Risk Factor Analysis of Elevator Brake Failure Based on DEMATEL-ISM

Abstract

With the acceleration of urbanization process, the number of elevators in China has surged. Concurrently, the prevalence of older elevators has increased, leading to a rise in frequent malfunctions. In recent years, there has been a troubling frequency of elevator accidents resulting in casualties, which has had a negative social impact. The elevator braking system is crucial for ensuring the safe operation of the elevator, and brake failure is a significant contributor to elevator accidents. The failure modes of elevator brakes are complex and diverse, and the failure risk factors are mixed, correlated and unknown. Therefore, this paper is based on the Failure Mode and Effects Analysis (FMEA), focusing on the structural characteristics of the elevator brake to determine the equipment failure risk factors. Based on the accident prevention theory model (24Model) for comprehensive analysis of internal and external causes, this study identifies the comprehensive failure risk factors for elevator brakes. The study employs affiliation function to build the failure risk factor indicator system, the use of the Decision-making Trial and Evaluation Laboratory (DEMATEL) and Interpretative Structural Modeling (ISM) methods to analyze the hierarchical structure and internal relationship between the factors. Based on the research results, the factors contributing to the failure of elevator drum brakes can be identified and the interrelationships among these factors can be systematically elucidated. This analysis can serve as a valuable tool in pinpointing critical areas for routine elevator maintenance and upkeep, with the aim of minimizing the likelihood of drum brake malfunctions. Furthermore, the insights gained can inform the design and implementation of elevator monitoring and management systems, enabling a clearer focus on pertinent factors. Ultimately, this study furnishes a theoretical framework for the prevention and mitigation of such accidents.

1. Introduction

As a critical component of vertical transportation in buildings, elevators are indispensable electromechanical devices, especially in modern high-rise buildings. They bring convenience to us and improves our working efficiency and living standards [1]. With the rapid urbanization in China, elevator ownership has surged significantly [2]. At the same time, the number of aging elevators is increasing annually, leading to a rise in frequent malfunctions and, consequently, a notable increase in accidents with casualties [3]. Currently, a multitude of factors contribute to elevator accidents, and these factors are intricately interconnected. The task of detecting all potential faults during routine elevator maintenance is challenging, thereby potentially elevating the risk of elevator accidents. Furthermore, the current advancement in elevator monitoring systems primarily focuses on predicting faults by monitoring extensive individual datasets. However, these systems often overlook the interdependencies among various faults, rendering it difficult for them to comprehensively analyze all contributing fault factors. The elevator braking system serves a vital role in ensuring the safe operation of elevators [4]. The control and safety functions of elevators are ultimately reliant on the brake system [5,6]. Once the safety function of the brake fails, it often leads to such serious accidents as falling, roofing, and shearing of the elevator car, which brings unacceptable risks and great threats to passengers’ lives and property [7,8]. Elevator brake failure is a leading cause of elevator accidents [9]. For this reason, the State Administration for Market Regulation has launched a national elevator brake hidden trouble special investigation and management work. Aiming at the problems of high failure rate, large failure hazards, and serious accident hazards of elevator brakes, it is of great significance to explore the risk factors of elevator brake failure and control them to improve the level of elevator safety governance.

Brake failure modes are complex and varied, with research into these failures being essential for understanding risks [10]. Brake failure has the characteristics of mixed, correlation and unknown [11]. At present, many scholars have studied and analyzed brake failures from different perspectives. David [12] proposed several typical failure forms, failure consequences, and failure causes of elevator brakes, and put forward modification suggestions for the current standard. Some scholars [13,14] analyze the brake failure of elevators based on a variety of failure conditions and study the prevention and control measures of brake failure. Some scholars [15,16,17,18,19,20] analyze the causes of elevator brake failure through simulation technology, theoretical calculations, test methods and so on. However, the existing research mainly focuses on the causes of brake failure, life prediction, etc., and lacks a deep and systematic research on the relationship between the risk factors of elevator brake failure.

