Modelling of Safety Performance in Building Construction Projects Using System Dynamics Approach in Tanzania

Abstract

Issues in construction safety in Tanzania cast a long shadow, claiming lives and hindering project success. Understanding the complex dynamics at play is crucial for improving safety performance. This research aims to develop a system dynamics model to understand the factors influencing safety performance in building construction projects. Smart PLS was used to identify key variables using factor reduction, and 19 factors were determined as key factors to be used in this study from 143 variables from a questionnaire; then, STELLA was used to develop system dynamic modelling. A study was conducted on 255 building construction projects in five regions of Tanzania, Dar es Salaam, Dodoma, Arusha, Mwanza, and Mbeya, and later, the model was tested in one contractor’s company. By simulating the interactions between these diverse elements and their impact on accident rates, it was found that both safety performance and safety management processes for construction projects are not stagnant but are expected to rise at the beginning of the project and to grow steadily as the project execution approaches its end. The sensitivity analysis conducted on the system dynamics model found that the extent, frequency, and cost of incidences are positively correlated. This study contributes facts on the status of safety climate, a new definition of safety climate, and the integration of different analysis methods in evaluating safety performance in Tanzania.

1. Introduction

Tanzania’s construction sector is expanding steadily and is the second biggest driver of the country’s real GDP growth, behind agriculture. Agriculture contributed around 26.9 percent of the total; buildings contributed about 14.4 percent; lodging and restaurants 10 percent; and trade and repair 8.4 percent [1]. Like many others globally, the construction industry in Tanzania faces a challenge in ensuring worker safety. Despite safety rules and regulations, acts (Occupational Health and Safety Act, 2003), and policy (National Occupational Health and Safety Policy, 2010) established by the Occupational Safety and Health Authority (OSHA), increasing construction activities, predominantly building construction projects, continue to experience a high incidence of accidents [2,3,4,5]. Tanzania’s construction industry is experiencing growth, but there is constantly the possibility of events that take lives, entail disruptions in projects, and limit economic growth. The fatality rate in Tanzania’s construction industry is two times higher than that of the manufacturing industry [6], while falling and being struck are, worldwide, the most common accidents in projects [7]. These incidents undermine project budgets, productivity, and the country’s development goals, and have a devastating human cost [8]. To address this challenge, more is required beyond regular compliance inspections [9].

The complex framework of construction safety is linked by various factors, including organisational culture, worker training, safety regulations, and even financial limitations. Each link interacts with others to establish a complex structure that ultimately impacts the extent of accidents [10,11,12,13]. Traditional methods usually struggle to capture this dynamic interaction [14,15]. There is a need for a better understanding of how these variables interact and change over time. Understanding these complex interactions is important to implement safer measures and prevent disasters.

This study attempts to quantify the issue and fully understand its complex origins [16]. It makes it perfectly apparent that a safety climate is more complex than just compliance but a dynamic fabric made up of many components. A complicated network of interrelated elements affects the general frequency of accidents, such as worker training, safety regulations, organisational culture, and even economic constraints [17].

To unravel this interaction, a powerful tool, system dynamics (SD), was introduced [18]. In many different domains, system dynamics modelling (SDM) has been shown to be highly valuable in assisting decision makers in comprehending and forecasting the dynamic behaviour of intricate systems, which is crucial for the creation of successful policy initiatives [19].

Using system dynamics (SD), a virtual replica of Tanzanian construction is created, simulating how the various factors interact to influence accident rates. Visualising this hidden network provides valuable insight into the “why” behind safety performance. By locating critical leverage points within the system, effective interventions are identified to create change. By simulating various scenarios, the model identifies leverage points that are critical areas where targeted interventions can produce the most significant safety improvements.

On the other hand, this research presents the analysis and findings of a system dynamics model simulation aimed at understanding the dynamics of safety climate maturity in construction projects in Tanzania. Moreover, it presents the findings and analysis of a sensitivity analysis conducted on a system dynamics model aimed at understanding safety performance in construction projects in Tanzania.

The sensitivity analysis focuses on evaluating the impact of changes in safety leading factors and safety management process-related factors on safety performance metrics including the frequency, extent, and cost of safety performance parameters. Additionally, this research includes details on model validation and the software used for model development.

The objectives of the simulation study are as follows:

• To identify key variables and relationships that influence safety performance;
• To develop a system dynamics model simulation for safety performance in construction projects in Tanzania;
• To analyse the impact of the safety management process and safety leading factors on safety performance;
• To assess the sensitivity analysis of safety key performance indicators (frequency, extent, and cost of safety performance indicators) to changes in project management-related factors, worker-related factors, site environment-related factors, external-related factors, and safety management process-related factors;
• To provide insights for decision making and prioritisation of interventions to improve safety performance.

