specifically, experts were required to evaluate the relationship between quality factors a i and a j . The evaluation standard was as follows: when there is a direct relationship between a i and a j , the evaluation is divided into 1. When there is no direct relationship between a i and a j , the evaluation is divided into 0 (according to the scores of each expert, the average score of each relationship was calculated, and the relationship equal to or greater than 0.5 was judged to be relevant). According to the comprehensive evaluation of experts, the adjacency matrixes of design, production, transportation, and construction

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Sustainability 2023 , 15 , 9682 10 of 31 stages were determined. Taking the design stage as an example, Table 3 showed the adjacency matrix of the quality factor in this stage Based on the results of the adjacency matrix in the design stage shown in Table 3 , the adjacency matrix was adjusted and iterated according to the steps in Section 2.2 The reachability matrix of the design stage was shown in Table 4 . The adjacency matrix in Table 4 and the reachable matrix in Table 5 corresponded to the factors affecting the quality of the design stage in Table 1 . Therefore, the structural model of this stage was established by dividing the reachable matrix of the design stage. The steps of building the structural models in the production, transportation, and construction stages were similar to those in the design stage. The reachability matrixes of the remaining three stages were shown in Appendix A (Tables A 8 – A 10 ). Table 4. Adjacency matrix in the design stage D 1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 1 0 0 0 0 0 0 0 0 0 D 2 0 0 1 1 0 0 0 0 0 D 3 0 0 0 0 1 0 0 0 0 D 4 0 0 0 0 0 0 0 1 0 D 5 0 0 0 0 0 0 0 0 0 D 6 0 0 0 0 1 0 1 0 0 D 7 1 0 0 0 0 1 0 0 0 D 8 0 0 0 0 0 0 0 0 0 D 9 0 0 1 1 0 0 1 0 0 Table 5. Reachability matrix in the design stage D 1 D 2 D 3 D 4 D 5 D 6 D 7 D 8 D 9 D 1 1 0 0 0 0 0 0 0 0 D 2 0 1 1 1 1 0 0 1 0 D 3 0 0 1 0 1 0 0 0 0 D 4 0 0 0 1 0 0 0 1 0 D 5 0 0 0 0 1 0 0 0 0 D 6 1 0 0 0 1 1 1 0 0 D 7 1 0 0 0 1 1 1 0 0 D 8 0 0 0 0 0 0 0 1 0 D 9 1 0 1 1 1 1 1 1 1 3.3.2. Determining Basic Structure The structural models can be established by dividing the reachable matrixes. The division results of the accessibility matrix of design, production, transportation, and construction stages are shown in Figure 2 . Based on the analysis of the accessibility matrix and the establishment method of the structural model, the structural models for each stage can be divided into three layers: the fundamental factor layer, the indirect factor layer, and the direct factor layer. Taking the design stage as an example, D 6 (Design standardization is not high), D 9 (Design time is tight), and D 2 (Insufficient responsibility of designers) were three factors in the fundamental factor layer, which had a direct impact on the indirect factors including D 3 (Inadequate communication and coordination among professional designers), D 4 (Insufficient communication between designers and other stakeholders) and D 7 (Lack of coordination between traditional design and prefabricated design). D 1 (Lack of precast design skills or experience), D 5 (Split design is unreasonable or not in place), and D 8 (Lack of coordination between prefabricated design and construction plan) were three factors that had a direct effect on the target node. The structural models of production, transportation, and construction stages are shown in Figure 3 (D represents quality problems in the design stage; P represents quality problems in the production stage of prefabricated components;

[Find the meaning and references behind the names: Ranking, Deals]

Sustainability 2023 , 15 , 9682 11 of 31 T represents quality problems in the transportation stage; C represents quality problems in the construction stage; and Q represents quality problems in prefabricated buildings) Sustainability 2023 , 15 , x FOR PEER REVIEW 12 of 33 Figure 3. Bayesian network structure. 4. Discussions and Results 4.1. Node Distribution of the Model Figure 4 presents a model of factors affecting the quality of prefabricated buildings. Compared to similar articles in the field [5], this paper deals with more factors and clearly divides the prefabricated building into four stages. By examining the distribution probability of nodes in each stage, the design stage had the lowest probability of quality problems, with a high-risk probability of only 13%. In the production stage of prefabricated components, the probability of quality problems at high risk was 24%, ranking third among the four stages. In the transportation stage, the probability of quality problems at high risk was 25%, ranking second among the four stages. Finally, in the construction stage, the probability of quality problems at high risk was 30%. Compared with the factors in the previous three stages, the high-risk probability values of C 1 (Insufficient practical experience of construction workers and managers), C 6 (Insufficient connection strength of prefabricated components), and C 11 (Component installation accuracy is not enough) were higher. The factors affecting the overall quality of prefabricated concrete buildings were mainly in the construction stage. Figure 3. Bayesian network structure 4. Discussions and Results 4.1. Node Distribution of the Model Figure 4 presents a model of factors affecting the quality of prefabricated buildings Compared to similar articles in the field [ 5 ], this paper deals with more factors and clearly divides the prefabricated building into four stages. By examining the distribution probability of nodes in each stage, the design stage had the lowest probability of quality problems, with a high-risk probability of only 13%. In the production stage of prefabricated components, the probability of quality problems at high risk was 24%, ranking third among the four stages. In the transportation stage, the probability of quality problems at high risk was 25%, ranking second among the four stages. Finally, in the construction stage, the probability of quality problems at high risk was 30%. Compared with the factors in the previous three stages, the high-risk probability values of C 1 (Insufficient practical experience of construction workers and managers), C 6 (Insufficient connection strength of prefabricated components), and C 11 (Component installation accuracy is not enough) were higher. The factors affecting the overall quality of prefabricated concrete buildings were mainly in the construction stage.