This paper employs Failure Mode and Effects Analysis (FMEA) to examine the structural characteristics of elevator brakes and identify equipment failure risk factors. Based on the accident prevention theory model (24Model), this paper provides comprehensive internal and external causes to determine the brake failure risk factors of elevators. An affiliation function is used to build the failure risk factor indicator system, and Decision-making Trial and Evaluation Laboratory (DEMATEL), and Interpretative Structural Modeling (ISM) method are applied to study the hierarchical structure and internal relationship between the factors. Finally, based on the research results, several suggestions are proposed to mitigate the risk of elevator brake failures, offering a theoretical foundation for preventing and controlling elevator drum brake accidents.

The Grey DEMATEL-ISM methodology, which integrates Grey System Theory with DEMATEL and ISM, introduces substantial innovations in the study of elevator drum brake fault factor interrelations. Its academic merits are evident in several key areas: (1) it significantly improves precision and reliability in addressing the inherent uncertainties and ambiguities associated with fault factors, thereby providing a more robust analytical framework; (2) it offers deep insights into the hierarchical fault propagation structures and critical pathways, enabling a comprehensive understanding of the mechanisms underlying fault occurrences; (3) by considering both direct and indirect fault impacts, it expands the analytical perspective and uncovers novel fault patterns, thereby contributing to the advancement of elevator safety design and maintenance methodologies; and (4) its application serves as a valuable methodological reference for fault analysis in other complex systems, enriching the broader field of elevator safety research and fostering technological progress.

2. Identification of Different Risk Factors for Elevator Brake Failure

2.1. Identification of Equipment Failure Risk Factors

FMEA is an analysis method for finding faults from a reliability point of view. It involves analyzing the occurrence of the failure of each component unit in the equipment and evaluating the impact of these failures on the overall equipment [21]. The process typically follows a structured approach of ‘structure–function–failure–risk’, assessing the function of each component based on the equipment’s design. Then, the risk is assessed qualitatively based on three indicators: Severity, Occurrence and Detection. The primary advantage is that the equipment structure is decomposed to comprehensively consider all possible failure modes and influencing factors in a form that does not miss or repeat, which helps to identify potential problems. However, FMEA has limitations, including (1) It is subject to subjective judgment and relies on qualitative rather than quantitative analysis of problems; (2) It is suitable for single-factor failure analysis and cannot be applied to failure analysis under the interaction of multiple factors; (3) It does not account for personnel-related impacts. To address these shortcomings, the equipment-level failure risk factors for elevator brakes were determined by avoiding the shortcomings of FMEA and taking advantage of its non-missing or non-repeating advantages, as shown in

Table 1. Table of risk factors for failure of elevator brake equipment.

Failure Risk Factors	Potential Forms of Failure
Brake Springs	Abnormal stiffness drop
	Abnormal deformation
	Fracture
Gate Tile Assemblies	Poor heat resistance of friction discs
	Pollution or damage of friction discs
	Inadequate fit
	Abnormal deformation of the gate tile assembly
	Damage, fracture of gate tile assembly
Rotors	Surface contamination or damage
	Inadequate fit
	Abnormal deformation
	Damage, breakage
Spring-loaded Rod	Spring-loaded Rod failure
Brake Arm	Abnormal deformation
	Damage, breakage
Gate Valve Pins	Poor movement of the gate tile assembly
	Abnormal deformation
	Damage, breakage
Brake Arm Pin	Poor brake arm movement
	Abnormal deformation
	Damage, breakage
Saddle	Abnormal deformation
	Damage, breakage
Solenoid Assembly	Long electromagnetic force release time or incomplete elimination
	Cannot overcome the spring force
	Solenoid coil burns out
	Scuffing
	Jamming of the plunger assembly movement
Clearance Bolt	Higher wear on contact surfaces
	Deformation or fracture
	Gap not adjusted (too large)
Buffer Cushion	Buffer cushion failure
	not adjustable/not adjustable in time
Manual Release Assembly	Jamming of the plunger assembly movement and groove
	Excessive wear on contact surfaces
	Decreased or loss of elasticity of torsion springs
	Limit rods or torsion springs failure
Motion Travel Switches, Switching Cables	Damaged switch wiring
Switching Top Bar	Abnormal stroke adjustment
	unstable signal output

(All the tables in this study were created using Microsoft Office LTSC Standard 2021 software).