2. Literature Review

In the construction industry, safety is of utmost importance due to the inherent risks and hazards associated with the unique, dynamic, and temporary nature of construction projects. It is crucial to understand the factors that influence safety performance in construction projects to mitigate risks and improve safety outcomes [20,21]. According to the reviewed literature, several factors have been identified as influential in improving safety performance in construction projects [22,23,24].

These factors include management commitment, safety training, enforcement of safety rules and regulations, stakeholder collaboration, implementation of a safe working environment, and implementation of a safe plant and equipment. Additionally, the literature emphasises the importance of integrated safety and quality management in construction projects. The literature review also highlights some barriers to successful quality management in construction projects, including poor implementation, the nature of construction work, and the industry itself [25].

Overall, the literature review suggests that a comprehensive approach to safety management, which includes factors such as management commitment, training, collaboration, and a focus on worker behaviour and safety climate, can greatly improve safety performance in construction projects [24]. This research established three categories of factors used in determining the safety climate factors at construction sites in Tanzania. These are safety leading factors, safety management process factors, and safety lagging factors (safety performance) [26,27,28,29,30,31,32].

Safety leading factors are the factors that influence the safety climate of a construction site. These factors can be grouped into three categories [31]. Table 1, Table 2 and Table 3 represent safety categories as defined by different studies.

Table 1. Safety leading factors.

Factors Origin	Description	Sources
Project management-related factors	These are factors obtained from five basic functions, namely, planning, organising, staffing, leading, and controlling safety issues within a project.	[33] Brazil, [34] Australia, [35] Qatar, [36] Brazil
Worker-related factors (individual factors)	These are personal attitudes, abilities, habits, and personalities that individual workers bring to their work, which can be strengths or weaknesses depending on the demands of the task.	[37] USA, [38] Indonesia, [39] Sweden, [40] USA
Site-related factors (workplace factors)	These are elements of the workplace that can have a positive or negative impact on a worker’s ability to perform their job effectively.	[41] Korea, [42] India, [43] Iran, [44] Greece
External related factors	These are external safety factors that have an impact on the construction project’s safety performance.	[45] Nigeria, [46] Nigeria, [47] Spain, [48] South Africa, [49] Australia

Table 1. Safety leading factors.

Factors Origin	Description	Sources
Project management-related factors	These are factors obtained from five basic functions, namely, planning, organising, staffing, leading, and controlling safety issues within a project.	[33] Brazil, [34] Australia, [35] Qatar, [36] Brazil
Worker-related factors (individual factors)	These are personal attitudes, abilities, habits, and personalities that individual workers bring to their work, which can be strengths or weaknesses depending on the demands of the task.	[37] USA, [38] Indonesia, [39] Sweden, [40] USA
Site-related factors (workplace factors)	These are elements of the workplace that can have a positive or negative impact on a worker’s ability to perform their job effectively.	[41] Korea, [42] India, [43] Iran, [44] Greece
External related factors	These are external safety factors that have an impact on the construction project’s safety performance.	[45] Nigeria, [46] Nigeria, [47] Spain, [48] South Africa, [49] Australia

The safety leading factors are important because they can have a significant impact on the safety climate of a project and organisation. By understanding these factors, organisations can take steps to improve their safety climate and reduce the risk of accidents and injuries. The safety management process factors are the safety processes that organisations undertake to implement a safe work environment [50,51,52,53].

This research applies the Deming cycle (plan–do–check–act (PDCA)) to measure the whole safety climate process of the model. PDCA is a four-step process for continuous improvement. It is a cyclical process that can improve any process or system.

The PDCA cycle is conducted repeatedly until the goal is achieved or until it is determined that the goal is not achievable. The PDCA cycle is a simple but powerful tool that can be used to improve any process or system. It is a cyclical process, which means that it can be repeated as needed to continuously improve the process or system. The PDCA cycle is often used in quality management, but it can be used in any field where improvement is desired. It is a versatile tool that can be used to improve a wide variety of processes, from manufacturing to customer service.

Table 2. Safety management process factors.

Process	Denotes	Description	Sources
Plan	Safety process design	An improvement’s purpose is established and a strategy is created to meet it.	[54] USA, [41] Korea, [55] USA
Do	Safety process implementation	During the doing stage, the plan is carried out. This entails carrying out the actions that were determined during the planning stage.	[56] Saudi Arabia, [57] Brazil
Check	Safety process evaluation	The outcomes of the implementation are assessed at the evaluation stage. This entails gathering information to determine whether the objective was accomplished and to spot any issues that arose during implementation.	[58] UK, [59] Canada, [60] Taiwan
Act	Safety process improvement	The plan is improved with the help of the checking phase’s findings. This could entail updating the strategy, putting new protocols into place, or offering more training.	[61] USA, [62] USA

Table 2. Safety management process factors.