Sustainability 2023 , 15 , 9682 12 of 31 Sustainability 2023 , 15 , x FOR PEER REVIEW 13 of 33 Figure 4. ISM-BN model. Figure 4. ISM-BN model.

Sustainability 2023 , 15 , 9682 13 of 31 Note: The Bayesian network nodes depicted in Figure 4 are approximations of the exact values. For precise values, please refer to Table 6 . Table 6. Exact value of the node R 1 R 2 R 3 D 0.1776 0.6969 0.1255 D 1 0.3374 0.4842 0.1784 D 2 0.3528 0.5426 0.1046 D 3 0.2178 0.6040 0.1782 D 4 0.2907 0.5442 0.1651 D 5 0.2838 0.5518 0.1644 D 6 0.2871 0.5426 0.1703 D 7 0.2047 0.6039 0.1914 D 8 0.2529 0.5886 0.1585 D 9 0.2506 0.5061 0.2433 P 0.3069 0.4573 0.2358 P 1 0.2579 0.5572 0.1849 P 2 0.3090 0.5718 0.1192 P 3 0.4126 0.4661 0.1213 P 4 0.4252 0.4757 0.0991 P 5 0.3821 0.4396 0.1783 P 6 0.4309 0.4451 0.1240 P 7 0.4039 0.4915 0.1046 P 8 0.3674 0.5207 0.1119 P 9 0.3453 0.4636 0.1911 P 10 0.3190 0.5237 0.1573 P 11 0.3962 0.4831 0.1207 P 12 0.2944 0.4915 0.2141 T 0.3172 0.4305 0.2523 T 1 0.3528 0.5353 0.1119 T 2 0.3820 0.5061 0.1119 T 3 0.4035 0.4620 0.1345 T 4 0.3765 0.4697 0.1538 T 5 0.3491 0.5049 0.1460 T 6 0.4180 0.4755 0.1065 T 7 0.3281 0.5267 0.1452 T 8 0.3533 0.5048 0.1419 T 9 0.4034 0.4606 0.1360 C 0.2990 0.4025 0.2985 C 1 0.2287 0.4988 0.2725 C 2 0.2652 0.5207 0.2141 C 3 0.2944 0.5499 0.1557 C 4 0.2506 0.5718 0.1776 C 5 0.2582 0.5984 0.1434 C 6 0.2828 0.4096 0.3076 C 7 0.3309 0.4842 0.1849 C 8 0.2579 0.5791 0.1630 C 9 0.2950 0.5585 0.1465 C 10 0.2940 0.5263 0.1797 C 11 0.2590 0.4332 0.3078 C 12 0.2856 0.5230 0.1914 C 13 0.3459 0.5122 0.1419 Q 0.2808 0.5487 0.1705 4.2. Backward Reasoning Analysis Backward reasoning analysis is also called reverse diagnostic reasoning. When the occurrence of the target node is determined, the probability of risk occurrence of other

[Find the meaning and references behind the names: Top, Map, Change, Dark, Color, Lower, Small]

Sustainability 2023 , 15 , 9682 14 of 31 nodes is derived [ 38 , 39 ]. Table 7 shows the factors with a relatively high rate of change in the posterior probability test of the design stage, the component production stage, the transport stage, and the construction stage of the prefabricated building project Table 7. Results of backward reasoning Stage Factors Design stage D 1 D 5 D 6 D 7 D 8 Component production stage P 5 P 6 P 9 Transport stage T 3 T 8 Construction Stage C 2 C 5 C 11 C 12 C 13 According to the factors listed in Table 6 and the backward reasoning analysis figures in Appendix B (Figures A 1 – A 4 ), D 1 (Lack of precast design skills or experience) and D 8 (Lack of coordination between prefabricated design and construction plan) had a change rate of more than 1 for these two factors. Additionally, D 5 (Split design is unreasonable or not in place), D 7 (Lack of coordination between traditional design and prefabricated design), and D 6 (Design standardization is not high) had relatively large change rates, which were significantly different from other factors in this stage. In the production stage, P 5 (The curing conditions do not meet the requirements), P 6 (Unreasonable ratio of raw materials), and P 9 (The production process cannot meet the quality requirements) had relatively large change rates, while the change rate of other factors in this stage was significantly lower. The posterior probabilities for these three factors were notably different compared to the other factors in this stage. In the transportation stage, T 3 (Unreasonable selection of transport tools) and T 8 (Prefabricated components transportation protection measures are not in place) were the top two factors. The rate of change for these two factors was not significantly different from that for other factors in this stage. In the construction stage, C 2 (Insufficient sense of responsibility of construction personnel), C 5 (Prefabricated components are checked carelessly), C 11 (Component installation accuracy is not enough), C 12 (Improper stacking of prefabricated components), and C 13 (Construction workers lack reasonable working surfaces) had a relatively large rate of change and ranked among the top five factors. The rate of change for factors in this stage was lower than that of the other three stages, but the posterior probability value of high risk was generally higher. The factors in the construction stage significantly impacted the overall quality of the prefabricated building 4.3. Sensitivity Analysis Sensitivity analysis can determine which factors have a small change but can cause quality problems at a particular stage [ 40 , 41 ]. In Bayesian network graphs, dark nodes are usually used to indicate high-sensitivity variables, while lighter nodes indicate lowersensitivity variables. Table 8 shows the nodes with high sensitivity in the design, component production, transportation, and construction stages. The sensitive factor identification map of the four stages was shown in Appendix B (Figures A 5 – A 8 ), with factors of higher sensitivity marked in dark color. In the design stage, D 1 (Lack of precast design skills or experience), D 8 (Lack of coordination between prefabricated design and construction plan), and D 9 (Design time is tight) were highly sensitive factors at this stage. Therefore, design experience, coordination of schemes, and project deadlines had a greater impact on design quality. In the component production stage, P 5 (The curing conditions do not meet the requirements), P 6 (Unreasonable ratio of raw materials), P 7 (Lack of technical specifications and standards for component production), P 8 (Lack of production quality management information system) were high sensitivity factors at this stage. Therefore, production standards and methods, raw material ratios, and management systems had a greater impact on production quality. In the transport stage, T 1 (Transport personnel are not professional enough), and T 2 (Insufficient sense of responsibility of transport personnel) were highly sensitive factors. Therefore, practitioners’ professionalism and sense