2.2. Identification of Comprehensive Failure Risk Factors

Elevator brake failure risk factors encompass not only equipment-level factors, but also a variety of integrated factors such as management, personnel, and environment. To address these complexities, the 24Model method is employed to determine the comprehensive failure risk factors of elevator brakes [22]. 24Model considers that internal and external causes jointly lead to accidents. The 24Model categorizes these causes into four primary behavioral phases: Guiding Behavior, Operational Behavior, Habitual Behavior, Disposable Behavior and Physical State [23,24], along with one main category for External Causes, as illustrated in Figure 1 (All the figures in this study were created using Microsoft Office LTSC Standard 2021 software). On this basis, continue to subdivide to determine the comprehensive failure risk factors. By integrating FMEA analysis to determine the failure risk components of the elevator brake equipment, namely, Unsafe Object State, a total of 33 factors influencing the failure risk of the elevator brake. The 33 factors influencing the failure of the elevator drum brake in varying degrees. Based on the expert scoring method and the affiliation function [25], 16 important factors were screened out, the formation of a comprehensive failure risk factor indicator system, as shown in

Table 2. Comprehensive failure risk factor indicator system.

Category of Cause	Behavioral Stages	Main Category	Failure Risk Factors
Internal Causes	Stage I Disposable Behavior and Physical State	Unsafe Actions	Error Action S1
			Unauthorized Action S2
		Unsafe Object State	Brake Spring S3
			Spring-loaded Rod S4
			Gate Tile Assemblies S5
			Solenoid Assembly S6
			Manual Release Assembly S7
	Stage II Habitual Behavior	Personal Behavior	Technical Qualification S8
			Safety Knowledge S9
			Attitude of Responsibility S10
	Stage III Operational Behavior	Safety Management Systems	Policy Planning S11
			Management Control S12
	Stage IV Guiding Behavior	Safety Culture	Subjective Responsibility S13
			Safety Participation S14
External Causes	/	External Factors	Contracting Units S15
			Government and Industry Organizations S16

.

3. Improved DEMATEL-ISM Analytical Methods

FMEA and other failure analysis methods are generally focus on qualitative assessments of single-factor failures, often lacking research on the linkage or coupling between the failure risk factors of elevator brakes. To address this gap, this paper employs DEMATEL-ISM to carry out a comprehensive analysis of failure risk factors based on the comprehensive failure risk factor indicator system of elevator brakes.

The DEMATEL method has been utilized to identify key factors across various fields such as safety management [26], supply chain management [27], performance management [28], efficiency management [29], etc. It is a method that can analyze the causal relationships and the degree of importance of each factor of the system, but it lacks the ability to analyze the hierarchical structure of the system elements [30]. Conversely, the ISM method provides a clear and intuitive depiction of the hierarchical structure and logical relationships between factors by creating factor relationship matrices and topological diagrams, but the method cannot determine the importance of factors [31]. ISM method can enable the classification of complex system on the basis of DEMATEL method, reflecting both the influence paths and hierarchical structure of the factors in the complex system, and mixed modeling of the two can identify the hierarchical structure and the importance of the factors in the system, and determine the key factors in the complex causal relationship. The combination of the two methods has been demonstrated in such as fields of coal mine production [32], gas pipeline network operation and maintenance [33] and steel production [34], which can not only determine the causal relationships and importance of the factors, but also clarify the hierarchical structure of the logical relationships of each factor.