Process	Denotes	Description	Sources
Plan	Safety process design	An improvement’s purpose is established and a strategy is created to meet it.	[54] USA, [41] Korea, [55] USA
Do	Safety process implementation	During the doing stage, the plan is carried out. This entails carrying out the actions that were determined during the planning stage.	[56] Saudi Arabia, [57] Brazil
Check	Safety process evaluation	The outcomes of the implementation are assessed at the evaluation stage. This entails gathering information to determine whether the objective was accomplished and to spot any issues that arose during implementation.	[58] UK, [59] Canada, [60] Taiwan
Act	Safety process improvement	The plan is improved with the help of the checking phase’s findings. This could entail updating the strategy, putting new protocols into place, or offering more training.	[61] USA, [62] USA

On the other hand, safety lagging factors are the factors that measure how well an organisation is managing its safety risks in a project. It is typically measured by many features, such as several accidents and injuries that occur. Still, it can also be measured by other factors, such as the number of near misses, safety violations, and cost of accidents and injuries [27].

Table 3. Safety lagging factors.

Items Origin	Description	Sources
Incidents	An uncommon isolated, random, and sudden instance or event that can disturb a person’s daily routine (good or bad/pleasant or unpleasant/big or small/loss or even profit).	[63] China, [64] USA, [65] Brazil
Injuries	Harm caused by accidents, falls, hits, weapons, and more.	[66] China, [67] France, [68] USA, [69] Iran
Accidents	An unfortunate event that occurs suddenly and unexpectedly that often results in damage, injury, or loss.	[70] Turkey, [71] Sri Lanka, [72] UK
Near misses	An unplanned event that has the potential to cause, but does not result in, human injury, environmental or equipment damage, or an interruption to normal operation.	[73] Israel, [74] China, [75] USA
Fatalities	An accident or disaster resulting in death.	[76] USA, [77] USA, [78] USA
Damages of property	Destruction of real or tangible personal property, caused by negligence, willful destruction, or an act of nature.	[79] Czech Republic,
Financial loss	A disparity in a company between the money they are bringing in and the money going out, leaving them with a net deficit.	[80] Malaysia, [81] Ukraine, [82] Czech Republic
Compensation due to accidents.	An award to somebody who has been involved in an accident that was not their fault.	[83] Taiwan, [84] Hong Kong, [85] Taiwan
Overtime is associated with slow operation	Overtime refers to any hours worked by a worker that exceed their normally scheduled working hours.	[86] Korea, [87] USA, [88] Canada
Production time lost	Production lost time refers to the time during which a production process or operation is not running or is operating at reduced capacity due to various reasons such as equipment breakdowns, maintenance, shortages of raw materials, or other disruptions.	[89] Nigeria, [90] Iran, [91] India
Slowdown in operation	A reduction in speed, activity, or the rate that things are produced.	[92] Nigeria, [93] India
Decrease in morale	When workers feel poorly about their work and the project.	[94] China, [95] Spain, [96] New Zealand
Loss of client	This is when the client does not want to continue their contract with the project.	[97] Turkey, [98] New Zealand
Equipment breakdown due to unsafe practice	The condition in which a piece of equipment fails to operate as intended due to mistakes, parts getting old, etc.	[99] Nigeria, [100] India, [101] India

Table 3. Safety lagging factors.

Items Origin	Description	Sources
Incidents	An uncommon isolated, random, and sudden instance or event that can disturb a person’s daily routine (good or bad/pleasant or unpleasant/big or small/loss or even profit).	[63] China, [64] USA, [65] Brazil
Injuries	Harm caused by accidents, falls, hits, weapons, and more.	[66] China, [67] France, [68] USA, [69] Iran
Accidents	An unfortunate event that occurs suddenly and unexpectedly that often results in damage, injury, or loss.	[70] Turkey, [71] Sri Lanka, [72] UK
Near misses	An unplanned event that has the potential to cause, but does not result in, human injury, environmental or equipment damage, or an interruption to normal operation.	[73] Israel, [74] China, [75] USA
Fatalities	An accident or disaster resulting in death.	[76] USA, [77] USA, [78] USA
Damages of property	Destruction of real or tangible personal property, caused by negligence, willful destruction, or an act of nature.	[79] Czech Republic,
Financial loss	A disparity in a company between the money they are bringing in and the money going out, leaving them with a net deficit.	[80] Malaysia, [81] Ukraine, [82] Czech Republic
Compensation due to accidents.	An award to somebody who has been involved in an accident that was not their fault.	[83] Taiwan, [84] Hong Kong, [85] Taiwan
Overtime is associated with slow operation	Overtime refers to any hours worked by a worker that exceed their normally scheduled working hours.	[86] Korea, [87] USA, [88] Canada
Production time lost	Production lost time refers to the time during which a production process or operation is not running or is operating at reduced capacity due to various reasons such as equipment breakdowns, maintenance, shortages of raw materials, or other disruptions.	[89] Nigeria, [90] Iran, [91] India
Slowdown in operation	A reduction in speed, activity, or the rate that things are produced.	[92] Nigeria, [93] India
Decrease in morale	When workers feel poorly about their work and the project.	[94] China, [95] Spain, [96] New Zealand
Loss of client	This is when the client does not want to continue their contract with the project.	[97] Turkey, [98] New Zealand
Equipment breakdown due to unsafe practice	The condition in which a piece of equipment fails to operate as intended due to mistakes, parts getting old, etc.	[99] Nigeria, [100] India, [101] India