[Find the meaning and references behind the names: Path, Arc]

Sustainability 2023 , 15 , 9682 15 of 31 of responsibility have a greater impact on the quality of transportation. In the construction stage, C 2 (Insufficient sense of responsibility of construction personnel), C 5 (Prefabricated components are checked careless), C 8 (Instructions for on-site assembly and construction are not detailed or accurate), and C 13 (Construction workers lack reasonable working surfaces) were highly sensitive factors at this stage. Therefore, the quality awareness of practitioners and the rationality of construction standards and construction schemes had a greater impact on construction quality Table 8. High sensitivity factor table Stage Factors Design stage D 1 D 8 D 9 Component production stage P 5 P 6 P 8 P 7 Transport stage T 1 T 2 Construction Stage C 2 C 5 C 8 C 13 4.4. Critical Factor Analysis Critical quality factor analysis can identify each stage’s most approximate cause chain and critical risk path. The directed arc’s width represents the influence intensity between the two nodes [ 42 ]. Table 9 displays the critical factors in the design, component production, transportation, and construction stages Table 9. Critical factor table Stage Factors Design stage D 2 D 4 D 7 D 9 Component production stage P 3 P 7 P 8 Transport stage T 1 T 2 T 5 T 4 T 6 Construction Stage C 1 C 2 C 3 C 9 Based on the factors listed in Table 9 and the critical factor analysis chart in Figure 5 , we could obtain the nodes with the highest connection strength in the four stages by comparing the connection strength between the parent and child nodes. During the design stage, D 7 (Lack of coordination between traditional design and prefabricated design) for D 1 (Lack of precast design skills or experience) had the greatest effect intensity. Critical factors to consider at this stage include staff accountability and program coordination issues. During the production stage, P 8 (Lack of production quality management information system) for P 11 (Workshop temperature and humidity do not meet the requirements) had the greatest effect intensity. The critical factors at this stage mainly focused on production management issues and technical specifications. During the transport stage, T 1 (Transport personnel are not professional enough) for T 3 (Unreasonable selection of transport tools) had the greatest effect intensity. Critical factors to consider at this stage included the experience and sense of responsibility of staff and the rationality of the transportation plan. During the construction stage, C 9 (Unreasonable construction schedule) for C 13 (Construction workers lack reasonable working surfaces) had the greatest intensity. The critical factors at this stage were mainly focused on the staff’s level of experience and responsibility and the issue of coordinating program management 4.5. Results of Comparison By comparing the three analyses (Table 10 ), C 2 (Insufficient sense of responsibility of construction personnel) was the factor that require the most intensive control. This factor belonged to the construction stage. Therefore, project managers should strengthen staff training and enhance their quality awareness and sense of responsibility.

Sustainability 2023 , 15 , 9682 16 of 31 Sustainability 2023 , 15 , x FOR PEER REVIEW 17 of 33 Figure 5. Critical factor analysis. Figure 5. Critical factor analysis.

[Find the meaning and references behind the names: Story, South, Code, Human, Road, Villas, West, Main, River, Case, Parts, Rooms]