3.1. Grey DEMATEL Method

DEMATEL analysis is based on expert judgement, but the numerical value given through expert judgement often fail to capture the inherent fuzziness in the relationships between factors. Grey System Theory offers a solution to this issue of system ambiguity by using grey numbers or intervals rather than precise values in the decision-making process. This approach introduces greater flexibility and aligns more closely with real-world scenarios. The specific numerical values of expert judgement and expert authority weights are converted into grey number intervals to deal with the ambiguity in the decision-making process. To this end, grey system theory can be combined with DEMATEL to analyze the causal and logical relationships between the risk factors of elevator brake failure. The specific steps are as follows:

(1)

Experts are organized to evaluate the mutual influence relationship of each influencing factor in the comprehensive failure risk factor indicator system, and the influence degree from low to high is classified into five categories: no influence, low influence, general influence, high influence and very high influence, respectively. The corresponding grey numbers of the intervals corresponding to the experts’ scores were determined, as shown in

Table 3. Grey semantic scale for expert judgement values.

Grey Language	Grey Number Interval
No influence (0 points)	[0, 0]
Low influence (1 point)	(0, 0.25]
General influence (2 points)	(0.25, 0.5]
High influence (3 points)	(0.5, 0.75]
Very high influence t (4 points)	(0.75, 1]

. The experts, coming from various roles, provide different perspectives on elevator brake failure risks. Combined with the grey system theory, the grey number of intervals corresponding to the authority of the experts were determined, as shown in

Table 4. Grey semantic scale for expert authority.

Grey Language	Grey Number Interval
No influence	[0, 0.3]
Low influence	(0.3, 0.5]
General influence	(0.4, 0.7]
High influence	(0.5, 0.9]
Very high influence	(0.7, 1]

.

(2)

The grey number matrix was formed by combining Table 3 with the direct influence matrix of elevator brake failure risk.

(3)

The grey number matrix is standardized and clarified through Formulas (1)–(3), while the same operation is performed for the authority of the experts according to Table 4, and the expert authority matrix $Z$ is found using Formula (4), where $Z_{ij}$ is the element of the ith row and the jth column in the expert authority matrix.

$$\underset{\_}{\otimes }{x}_{ij}^{\overline{k}}=(\underset{\_}{\otimes }{x}_{ij}^k-\min \underset{\_}{\otimes }{x}_{ij}^k)/{\Delta }_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$$

(1)

$$\overline{\otimes }{x}_{ij}^{\overline{k}}=(\overline{\otimes }{x}_{ij}^k-\min \overline{\otimes }{x}_{ij}^k)/{\Delta }_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$$

(2)

$${\mathsf{\Delta }}_{\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathrm{m}\mathrm{a}\mathrm{x}}=\max \overline{\otimes }{x}_{ij}^k-\min \overline{\otimes }{x}_{ij}^k$$

(3)

Formal: $\overline{\otimes }{x}_{ij}^k$ and $\underset{\_}{\otimes }{x}_{ij}^k$ are the upper and lower limits of the scoring results of the Kth expert; $\overline{\otimes }{x}_{ij}^{\overline{k}}$ and $\underset{\_}{\otimes }{x}_{ij}^{\overline{k}}$ are the upper and lower limits of the scoring results of the Kth expert after the clarity process; and ${\Delta }_{\min }^{\max }$ is the difference between the maximum value of the upper limit and the minimum value of the lower limit of the scoring results of all experts.

$$Z_{ij}=w_1{Z}_{ij}^1+w_2{Z}_{ij}^2+\cdots +w_n{Z}_{ij}^n, \sum _{i=1}^n{w}_i=1$$

(4)

(4)

Through the normalization of $Z$ by Formulas (5) and (6), $Z$ achieves the normalization and directly affects the matrix $N$. Formula (7) is calculated for $N$ to obtain the comprehensive influence matrix $H(H={[h_{ij}]}_{n\times n}),{\lambda }_i(1,2,\cdots ,n)$. ${\lambda }_i$ is the characteristic root of the comprehensive influence matrix $H$.

$$N=S\cdot Z$$

(5)

$$S={\displaystyle \frac{1}{\genfrac{}{}{0pt}{}{\mathrm{m}\mathrm{a}\mathrm{x}}{1\le i\le n}{\sum }_{j=1}^n{Z}_{ij}}} , i,j=\mathrm{1,2},\cdots ,n$$

(6)

$$H=N+N^2+N^3+\cdots =N(I-N{)}^{-1} , \left|{\lambda }_i\right|<Lim{N}^i=[0{]}_{n\times n}$$