3. Materials and Methods

3.1. Data Collection

The population samples collected from the Contractors Registration Board (CRB) registry show a total of 757 registered building projects within Classes 1–4, which makes 757 respondents. Although contractors in Tanzania are categorised in Classes 1–7, Classes 1–4 contractors’ projects were chosen as the population size because they are the most affected by the impact on safety performance due to risks subject to project design and cost. It should be noted that the impact on project safety performance increases as the complexity of the project increases [1,102]. The sample size formula for the small and finite population is provided by [103] and is given as

$$n=\left(Z^{2}Npq\right)/(<N-1>e^2+Z^{2}pq)$$

(1)

where

Z	Z value which is 95 percent or 1.96.
N	Population size (757 respondents).
p	Sample proportion = 0.5, q = 1 − p = 0.5.
$e^2$	Margin error = 5, percent = 0.05.

The sample size for this research was 255 respondents, of which 26 were from Class 1, 50 were from Class 2, 74 were from Class 3, and 105 were from Class 4 contractor companies. To identify the factors affecting safety climate in construction sites, an in-depth literature review was carried out. From this, 143 factors that affect safety climate in construction sites were compiled. Then, these factors were examined by preparing a survey questionnaire in which various construction safety professionals (including owners, managers, engineers, supervisors, etc.) in five Tanzanian regions, namely, Dar es Salaam, Dodoma, Arusha, Mwanza, and Mbeya, participated; the respondent demographics are shown in

Table 4. Demographics of the respondents.

Region	Frequency	Percent	Cumulative Percent
Dar es Salaam	123	48.2	48.2
Arusha	45	17.6	65.9
Mbeya	20	7.8	73.7
Mwanza	15	7.9	79.6
Dodoma	52	20.4	100.0
Total	255	100

.

The purpose of this questionnaire was to identify the most important factors that affect the safety climate of construction projects in Tanzania. Data on safety climate including safety leading factors, the safety management process, safety performance, and other relevant factors from construction projects were collected and analysed. Smart PLS (version 4) was used to identify key variables using factor reduction, and 19 variables were determined as key factors due to their high loading values and were selected to be used in this study. Then STELLA software Version 3.5 (3121) used them to develop system dynamics modelling. The variables formed the basis for developing the simulation model and are indicated in

Table 5. Safety leading factor loadings.

Factors	Denotes	Variables	Factor Loadings
Project management-related factors (MRF)	MRF6	Management takes corrective actions promptly about safety.	1
Worker-related factors (WRF)	WRF7	Workers feel comfortable reporting safety concerns and unsafe conditions.
	WRF8	Workers participate in safety activities, such as safety meetings, training, and inspections.
Site environment-related factors (SRF)	SRF16	The safety practices are adequate to prevent slips, trips, and falls.	1
External-related factors ERF	ERF1	The project safety practices comply with all applicable industry safety regulations.	0.888
	ERF2	The project has been inspected by government safety agencies	0.837

,

Table 6. Safety management process factor loadings.

Factors	Denotes	Variables	Factor Loadings
Safety process design—SMP1	SMP1.3	The project has a process for risks assessment.	0.998
	SMP1.4	There is a risk management plan for handling safety issues.	0.998
Safety process implementation—SMP2	SMP2.2	Safety inspections are conducted regularly.	0.779
	SMP2.3	Workers feel comfortable reporting safety concerns.	0.914
Safety process evaluation—SMP3	SMP3.2	The project conducts regular safety audits to assess the effectiveness of its safety processes and systems.	0.892
	SMP3.3	Workers feel comfortable providing feedback on safety processes and systems.	0.897
Safety process improvement—SMP4	SMP4.1	The project makes changes to its safety processes and systems based on the results of its safety process reviews.	0.87
	SMP4.2	The project communicates changes to its safety processes and systems to workers in a timely and effective manner.	0.849

and

Table 7. Safety performance factor loadings.

Factors	Denotes	Variables	Factor Loadings
Safety performance extent (SPE)	SPE14	Extent of equipment breakdown due to unsafe practice.	1
Safety performance frequency (SPF)	SPF3	Frequency of accidents.	0.977
	SPF4	Frequency of near misses.	0.985
Safety performance costs (SPC)	SPC9	Costs of overtime associated with slowdown in operation.	0.721
	SPC10	Costs of production time loss.	0.785

.