Sustainability 2023 , 15 , 9682 17 of 31 Table 10. Results of comparison Backward Reasoning Analysis Sensitivity Analysis Critical Factor Analysis Design stage D 1 D 5 D 6 D 7 D 8 D 1 D 8 D 9 D 2 D 4 D 7 D 9 Component production stage P 5 P 6 P 9 P 5 P 6 P 8 P 7 P 3 P 7 P 8 Transport stage T 3 T 8 T 1 T 2 T 1 T 2 T 5 T 4 T 6 Construction Stage C 2 C 5 C 11 C 12 C 13 C 2 C 5 C 8 C 13 C 1 C 2 C 3 C 9 Some quality factors need a little attention in each stage. In the design stage, attention should be paid to D 1 (Lack of precast design skills or experience), D 7 (Lack of technical specifications and standards for component production), D 8 (Lack of coordination between prefabricated design and construction plan), and D 9 (Design time is tight). In the production stage, attention should be paid to P 5 (The curing conditions do not meet the requirements), P 6 (Unreasonable ratio of raw materials), P 7 (Lack of technical specifications and standards for component production), and P 8 (Lack of production quality management information system). In the transport stage, attention should be paid to T 1 (Transport personnel are not professional enough) and T 2 (Inadequate responsibility of transport personnel). In the construction stage, attention should be paid to, C 5 (Prefabricated components are checked carelessly), and C 13 (Construction workers lack reasonable working surfaces). The results of this paper are partially similar to those of Tao Yu et al. [ 5 ] in that the human factors in the project have a greater impact on the quality of assembled buildings. However, this paper has a broader study of factors, and the influence of code standards, the rationality of design solutions, and the ratio of materials on the quality of prefabricated buildings is also significant 5. The Case Study 5.1. Basic Information of the Project Yingyuan Subdistrict Phase II Project is located on the south side of Shanghai Road and west of Huangpu River, with a prefabrication rate of 50%. The project consists of four 26-story residential buildings, one 18-story residential building, two 15-story residential buildings, 12 villas, basements, supporting rooms, garages, and ancillary facilities, totaling 105,400 m 2 . Prefabricated parts and components include main and outer enclosure structures and inner and interior building components. On-site interviews and surveys were conducted by the relevant staff, who completed 30 questionnaires. Table 11 shows their educational background, unit nature, and years of employment Table 11. Basic information of relevant staff Constitution Classification Number Nature of the unit Design 8 Construction 8 Proprietor 3 Supervision 2 Others 9 Years of employment Less than 3 years 4 3 to 7 years 5 8 to 12 years 7 13 to 17 years 5 More than 18 years 9 Education background Junior college 3 Undergraduate course 16 Master’s degree 9 Doctor 1 Others 1

[Find the meaning and references behind the names: Resources, Scrap, Hold, Smooth, Sessions, Owner, Welding, Seam]

Sustainability 2023 , 15 , 9682 18 of 31 5.2. Analysis of Quality Problems The questionnaire analysis results of the project case were input into the Bayesian network quality evaluation model. Figure 6 obtained the critical factor distribution map for the project case. The analysis results, in this case, were consistent with the previous evaluation model analysis (1) The influence of the “employee” factor. The unprofessionalism of transportation personnel was primarily evident during the transportation stage. Therefore, adequate training and resources should be provided to the staff to equip transportation personnel with the necessary professional tools to effectively handle challenges encountered during transportation. For example, the local government can organize training sessions to clarify and unify design principles and industrial standards and specifications. In contrast, construction organizations should timely hold workshops or seminars to facilitate internal experience sharing and technical exchange among designer professionals. During the construction stage, inadequate staff experience and poor communication between different units and construction personnel were the main problems. Therefore, staff allocation should be performed well, and professional personnel should be hired to solve the technical problems at each link (2) The influence of “technical method or process” factors at each stage. Designing prefabricated structures may face issues of inconsistency with traditional modes or construction methods. Therefore, the type, connection method (e.g., bolting, welding, mortise, and tenon joints), and construction process of the assembled components need to be clarified in the design stage to ensure the smoothness of the subsequent stages. Clarifying the types of assembly components, connection methods, and construction processes helps designers and manufacturers work collaboratively in different project stages. Prefabricated components were prone to appearance quality defects, such as cracks, shape defects, and local uncompacted concrete. Therefore, a complete production management system should be established. Component production standards and specifications should be formulated. Unreasonable selection of transportation means or unreasonable transportation route planning may cause the loss of some components. This will reduce quality problems and scrap rates in production and improve productivity and resource utilization. Selecting transportation and hoisting tools according to the size and shape of the components was necessary to ensure the smooth progress of subsequent construction. Installing prefabricated components was a key process to ensure the quality of the construction stage—the installation involved flatness control, seam check, joint welding quality, etc. Therefore, the on-site assembly should be carried out in strict accordance with the drawing requirements and construction specifications. For the contractors and the owner, it improves the quality of the installation of prefabricated components during the construction stage, ensures the accurate positioning and stable connection of the components, and enhances the safety and stability of the overall building structure (3) The construction stage had the greatest impact on the quality of prefabricated buildings. The construction stage of prefabricated buildings should consider the building’s durability, safety, and reliability. Therefore, attention should be paid to the acceptance of component quality, the inspection of concealed projects, and the reasonable arrangement of construction planned to ensure construction quality while improving efficiency and saving costs (4) In the case study of this project, the correlation between C 9 (Unreasonable construction schedule) and its sub-node was clearly enhanced. The project’s time-setting requirement was too high, and the construction period was short. The difficulty of construction was increased, resulting in a very tight project schedule. The construction plan was required to be modified or rearranged.

[Find the meaning and references behind the names: Cases]

Sustainability 2023 , 15 , 9682 19 of 31 Sustainability 2023 , 15 , x FOR PEER REVIEW 21 of 33 Figure 6. Quality Factor Evaluation Results of Project Cases. Figure 6. Quality Factor Evaluation Results of Project Cases.