(7)

(5)

Formulas (8) and (9) are used to derive the Influence Degree $D_i$ and the Influenced Degree $C_i$. The Influence Degree $D_i$ and the Influenced Degree $C_i$ can better describe the interaction relationship between each influencing factor. The Influence Degree $D_i$ is obtained by adding up the scores of each row of influencing factors in the comprehensive influence matrix; the Influenced Degree $C_i$ is obtained by adding up the scores of each column of influencing factors in the comprehensive influence matrix.

$$\begin{array}{ll}D& =(D_1,D_2,D_3,\cdots ,D_1)\\ D_i& ={\displaystyle \sum _{j=1}^n}{h}_{ji},(i=\mathrm{1,2},3,\cdots ,n)\end{array}$$

(8)

$$\begin{array}{ll}C=& (C_1,C_2,C_3,\cdots ,C_n)\\ C_i=& {\displaystyle \sum _{j=1}^n}{h}_{ji},(i=\mathrm{1,2},3,\cdots ,n)\end{array}$$

(9)

(6)

Through Formulas (10) and (11), the Centre Degree $M_i$ and the Cause Degree $R_i$ can be calculated. The Centre Degree indicates the position and the degree of importance of a certain influencing factor in the whole assessment process; the Cause Degree can be positive or negative, if the value is positive, it means that the influencing factor has a great influence on other influencing factors; if it is negative, it means that the influencing factor is greatly influenced by other influencing factors.

$$M_i=D_i+C_i$$

(10)

$$R_i=D_i-C_i$$

(11)

(7)

Finally, based on the calculated Centre Degree and Cause Degree of each influencing factor, a Cartesian coordinate system is constructed.

3.2. ISM Methodology

Based on the comprehensive influence matrix $H$, a recursive hierarchical diagram is created by ISM as follows:

(1)

Setting a threshold value $\lambda$, eliminating relationships where the factors have a small influence degree, simplifying the ISM hierarchical structure, and in order to overcome the subjectivity that exists in expert judgement, introducing the mean and standard deviation based on a statistical distribution to calculate $\lambda$, i.e., $\lambda =\alpha +\beta$. Where $\alpha$ is the mean value of all the factors in the comprehensive influence matrix, and $\beta$ is the standard deviation in the comprehensive influence matrix.

(2)

Determine the adjacency matrix $A=\left\{a_{ij}\right\}$ based on the size of the threshold $\lambda$, where $a_{ij}=\left\{\begin{array}{l}1,t_{ij}\ge \lambda \\ 0,t_{ij}<\lambda \end{array}\right.$.

(3)

Adding the adjacency matrix $A$ to the identity matrix $I$ gives the resultant matrix $B=A+I$.

(4)

A power operation is performed on $B$. If the matrix $K$ satisfies the condition $K=B^{i+1}=B^i\ne B^{i-1}$, then a reachable matrix is obtained.

(5)

Determine the reachable set $U_i$ and the set of antecedents $V_i$. Based on the reachability matrix $K$, the reachable set $U_i=\left\{x_j|x_j\in X,t_{ij}\ne 0\right\}$ and the set of antecedents $V_i=\left\{x_j|x_j\in X,t_{ji}\ne 0\right\}$ of the influences $x$ can be determined., where the reachable set $U_i$ is the set of all factors affected by factor $x_i$; the set of antecedents $V_i$ is the set of all factors that have an effect on factor $x_i$; and $X$ represents the set of all elements.

(6)

If the reachable set and the set of antecedents satisfy $U_i=U_i\cap V_i$, then any factor $x_i$ corresponding to a factor in the reachable set $U_i$ can find an antecedent in the set of antecedents $V_i$, which is classified as the highest level factor, and then, the rows and columns corresponding to that factor are removed from the reachable matrix $K$.

(7)

Repeat steps (5) and (6) until all rows and columns of factors are removed. Finally, a recursive hierarchical chart is created based on the order in which the factors are removed.