3.2. Model Development

3.2.1. Variable Identification

The first step in the model formulation was to identify the key variables that influence safety climate maturity in construction projects. These variables were categorised into three main groups: safety leading factors, safety management process, and safety performance. Figure 1 represents variables used to develop an SDM model.

3.2.2. Hypothesis (Causal Loop) SDM Diagram

The second step was to develop a hypothesis where the (causal loop) SDM diagram was developed. This involved developing a conceptual model of the system, which includes the relationships between the key variables. The conceptual model is usually represented using causal loop diagrams (hypothesis SDM diagram) as represented in Figure 2.

Next, a causal loop diagram was developed to illustrate the relationships between the key variables [104]. These diagrams helped identify feedback loops and dynamic interactions that influence safety climate maturity over time. For example, a reinforcing loop might exist between the safety process design and the safety management process, where increased safety process design leads to a higher safety management process, which in turn reinforces safety performance. The feedback loop is indicated by an arrow with the (+) sign, which shows the reinforced feedback loop.

Mathematical equations were then formulated to describe the dynamics of the system. These equations represented the rates of change of the endogenous variables over time, taking into account the influences of exogenous variables and feedback loops as shown in

Table 8. Equations deployed in the model.

Variable	Equation
Top-level model
Safety leading factors(t)	Safety leading factors(t − dt) + (rate of leading factors) * dt
Safety management process(t)	Safety Management Process(t − dt) + (rate of safety management process) * dt
SAFETY_PERFORMANCE_COST(t)	SAFETY_PERFORMANCE_COST(t − dt) + (SPC_10 + SPC_9) * dt
SAFETY_PERFORMANCE_EXTENT(t)	SAFETY_PERFORMANCE_EXTENT(t − dt) + (RATE_OF_CHANGE_OF_SPE) * dt
SAFETY_PERFORMANCE_FREQUENCY(t)	SAFETY_PERFORMANCE_FREQUENCY(t − dt) + (SPF_4 + SPF_3) * dt
RATE_OF_CHANGE_OF_SPE	(Safety Management Process * Safety leading factors)/SPE_14
Rate of leading factors	GRAPH((ERF + SRF + WRF + MRF) * (1/(Safety_lead-ing_factors * Safety_Management_Process * SAFETY_PERFORMANCE_EXTENT * SAFETY_PERFORMANCE_FREQUENCY))) Points: (0.000, 0.105), (0.500, 0.127), (1.000, 0.253), (1.500, 0.262), (2.000, 0.310), (2.500, 0.445), (3.000, 0.541), (3.500, 0.620), (4.000, 0.773), (4.500, 0.917), (5.000, 0.956)
Rate of safety management process	GRAPH((Safety_Management_Process * LN(Safe-ty_Management_Process)/(GROWTH(PERCENT(MEAN(SMP1, SMP2, SMP3, SMP4))))) * (1/SAFETY_PERFORMANCE_EXTENT + 1/Safety_leading_factors + 1/ SAFETY_PERFORMANCE_FREQUENCY)) Points: (0.000, 0.624), (0.500, 0.616), (1.000, 0.371), (1.500, 0.472), (2.000, 0.253), (2.500, 0.406), (3.000, 0.100), (3.500, 0.332), (4.000, 0.035), (4.500, 0.031), (5.000, 0.035)
SPC_10	NORMAL(1/(Safety leading factors * SAFETY_PERFORMANCE_COST))
SPC_9	NOR-MAL(SAFETY_PERFORMANCE_EXTENT/(SAFETY_PERFORMANCE_COST * SPC_10))
SPF_3	(1/(SAFETY_PERFORMANCE_FREQUENCY * (Safety_leading_factors + Safety_Management_Process))) * f(x;$\mathsf{\lambda }$,k)
SPF_4	SAFE-TY_PERFORMANCE_FREQUENCY/(SAFETY_PERFORMANCE_FREQUENCY * (1/Safety_Management_Process + 1/Safety_leading_factors))
“SMP1.3”	RANDOM (1, 5)
“SMP1.4”	RANDOM (1, 5)
“SMP1.Change_factor”	0.15
“SMP2.2”	RANDOM (1, 5)
“SMP2.3”	RANDOM (1, 5)
“SMP2.change_factor”	0.13
“SMP3.2”	RANDOM (1, 5)
“SMP3.3”	RANDOM (1, 4)
“SMP3.5”	RANDOM (1, 5)
“SMP3.change_factor”	0.14
“SMP4.1”	TRIANGULAR (1, 2, 5)
“SMP4.2”	TRIANGULAR (2, 3, 4)
“SMP4.5”	TRIANGULAR (1, 3, 5)
“SMP4.change_factor”	0.15
EFR1	RANDOM (1, 5)
EFR2	RANDOM (1, 5)
ERF	(EFR1 + EFR2) * ERF_CHANGE_FACTOR
ERF_CHANGE_FACTOR	MEAN (0.837, 0.888)
MRF	MRF6 + MRF6 * MRF_CHANGE_FACTOR
MRF_CHANGE_FACTOR	0 * 9
MRF6	RANDOM (1, 5)
Project time frame	18
SFR16	RANDOM (1, 5)
SMP1	GRAPH((“SMP1.3” + “SMP1.4”) * “SMP1.Change_factor”) Points: (1.000, 0.664), (1.400, 1.170), (1.800, 1.100), (2.200, 1.109), (2.600, 1.066), (3.000, 1.048), (3.400, 1.074), (3.800, 0.961), (4.200, 1.022), (4.600, 1.345), (5.000, 1.563)
SMP2	(“SMP2.2”+“SMP2.3”) * “SMP2.change_factor”
SMP3	NORMAL(MEAN(“SMP3.2”, “SMP3.5”,“SMP3.3”, “SMP3.change_factor”), “SMP3.change_factor”)
SMP4	GRAPH(NORMAL(MEAN(“SMP4.1”, “SMP4.2”, “SMP4.5”, “SMP3.3”, “SMP4.change_factor”), “SMP4.change_factor”)) Points: (0.000, 2.341), (0.200, 1.869), (0.400, 1.869), (0.600, 1.607), (0.800, 1.520), (1.000, 1.502), (1.200, 1.537), (1.400, 1.712), (1.600, 1.380), (1.800, 2.026), (2.000, 1.939)
SPE_14	SAFETY_PERFORMANCE_EXTENT/4.5
SRF	NORMAL(SFR16, SRF_CHANGE_FACTOR, 1, 5)
SRF_CHANGE_FACTOR	1
WRF	NOR-MAL(MEAN(WRF8,WRF7,WRF13),WRF_CHANGE_FACTOR)
WRF_CHANGE_FACTOR	0.13
WRF13	TRIANGULAR (1, 3, 5)
WRF7	TRIANGULAR (1, 3, 5)
WRF8	TRIANGULAR (1, 3, 5)