Sustainability 2023 , 15 , 9682 20 of 31 Note: The Bayesian network nodes depicted in Figure 6 are approximations of the exact values. For precise values, please refer to Table 12 . Table 12. Exact value of the case node R 1 R 2 R 3 D 0.2999 0.4706 0.2295 D 1 0.4376 0.2850 0.2774 D 2 0.3656 0.5269 0.1075 D 3 0.2843 0.4747 0.2410 D 4 0.3407 0.4046 0.2547 D 5 0.3623 0.3833 0.2544 D 6 0.3656 0.4624 0.1720 D 7 0.2440 0.5141 0.2419 D 8 0.3031 0.4812 0.2157 D 9 0.3333 0.4624 0.2043 P 0.3391 0.3484 0.3125 P 1 0.2043 0.5591 0.2366 P 2 0.3333 0.4946 0.1720 P 3 0.4572 0.4072 0.1356 P 4 0.4609 0.3669 0.1722 P 5 0.3995 0.3671 0.2334 P 6 0.4551 0.3248 0.2201 P 7 0.4624 0.3978 0.1398 P 8 0.3333 0.4946 0.1720 P 9 0.3579 0.3655 0.2766 P 10 0.3206 0.5016 0.1778 P 11 0.3948 0.4009 0.2043 P 12 0.3333 0.3656 0.3011 T 0.3608 0.3228 0.3164 T 1 0.4301 0.3656 0.2043 T 2 0.4946 0.3333 0.1721 T 3 0.4600 0.3335 0.2065 T 4 0.3819 0.3578 0.2603 T 5 0.4080 0.3584 0.2336 T 6 0.5209 0.2713 0.2078 T 7 0.3739 0.3013 0.3248 T 8 0.3700 0.3657 0.2643 T 9 0.4898 0.3307 0.1795 C 0.3224 0.3534 0.3242 C 1 0.2043 0.4301 0.3656 C 2 0.1398 0.5591 0.3011 C 3 0.2366 0.5269 0.2365 C 4 0.1720 0.6237 0.2043 C 5 0.2378 0.5198 0.2424 C 6 0.3062 0.3829 0.3109 C 7 0.3011 0.4301 0.2688 C 8 0.2043 0.5269 0.2688 C 9 0.2660 0.4396 0.2944 C 10 0.2388 0.4564 0.3048 C 11 0.2991 0.3479 0.3530 C 12 0.2450 0.4862 0.2688 C 13 0.2684 0.5248 0.2068 Q 0.3269 0.4142 0.2589 6. Conclusions The factors affecting prefabricated building quality were determined through relevant literature research and expert interviews. Then, the ISM-BN model was established to visualize the relationship between nodes. The model parameters were learned to obtain the probability of each node. The qualitative and quantitative combination of the ISM-BN model could help practitioners fully identify factors affecting project quality during implementation and formulate measures to improve prefabricated buildings’ quality. Through the analysis of the quality problems of a prefabricated building project in Nantong, it is found that the evaluation results of quality factors established in this case are consistent

[Find the meaning and references behind the names: Modern, Gps, Bim, List, Better, Final, Safe, Tailor, Offer, Take]

Sustainability 2023 , 15 , 9682 21 of 31 with the results of the previous analysis, indicating that the model is applicable in general prefabricated building projects According to the reverse reasoning analysis, sensitivity analysis, and key factor analysis of the ISM-BN model, the list of quality factors that need to be controlled and paid attention to find that these quality factors have the following characteristics and propose corresponding measures: (1) A prefabricated construction project in Nantong City was analyzed using the proposed evaluation model. The analysis results were consistent with similar evaluations, proving the practicality and reasonableness of the model. (2) The design stage had a lower probability of serious quality problems than the other three stages The important factors were focused on the lack of experience of designers, unreasonable design solutions or links, and design specifications. Increasing the training of design personnel and enhancing their sense of responsibility are essential steps for improving the quality of the design stage. Design organizations should arrange the design plan more reasonably and strengthen the coordination between the prefabricated design and the construction plan to ensure the design project is completed on time. Multiple factors such as functionality, feasibility, economy, and sustainability should be taken into consideration by designers when making design plans to facilitate project success. (3) The probability of serious quality problems in the production stage was significantly higher than that in the design stage, but it was overall slightly lower than that in the transportation and construction stages. The factors leading to production quality problems were mainly focused on the production process’s specification and supervision and the raw materials’ rationing To ensure prefabricated components meet production standards, production enterprises should introduce information technology management systems such as BIM to better tailor for the specific needs of the prefabrication process, which can offer effective inventory management, quality control, and precise progress management. In addition, standardized raw material ratios and component maintenance systems should be established, which can provide accurate maintenance records (e.g., time and personnel) to ensure the traceability and consistency of maintenance work. (4) The probability of serious quality problems in the transportation stage was slightly lower than in the construction stage. The factors leading to transportation quality problems were mainly focused on the lack of professionalism and responsibility of transportation personnel. For the transportation stage, transportation companies should strengthen the training of transportation personnel to ensure they can reasonably arrange component transportation plans. Modern technologies such as GPS and vehicle diagnostic systems should be adopted to ensure the transparency of the transportation process, which can significantly improve transportation efficiency by optimizing route planning and ensuring the safe and on-time arrival of the components (5) The construction stage was the most critical stage of a project. The probability of quality problems in this stage was significantly higher than in the other three stages. The factors leading to construction quality problems were mainly focused on the staff’s responsibility, the plan’s rationality, and the components’ quality. Therefore, a responsibility system should be established to urge workers to take their work seriously. For instance, quality supervision personnel should be appointed to conduct regular inspections and evaluations to implement quality monitoring in the construction stage. Reasonable construction plans should be formulated to ensure the construction process proceeds smoothly. Prefabricated components should be inspected strictly according to the requirements of the drawings to reduce deviations caused by component issues during the construction stage This paper had additional difficulties to solve: (1) The acquisition of quality factors for prefabricated buildings was mainly obtained through literature research and expert interviews. More scientific methods can be explored to revise and supplement the indicators, such as case study method, brainstorming method, field investigation method, etc (2) The final stage involved in the index of factors affecting prefabricated building quality established in this paper was the construction stage. The operation and maintenance stages after completion have not been involved. The operation and maintenance stage involves the maintenance of prefabricated buildings and the actual interests of the owners. Future