4. Analysis of Risk Factors for Elevator Brake Failure

4.1. Grey DEMATEL-ISM Computational Analysis

In order to analyze the relevance and importance of the risk factors of elevator brake failure, the grey DEMATEL method was applied. The five experts selected cover five key aspects of elevator research, manufacturing, inspection, supervision and installation. They are all personnel who have been working in the elevator industry for many years and have participated in the development of China’s national standards for elevators, making them representative. They have rich knowledge of the elevator drum brake studied, and are able to evaluate the influencing factors of the elevator drum brake and make reasonable ratings among them. In addition, five experts have been requested to avoid subjective judgments as much as possible during the scoring process, ensuring the rationality of the results. This assessment yielded a comprehensive influence matrix, as shown in Figure 2 (Figure 2 was created using Microsoft Office LTSC Standard 2021 software). Based on the comprehensive influence matrix, Influence Degree, Influenced Degree, Centre Degree and Cause Degree of each influencing factor were calculated, as shown in

Table 5. The results of the calculation of Influence Degree, Influenced Degree, Centre Degree and Cause Degree.

	Influence Degree	Influenced Degree	Centre Degree	Cause Degree
S1	1.6616	2.0082	3.6697	−0.3466
S2	1.8239	2.0012	3.8252	−0.1773
S3	0.2010	2.1550	2.3560	−1.9540
S4	0.4510	1.8158	2.2669	−1.3648
S5	0.2699	2.0886	2.3585	−1.8187
S6	0.4178	1.9282	2.3460	−1.5103
S7	0.3043	1.9625	2.2668	−1.6582
S8	2.2648	0.6861	2.9510	1.5787
S9	2.3034	1.4071	3.7105	0.8963
S10	2.2342	1.2882	3.5224	0.9461
S11	2.2606	1.3206	3.5812	0.9400
S12	2.2932	1.4918	3.7850	0.8014
S13	2.5663	1.4158	3.9821	1.1505
S14	2.3651	1.7197	4.0848	0.6454
S15	1.6247	1.5324	3.1571	0.0923
S16	2.0205	0.2411	2.2616	1.7794

. Based on the data in Table 5, a Centre Degree-Cause Degree diagram was created, as shown in Figure 3.

Based on the grey DEMATEL method, the ISM method is employed to construct a multi-level progressive structure model to analyze the influence relationship among the risk factors of elevator brake failure. Based on the comprehensive influence matrix calculation of the grey DEMATEL method, the mean a and standard deviation b of all factors in the comprehensive influence matrix are calculated, and a = 0.0979, b = 0.0677, with a threshold $\lambda$ = 0.1656 is obtained, and the reachable matrix is obtained. Furthermore, the reachable set, the set of antecedents, and the intersection of the reachable set and the set of antecedents are obtained. The failure risk factors are divided into hierarchical levels, and the hierarchical diagram of elevator brake failure risk factors is obtained by combining Centre Degree and Cause Degree, as shown in Figure 4. The processes in this section were calculated by Python software (version 3.11).

4.2. Analysis of Results

4.2.1. Grey DEMATEL Analysis

In the DEMATEL method, the Centre Degree mainly indicates the risk factor’s influence on the comprehensive degree of the complex system, serving as a core parameter for assessing its importance. A higher Centre Degree indicates greater significance of the factor. Cause Degree indicates the extent of a risk factor’s influence on other factors in the system. A factor with a Cause Degree greater than 0 is classified as a Cause Factor, while a factor with a Cause Degree less than 0 is termed a Result Factor.

Therefore, the 16 influencing factors are divided into four categories, as shown in Figure 3. Category I factors have high Centre Degrees and are classified as strong Cause Factors, indicating that they have a significant impact on both elevator brake failure and other factors. Category II factors have low Centre Degrees and are also Cause Factors, suggesting that they have a minor impact on elevator brake failure but still affect other factors. Category III factors have low Centre Degrees and are classified as strong Result Factors, meaning they have a limited impact on elevator brake failure but are significantly influenced by other factors. Category IV factors have high Centre Degrees but are weak Result Factors, indicating that they have a substantial impact on elevator brake failure while being minimally affected by other factors.