. For example, the rate of change in safety incident rates might be influenced by factors such as safety-related factors effectiveness, project management-related factors, and safety process improvement.

The model equations also involved probabilistic distributions such as Weibull and normal distributions to capture the variability and uncertainty in safety performance metrics. For example, the frequency of safety incidents may be modelled using a Weibull distribution to account for the time-to-failure characteristics of safety systems, while the cost of safety incidents may be modelled using a normal distribution to capture the variability in financial impacts.

The equations in the table above represent the dynamic interactions between various factors influencing safety climate maturity in construction projects and serve as the foundation for the system dynamics model. The equations can be implemented using software such as Stella, which provides tools for building, simulating, and analysing system dynamics models.

4. Results

4.1. Model Implementation

The process of identifying the physical parts of the system so that they can be better understood and managed was conducted [66]. The formulated equations were implemented using the system dynamics software STELLA. This involved translating the mathematical equations into computational algorithms that could be simulated over time. STELLA Version 3.5 (3121 is a powerful system dynamics modelling software used for developing dynamic simulation models. It provides a user-friendly interface for building complex models that capture the dynamic behaviour of systems over time. The model run specifications are listed in

Table 9. Model simulation run specifications.

Run Specs
Start time	0
Stop time	project time frame (18 months set)
DT	0.25
Fractional DT	False
Save interval	0.25
Sim duration	20
Time units	Months
Pause interval	0
Integration method	Euler
Keep all variable results	True
Run by	Run
Calculate loop dominance information	True
Exhaustive search threshold	1000
Entry 1	Data
Entry 2	Data 1

.

The model was then calibrated using real-world data to ensure that it accurately represented the dynamics of safety performance in construction projects in Tanzania. Sensitivity analysis was conducted to assess the robustness of the model and identify key parameters that had a significant impact on the simulation results.

Table 10. Summary of the model.

Total	Count	Including Array Elements
Variables	19	19
Stocks	5	5
Flows	7	7
Converters	47	47
Constants	8	8
Equations	46	46
Graphics	18	18

represents a summary of the model during the simulation process.

4.2. Model Validation

The model was validated by comparing its outputs with data from the “Proposed seven-story commercial residential building on plot Nos. 623 and 624, block L in Temeke Municipality, Dar Es Salaam” project, which had a high safety key performance index. A sensitivity analysis was also performed to assess the robustness of the model. The model performance was measured by comparing the two variables of safety performance frequency, one variable of safety performance extent, and two variables of safety performance cost level. The results achieved are shown in Figure 3.

SPF, SPE, and SPC in

Table 11. Model validation for accidents.