[Find the meaning and references behind the names: Add, Read, Author, Focus]

Sustainability 2023 , 15 , 9682 22 of 31 research can focus on screening and supplementing the factor indicators affecting quality at this stage Author Contributions: Conceptualization, L.Z.; resources, J.Z.; writing and analysis, M.W.; modifying, M.C. All authors have read and agreed to the published version of the manuscript Funding: This research received no external funding Informed Consent Statement: Informed consent was obtained from all subjects involved in the study Data Availability Statement: The case analysis data used to support the findings of this study are available from the second author upon request Conflicts of Interest: The authors declare no conflict of interest Appendix A Table A 1. Quality Factor Questionnaire Stage Quality Factors Experts Add Design stage Lack of precast design skills or experience Insufficient responsibility of designers Inadequate communication and coordination among professional designers Insufficient communication between designers and other stakeholders Design standardization is not high Lack of coordination between prefabricated design and construction plan Design time is tight Prefabricated component production stage Relevant staff have weak quality awareness Insufficient professional competence of production personnel Production equipment does not meet the standard The curing conditions do not meet the requirements (standard curing room conditions) Lack of technical specifications and standards for component production Lack of production quality management information system The production process cannot meet the quality requirements Components not stored according to standard (industry standard) Workshop temperature and humidity do not meet the requirements Production time is tight Transport stage Transport personnel are not professional enough Insufficient sense of responsibility of transport personnel Unreasonable selection of transport tools Unreasonable selection of hoisting tools Unreasonable transportation route planning Improper loading and unloading of prefabricated components Prefabricated components transportation protection measures are not in place The transportation distance is too long Construction stage Insufficient practical experience of construction workers and managers Insufficient sense of responsibility of construction personnel Insufficient quality and level of supervisors Prefabricated components are checked careless Insufficient connection strength of prefabricated components (e.g., insufficient grouting strength, insufficient bolt strength) Lack of construction quality inspection tools Instructions for on-site assembly and construction are not detailed or accurate Unreasonable construction schedule Improper construction practices Improper stacking of prefabricated components Construction workers lack reasonable working surfaces

Sustainability 2023 , 15 , 9682 23 of 31 Table A 2. Influence relationships in the design stage Quality Factors Number Direct Influencing Factors Lack of precast design skills or experience D 1 Insufficient responsibility of designers D 2 Inadequate communication and coordination among professional designers D 3 Insufficient communication between designers and other stakeholders D 4 Split design is unreasonable or not in place D 5 Design standardization is not high D 6 Lack of coordination between traditional design and prefabricated design D 7 Lack of coordination between prefabricated design and construction plan D 8 Design time is tight D 9 Table A 3. Scores of factors affecting the quality of prefabricated buildings Score 1 2 3 4 5 Probability of occurrence Hardly happens Rarely occurs Generally More frequent Happens frequently Degree of impact Almost no effect Less affected Generally More serious Seriously affected Table A 4. Sample Questionnaire in the design stage Risk Factors Score Degree of Loss Probability of Occurrence 1 2 3 4 5 1 2 3 4 5 Lack of precast design skills or experience D 1 Insufficient responsibility of designers D 2 Inadequate communication and coordination among professional designers D 3 Insufficient communication between designers and other stakeholders D 4 Split design is unreasonable or not in place D 5 Design standardization is not high D 6 Lack of coordination between traditional design and prefabricated design D 7 Lack of coordination between prefabricated design and construction plan D 8 Design time is tight D 9 Table A 5. Sample Questionnaire in the production stage Risk Factors Score Degree of Loss Probability of Occurrence 1 2 3 4 5 1 2 3 4 5 Relevant staff have weak quality awareness P 1 Insufficient professional competence of production personnel P 2 Insufficient quantity of raw materials (such as steel bars, cement not in the prescribed quantity) P 3 Production equipment does not meet the standard P 4

Sustainability 2023 , 15 , 9682 24 of 31 Table A 5. Cont Risk Factors Score Degree of Loss Probability of Occurrence 1 2 3 4 5 1 2 3 4 5 The curing conditions do not meet the requirements (standard curing room conditions) P 5 Unreasonable ratio of raw materials P 6 Lack of technical specifications and standards for component production P 7 Lack of production quality management information system P 8 The production process cannot meet the quality requirements P 9 Components not stored according to standard (industry standard) P 10 Workshop temperature and humidity do not meet the requirements P 11 Production time is tight P 12 Table A 6. Sample Questionnaire in the transportation stage Risk Factors Score Degree of Loss Probability of Occurrence 1 2 3 4 5 1 2 3 4 5 Transport personnel are not professional enough T 1 Insufficient sense of responsibility of transport personnel T 2 Unreasonable selection of transport tools T 3 Unreasonable selection of hoisting tools T 4 Unreasonable shipping sequence of prefabricated components T 5 Unreasonable transportation route planning T 6 Improper loading and unloading of prefabricated components T 7 Prefabricated components transportation protection measures are not in place T 8 The transportation distance is too long T 9 Table A 7. Sample Questionnaire in the construction stage Risk Factors Score Degree of Loss Probability of Occurrence 1 2 3 4 5 1 2 3 4 5 Insufficient practical experience of construction workers and managers C 1 Insufficient sense of responsibility of construction personnel C 2 Inadequate communication between various units and on-site construction personnel C 3 Insufficient quality and level of supervisors C 4 Prefabricated components are checked careless C 5