In summary, from the grey DEMATEL analysis, it can be seen that category I risk factors of elevator brake failure are Safety Knowledge S9, Attitude of Responsibility S10, Policy Planning S11, Management Control S12, Subjective Responsibility S13, and Safety Participation S14, these factors have a greater impact on elevator brake failure, and also exert a significant influence on the other factors, and should be focused on this type of factor, and focus on the measures that can efficiently reduce the risk of elevator brake failure. At the same time, inefficient behaviors with too many inputs are avoided.

4.2.2. ISM Analysis

As illustrated in in Figure 4, the risk factors associated with elevator brake failure demonstrate a multi-layered and more complex relationship, and the 16 influencing factors of elevator brake failure risk are divided into six layers (L1 to L6), which are classified into the Direct Influence layer (L1 and L2), the Intermediate Influence layer (L3 and L4), and the Root Influence layer (L5 and L6).

The Direct Influence factors layer includes Error Action S1, Unauthorized Action S2, Brake Spring S3, Spring-loaded Rod S4, Gate Tile Assemblies S5, Solenoid Assembly S6, and Manual Release Assembly S7. These factors are easily affected by multiple factors in the Intermediate and Root Influence layers, which have a direct impact on the failure of the elevator brake. Analysis of various elevator brake failure cases shows that unsafe equipment states and unsafe human actions are the direct causes of these failures, aligning with the characteristics of the Direct Influence Layer.

The Intermediate Influencing factors layer includes Safety Knowledge S9, Attitude of Responsibility S10, and Safety Participation S14. These factors are influenced by the Root Influence factors layer, and also influence the factors in the Direct Influence factors layer, playing the role of connecting the previous and the next. They are critical nodes in the risk propagation network, and focusing on these factors can help address the interrelationships among factors and cut off risk propagation pathways.

The Root Influence factors layer includes Technical Qualification S8, Policy Planning S11, Management Control S12, and Subjective Responsibility S13. These are the basic high-efficacy factors within the hierarchical diagram, the most easily neglected factors, and the influence on the system as well as the other factors tends to be subtle. Among them, Subjective Responsibility S13 belongs to the lowest level, and the factor affects a more numerous and wide-ranging set of factors.

In addition, Contracting Units S15 and Government and Industry Organizations S16 have a weak influence on other factors within the recursive hierarchical diagram and are considered external causes.

4.2.3. Comprehensive Analysis

According to the grey DEMATEL-ISM integrated recursive hierarchical structure, it can be seen that Cause Factors in the grey DEMATEL analysis are all distributed in the recursive hierarchical structure from L3 to L6, and Result Factors are all distributed in the recursive hierarchical structure from L1 to L2. This distribution indicates a high degree of consistency between the grey DEMATEL and ISM analysis results, validating the robustness of the findings.

In the ISM hierarchical structure, the Root Influence Factors—Policy Planning (S11), Management Control (S12), and Subjective Responsibility (S13)—as well as the Intermediate Influence Factors—Safety Knowledge (S9), Attitude of Responsibility (S10), and Safety Participation (S14)—are classified as key influencing factors in the grey DEMATEL analysis. Notably, Technical Qualification (S8) among the Root Influence Factors has a high Cause Degree but a lower Centre Degree, indicating significant root-level impact with a relatively lower overall effect on the complex system.

It is thus determined that, in the process of controlling the risk factors of elevator brake failure, the focus should be on Policy Planning S11, Management Control S12, and Subjective Responsibility S13, to inhibit the risk of failure from the root cause; at the same time, it is also necessary to pay attention to Safety Knowledge S9, Attitude of Responsibility S10, and Safety Participation S14, to inhibit the risk of failure from the dissemination path.

4.3. Suggested Measures for Risk Management of Elevator Drum Brake Failure

(1)

With regard to Policy Planning S11, Management Control S12, and Subjective Responsibility S13, it is recommended that the elevator maintenance unit strictly implement the main responsibility of the unit and establish and improve the safety management system. Through the formulation of reasonable and comprehensive policy planning, management and control system, etc., so that safety education, safety training, safety supervision, safety repair, maintenance and other work are carried out in accordance with regulations, which can improve the safety participation of personnel in all links, further improving safety knowledge level and responsibility attitude of employees, reduce wrong actions and illegal actions in the operation process, and reduce the failure probability of each component of the brake.