Project Run Time	Spf v 3	Spf 3	Spf 3 Deviation (spf-spv)	Spf v 4	Spf 4	Spf 4 Deviation (spf-spv)
0	1.0395	0.0000	−1.0395	1.0395	0.0095	−1.0300
1	1.3130	0.4107	-0.9023	1.3130	0.4094	−0.9036
2	1.3462	0.5157	−0.8304	1.9960	0.7688	−1.2273
3	1.0796	0.5720	−0.5076	1.0796	0.9732	−0.1064
4	1.5068	0.5875	−0.9192	8.6176	1.1158	−7.5018
5	1.5455	0.5944	-0.9511	10.2141	1.2510	−8.9631
6	1.4589	0.5979	−0.8610	6.6436	1.3442	−5.2994
7	0.8649	0.6000	−0.2650	0.8649	1.4379	0.5730
8	1.4541	0.6013	−0.8527	6.4452	1.5294	−4.9158
9	1.4939	0.6023	−0.8916	8.0882	1.6235	−6.4647
10	1.2782	0.6030	−0.6752	1.2782	1.7081	0.4299
11	1.5175	0.6035	−0.9141	9.0619	1.7802	−7.2817
12	1.5415	0.6039	−0.9376	10.0494	1.8607	−8.1887
13	1.4692	0.6042	−0.8650	7.0677	1.9325	−5.1351
14	1.3782	0.6044	−0.7738	3.3186	2.0064	−1.3122
15	1.5215	0.6046	−0.9169	9.2244	2.0770	−7.1474
16	1.4326	0.6048	−0.8279	5.5615	2.1440	−3.4175
17	1.3829	0.6049	−0.7779	3.5093	2.2083	−1.3009
18	1.5158	0.6050	−0.9108	8.9902	2.2741	−6.7161

signify the model results, and SPF V, SPE V, and SPC V signify validation data. The model validation accident frequency level for SPF V3 is significantly higher than the model validation accident frequency level for SPF 3. The y axis in Figure 4 shows the level of frequency, and the x axis shows months. The data for SPF V3 are represented by the red line, and the data for SPF 3 are represented by the blue line. The red line starts at a level of 1 and increases to a level of around 1.4 over the months. The blue line starts at a level of 0 and increases to a level of around 0.6 over the months, as shown in Figure 4. Regarding the percentage level of frequency of accidents throughout the 18 months of the project execution, the model variable SPF 3 performed much better than validation data SPF V 3, as was expected; when there is a safety climate during project execution, frequency of accidents will be as low as possible, close to 0. From the results, the deviation of SPF 3 from SPF V 3 is below 0, which is a −0.82 average.

On the other hand, Figure 5 shows the results of the validation results that predict the frequency of near misses in 18 months at the construction sites. The red line represents the predicted frequency of near misses, while the blue line represents the actual frequency. The two lines appear to track one another very closely, which suggests that the model is successful at predicting the frequency of near misses (SPF 4) at construction sites from the beginning to the end of projects.

At the same time, Figure 6 and

Table 12. Model validation safety performance extent level results.

Project Time	Spe 14	Spe V 14	Deviation (Spe-Spe V)
0	1.460333	0.11336	1.346973
1	1.440642	0.33662	1.104022
2	1.286764	0.367031	0.919733
3	0.894241	0.203529	0.690712
4	0.705581	0.044733	0.660848
5	0.473366	0.33692	0.136445
6	0.416163	0.373222	0.04294
7	0.394	0.025169	0.368831
8	0.394	0.159336	0.234664
9	0.394	0.215774	0.178226
10	0.394	0.272043	0.121957
11	0.394	0.396997	−0.003
12	0.394	0.237385	0.156615
13	0.394	0.213651	0.180349
14	0.394	0.154366	0.239634
15	0.394	0.223931	0.170069
16	0.394	0.237634	0.156366
17	0.394	0.089526	0.304474
18	0.394	0.194447	0.199553

show the results of the validation that predict the extent of equipment breakdown due to unsafe practices in 18 months. The red line labelled “SPE V 14” represents the predicted percentage of equipment breakdown, while the blue line labelled “SPE 14” represents the actual percentage. Overall, the predicted equipment breakdowns (red line) are consistently lower than the actual equipment breakdowns (blue line). This could indicate that the model does not fully capture the extent of equipment breakdown due to unsafe practices. The difference between the red and blue lines seems to shrink over time. This could be due to the model being refined over time to better reflect reality and indicate how the situation will be improved within 18 months.

Also, the model seems to accurately predict the trend in the cost of loss of production time because both the predicted cost of loss of production time (SPC V10) and the actual cost of loss of production time (SPC 10) show a similar increasing trend over the period depicted in the graph, as indicated in Figure 7 and

Table 13. Model validation safety performance cost level results.