Sustainability 2023 , 15 , 9682 25 of 31 Table A 7. Cont Risk Factors Score Degree of Loss Probability of Occurrence 1 2 3 4 5 1 2 3 4 5 Insufficient connection strength of prefabricated components (e.g., insufficient grouting strength, insufficient bolt strength) C 6 Lack of construction quality inspection tools C 7 Instructions for on-site assembly and construction are not detailed or accurate C 8 Unreasonable construction schedule C 9 Improper construction practices C 10 Component installation accuracy is not enough C 11 Improper stacking of prefabricated components C 12 Construction workers lack reasonable working surfaces C 13 Table A 8. Reachability matrix in the production stage P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9 P 10 P 11 P 12 P 1 1 0 1 0 0 1 0 0 0 1 0 0 P 2 0 1 0 0 0 0 0 0 1 0 0 0 P 3 0 0 1 0 0 1 0 0 0 0 0 0 P 4 0 0 0 1 0 0 0 0 1 0 0 0 P 5 0 0 0 0 1 0 0 0 0 0 0 0 P 6 0 0 0 0 0 1 0 0 0 0 0 0 P 7 0 0 0 1 1 0 1 0 1 0 0 0 P 8 0 0 1 0 0 1 0 1 1 1 1 0 P 9 0 0 0 0 0 0 0 0 1 0 0 0 P 10 0 0 0 0 0 0 0 0 0 1 0 0 P 11 0 0 0 0 0 0 0 0 1 0 1 0 P 12 0 0 0 0 0 0 0 0 1 0 0 1 Table A 9. Reachability matrix in the transportation stage T 1 T 2 T 3 T 4 T 5 T 6 T 7 T 8 T 9 T 1 1 0 1 1 1 1 1 0 1 T 2 0 1 0 1 1 0 1 1 0 T 3 0 0 1 0 0 0 0 0 0 T 4 0 0 0 1 1 0 1 0 0 T 5 0 0 0 0 1 0 1 0 0 T 6 0 0 0 0 0 1 0 0 1 T 7 0 0 0 0 0 0 1 0 0 T 8 0 0 0 0 0 0 0 1 0 T 9 0 0 0 0 0 0 0 0 1 Table A 10. Reachability matrix in the construction stage C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 C 11 C 12 C 13 C 1 1 0 0 0 0 1 0 0 1 1 1 0 1 C 2 0 1 0 0 1 1 0 0 0 0 0 1 0 C 3 0 0 1 0 0 0 0 0 1 0 0 0 1 C 4 0 0 0 1 0 1 0 0 0 0 1 0 0 C 5 0 0 0 0 1 0 0 0 0 0 0 0 0 C 6 0 0 0 0 0 1 0 0 0 0 0 0 0 C 7 0 0 0 0 0 1 1 0 0 0 1 0 0

Sustainability 2023 , 15 , 9682 26 of 31 Table A 10. Cont C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 C 11 C 12 C 13 C 8 0 0 0 0 0 1 0 1 0 0 1 1 0 C 9 0 0 0 0 0 0 0 0 1 0 0 0 1 C 10 0 0 0 0 0 1 0 0 0 1 1 0 0 C 11 0 0 0 0 0 0 0 0 0 0 1 0 0 C 12 0 0 0 0 0 0 0 0 0 0 0 1 0 C 13 0 0 0 0 0 0 0 0 0 0 0 0 1 Appendix B Sustainability 2023 , 15 , x FOR PEER REVIEW 28 of 33 Table A 10. Reachability matrix in the construction stage. C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 C 11 C 12 C 13 C 1 1 0 0 0 0 1 0 0 1 1 1 0 1 C 2 0 1 0 0 1 1 0 0 0 0 0 1 0 C 3 0 0 1 0 0 0 0 0 1 0 0 0 1 C 4 0 0 0 1 0 1 0 0 0 0 1 0 0 C 5 0 0 0 0 1 0 0 0 0 0 0 0 0 C 6 0 0 0 0 0 1 0 0 0 0 0 0 0 C 7 0 0 0 0 0 1 1 0 0 0 1 0 0 C 8 0 0 0 0 0 1 0 1 0 0 1 1 0 C 9 0 0 0 0 0 0 0 0 1 0 0 0 1 C 10 0 0 0 0 0 1 0 0 0 1 1 0 0 C 11 0 0 0 0 0 0 0 0 0 0 1 0 0 C 12 0 0 0 0 0 0 0 0 0 0 0 1 0 C 13 0 0 0 0 0 0 0 0 0 0 0 0 1 Appendix B Figure A 1. Posterior probability of design stage. Figure A 1. Posterior probability of design stage Sustainability 2023 , 15 , x FOR PEER REVIEW 29 of 33 Figure A 2. Posterior probability of production stage. Figure A 3. Posterior probability of transport stage. Figure A 2. Posterior probability of production stage.

Sustainability 2023 , 15 , 9682 27 of 31 Sustainability 2023 , 15 , x FOR PEER REVIEW 29 of 33 Figure A 2. Posterior probability of production stage. Figure A 3. Posterior probability of transport stage. Figure A 3. Posterior probability of transport stage Sustainability 2023 , 15 , x FOR PEER REVIEW 30 of 33 Figure A 4. Posterior probability of construction stage. Figure A 5. Sensitivity analysis model in the design stage. Figure A 4. Posterior probability of construction stage.