(2)

When focusing on the three factors of Policy Planning S11, Management Control S12, and Subjective Responsibility S13, the focus can be on Safety Participation S14, which is ranked No. 1 in terms of centrality. The above three factors in the communication path all intersect in the Safety Participation S14, suggesting that elevator maintenance units can also utilize network notifications, SNS, office screens and other media to promote accident cases, risk information and other channels to disseminate information on accidents and risks. This strategy will boost staff safety awareness, foster a strong safety culture, and minimize unsafe behaviors and equipment states.

(3)

As illustrated in Figure 4, the Intermediate Influencing factors, Safety Knowledge S9 and Attitude of Responsibility S10, are important links in the propagation path, influencing all the factors in the Direct Influence factors, including Error Action S1, Unauthorized Action S2, Brake Spring S3, Spring-loaded Rod S4, Gate Tile Assemblies S5, Solenoid Assembly S6, and Manual Release Assembly S7. Improving employees’ safety knowledge and attitude of responsibility directly and efficiently cuts off risk propagation paths and reduces the risk of failure.

5. Conclusions

(1)

Given the complexity of failures in elevator drum brake systems, the analysis is conducted from two perspectives: equipment-level failure risk factors and comprehensive failure risk factors. To address equipment-level failures, this paper introduced FMEA, an analysis method focused on identifying failures from a reliability standpoint, and determined the equipment-level failure risk factors by considering all possible failure modes and influencing factors in a comprehensive manner through the decomposition of the equipment structure, ensuring omission and repetition; for the analysis of comprehensive failure risk factors, the 24Model methodology for solving complex system problems was introduced to determine comprehensive failure risk factors broken down by the four behavioral phases of Guiding Behavior, Operational Behavior, Habitual Behavior, Disposable Behavior and Physical State of internal causes, as well as by external causes. Finally, 16 important influencing factors were screened based on the expert scoring method and the affiliation function to form a comprehensive failure risk factor indicator system.

(2)

The causal attributes, level of importance of the 16 influencing factors were investigated using the DEMATEL method combined with grey system theory. The recursive hierarchical structure of these factors was determined through ISM, clarifying their logical relationships.

(3)

The grey DEMATEL analysis shows that among the 16 influencing factors, 9 are categorized as Cause Factors and 7 as Result Factors, and the 16 factors are classified into four categories; the 6-order ISM recursive hierarchical diagram was obtained through ISM analysis and the six strata were classified into Root Influence factors layer, Intermediate Influencing factors layer and Direct Influence factors layer. Combined with the results of grey DEMATEL-ISM analysis, three key control influences were identified, including policy planning, management control, and main responsibility. In response to the results of the study, suggested measures are proposed to enhance risk management for elevator brake failures based on these findings.

(4)

Comprehensive analysis of elevator brake failure factors enhances future maintenance and management, enabling prompt identification of fault origins and rational scheduling of inspections and maintenance. This reduces brake failure probability and improves elevator safety and reliability. Furthermore, it promotes advancements in elevator monitoring systems by prioritizing data collection and analysis of key factors, enabling early fault detection and providing technical support for safe operation. The proposed methodology is also applicable to analyzing similar fault determinants in other systems.

(5)

In future work, further investigation into the critical pathways of influencing factors is necessary. It is recommended to explore the integration of the methods used in this study with Bayesian networks to employ probabilistic inference techniques for identifying the most critical pathways of influence propagation.

(6)

In the process of grey DEMATEL-ISM analysis, although 16 influencing factors’ causal attributes were successfully identified, these methods struggle to handle the complexity brought about by dynamic changes among the factors. The evaluations based on expert scoring may be limited by the knowledge and experience of the experts, leading to biases in the estimation of importance. Future research should attempt to use data-driven methods, such as cluster analysis, to more objectively determine the relative importance of the influencing factors.