Sustainability 2023 , 15 , 9682 28 of 31 Sustainability 2023 , 15 , x FOR PEER REVIEW 30 of 33 Figure A 4. Posterior probability of construction stage. Figure A 5. Sensitivity analysis model in the design stage. Figure A 5. Sensitivity analysis model in the design stage Sustainability 2023 , 15 , x FOR PEER REVIEW 31 of 33 Figure A 6. Sensitivity analysis model in the prefabricated components production stage. Figure A 7. Sensitivity analysis model in the transportation stage. Figure A 6. Sensitivity analysis model in the prefabricated components production stage.

[Find the meaning and references behind the names: Eng, Liu, Lee, Civ, Nie, Masood, Dea, Decoration, Bristol, Western, Riley, Navaratnam, Yuan, Ngo, Soc, Choi, Shin, Han, Mendis, Adv, Sci, Tam, Inf, Qiao, Henderson, Nguyen, Okudan, Cham, Arab, Prod, Zhou, Cui, Lim, Camera, Image, Venkatesan, Zhong, Lean, House, Early, Shen, Springer]

Sustainability 2023 , 15 , 9682 29 of 31 Sustainability 2023 , 15 , x FOR PEER REVIEW 31 of 33 Figure A 6. Sensitivity analysis model in the prefabricated components production stage. Figure A 7. Sensitivity analysis model in the transportation stage. Figure A 7. Sensitivity analysis model in the transportation stage Sustainability 2023 , 15 , x FOR PEER REVIEW 32 of 33 Figure A 8. Sensitivity analysis model in the construction stage. References 1 Gunawardena, T.; Mendis, P. Prefabricated Building Systems—Design and Construction Encyclopedia 2022 , 2 , 70–95. 2 Fernández-Ordóñez Hernández, D. Early Developments of Concrete Prefabrication ; Springer International Publishing: Cham, Switzerland, 2017; pp. 2795–2801. 3 Chen, Y.; Okudan, G.E.; Riley, D.R. Sustainable performance criteria for construction method selection in concrete buildings Automat. Constr. 2010 , 19 , 235–244. 4 Wang, S.; Wang, C.; Li, W.; Zhao, D. Study on the operational efficiency of prefabricated building industry bases in Western China based on the DEA model Arab. J. Geosci. 2021 , 14 , 446. 5 Yu, T.; Man, Q.; Wang, Y.; Shen, G.Q.; Hong, J.; Zhang, J.; Zhong, J. Evaluating different stakeholder impacts on the occurrence of quality defects in offsite construction projects: A Bayesian-network-based model J. Clean. Prod. 2019 , 241 , 118390. 6 Navaratnam, S.; Satheeskumar, A.; Zhang, G.; Nguyen, K.; Venkatesan, S.; Poologanathan, K. The challenges confronting the growth of sustainable prefabricated building construction in Australia: Construction industry views . J. Build. Eng. 2022 , 48 , 103935. 7 Gan, Y.; Shen, L.; Chen, J.; Tam, V.; Tan, Y.; Illankoon, I. Critical Factors Affecting the Quality of Industrialized Building System Projects in China Sustainability 2017 , 9 , 216. 8 Deng, H.; Liu, J. Research on PC Component Quality Risk Evaluation Based on Intuitionistic Fuzzy Analytic Hierarchy Process In IOP Conference Series. Earth and Environmental Science ; IOP Publishing: Bristol, UK, 2020; Volume 525, p. 12043. 9 Xia, M.; Zhao, L.; Qiao, Y.; Yuan, Z.; Cui, Y.; Zhao, L.; Li, J. Analysis of Factors Affecting the Quality of Precast Components Based on Structural Equation Modeling Arab. J. Sci. Eng. 2022 , 47 , 4171–4185. 10 Yuan, Z.; Zhang, Z.; Ni, G.; Chen, C.; Wang, W.; Hong, J. Cause Analysis of Hindering On-Site Lean Construction for Prefabricated Buildings and Corresponding Organizational Capability Evaluation Adv. Civ. Eng. 2020 , 2020 , 8876102. 11 Lee, D.; Nie, G.; Han, K. Vision-based inspection of prefabricated components using camera poses: Addressing inherent limitations of image-based 3 D reconstruction J. Build. Eng. 2023 , 64 , 105710. 12 Shin, J.; Choi, B. Design and Implementation of Quality Information Management System for Modular Construction Factory Buildings 2022 , 12 , 654. 13 Zhong, C.; Zhang, M.; Cui, X.; Liu, Z. Comprehensive Evaluation of China’s Prefabricated Decoration Cost Based on Analytic Hierarchy Process Adv. Civ. Eng. 2020 , 2020 , 1583748. 14 Masood, R.; Lim, J.B.P.; González, V.A. Performance of the supply chains for New Zealand prefabricated house-building. Sustain. Cities Soc. 2021 , 64 , 102537. 15 Navaratnam, S.; Ngo, T.; Gunawardena, T.; Henderson, D. Performance Review of Prefabricated Building Systems and Future Research in Australia Buildings 2019 , 9 , 38. 16 Wang, Z.; Hu, H.; Zhou, W. RFID Enabled Knowledge-Based Precast Construction Supply Chain Comput.-Aided Civ. Inf. 2017 , 32 , 499–514. Figure A 8. Sensitivity analysis model in the construction stage.

[Find the meaning and references behind the names: Xie, North, Gao, Jiang, Urban, Int, Zuo, February, Gonz, Zhu, Luo, Sugumaran, Yao, Architecture, Smc, Ord, Fern, Hern, Stig, Xue]

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