Project Time	Spc 10	Spc v 10	Deviation (spc-spc v)
0	4.998748	1.039475	3.959273
1	0.26141	1.313005	−1.0516
2	0.125872	1.996038	−1.87017
3	0.109581	1.079565	−0.96998
4	0.101742	8.61758	−8.51584
5	0.095118	10.21413	−10.119
6	0.089335	6.643601	−6.55427
7	0.084198	0.864924	−0.78073
8	0.079595	6.44521	−6.36561
9	0.075447	8.088197	−8.01275
10	0.071691	1.278183	−1.20649
11	0.068273	9.06195	−8.99368
12	0.06515	10.04944	−9.98429
13	0.062285	7.067655	−7.00537
14	0.059649	3.318627	−3.25898
15	0.057215	9.224361	−9.16715
16	0.054961	5.561479	−5.50652
17	0.052869	3.509261	−3.45639
18	0.050921	8.990199	−8.93928

. Despite that, the predicted cost of loss of production time (SPC V10) is consistently lower than the actual cost of loss of production time (SPC 10), which indicates that the model may be underestimating the overall cost of loss of production time over 18 months. This could also indicate that the model does not fully capture the cost of loss of production time variable.

4.3. Sensitivity Analysis

A sensitivity analysis was conducted to assess the impact of different interventions and variables on safety climate maturity and performance. Various scenarios were simulated to explore the effects of changes in key variables and parameters. Changes were made to selected variables and parameters within the model, including project management-related factors (MRF), worker-related factors (WRF), site environment-related factors (SRF), external-related factors (ERF), and safety management process-related factors (SMP). These changes were systematically applied across a range of values to assess their impact on safety performance metrics.

4.3.1. Sensitivity Analysis when SP Changed

Hypothesis 1. 

Safety-Related Factors (SRF) are influenced by the Safety Management process.

$$dSRF/DT=f\left(SMP\right)$$

(2)

Changes were made to selected variables and parameters related to safety-related factors and safety management processes. These changes were systematically applied across a range of values to assess their impact on safety performance metrics. For example, a proactive safety management approach may allocate resources towards improving safety-related factors, which in turn enhances safety performance. This forms a reinforcing loop where improvements in safety management lead to better safety-related factors, which further enhance safety performance.

Table 14. Hypothesis 1 model distribution.

Distribution	Weibull and Normal Distribution
Runs	25 runs (all combination runs)
Mean	2
STD	0.8
Min	1
Max	5

represent model distribution for hypothesis one.

The safety performance extent (SPE) in Figure 8 appears to be trending significantly over time, as the graph suggests. This indicates that over 18 months, it will become more expensive to maintain a given degree of safety climate.

This can be determined from the fact that the percentile lines (which could be the 50th, 75th, 95th, and 100th) appear to be growing over the months-based x axis. The variation in safety performance extent throughout the 25 scenario analysis runs is shown by the shaded area. The darkened area’s width indicates that this variability rises with time. This implies that the further you look, the more unclear the future extent of preserving safety in a project is.

On the other hand, according to the scenario analysis shown in Figure 9, cost level and safety performance are positively correlated. Both the cost level and safety performance seem to be trending upward throughout the 25 simulations. Over time, it seems that the safety performance cost level rises in all percentiles (50th, 75th, 95th, and 100th). This implies that as time passes, the system’s cost of safe operation will probably increase. The variation in the cost level between the various runs is indicated by the breadth of the darkened area. The spread seems to widen with time, indicating that the farther out you go, the less clear it may be how much it will cost to operate the system safely in the future.

The scenario analysis in Figure 10 compares safety leading factors with the safety management process to assess their impact on safety outcomes. Both safety leading factors and the safety management process are depicted on separate graphs. The graphs likely show lines representing percentiles (possibly 50th, 75th, 95th, and 100th). It appears the safety leading factors have a higher overall level of occurrence compared to the safety management process (policies, procedures, etc.). This is because the lines for safety leading factors are higher on the graph compared to the safety management process lines. Both graphs show an upward trend over time. This would indicate that both safety leading factors and safety management processes are becoming more effective at preventing accidents over the months. All 25 runs of scenario one are represented in

Table 15. Twenty-five runs of scenario one.

Runs	Safety Leading Factors	Safety Management Process	Safety Performance Cost perc.	Safety Performance Extent perc.	Safety Performance Frequency perc.
Run 1	3.265169729	3.156681635	3.071297107	63.72238931	52.82045
Run 2	3.265169729	3.029763143	3.070921025	63.54049632	53.33397
Run 3	3.265169729	2.245458052	3.066823383	60.96516211	52.92564
Run 4	3.265169729	2.954489271	3.070731719	63.2834999	52.61186
Run 5	3.265169729	3.737851832	3.071761015	65.36787131	52.51335
Run 6	1.226437425	3.156681635	4.075916906	44.79558503	41.31019
Run 7	1.226437425	3.029763143	4.071025419	44.75591937	40.9177
Run 8	1.226437425	2.245458052	4.020943314	43.70697207	41.37228
Run 9	1.226437425	2.954489271	4.077321194	44.47621743	41.17582
Run 10	1.226437425	3.737851832	4.133730564	44.78698653	40.60044
Run 11	1.570692765	3.156681635	3.848791037	47.13588145	43.26211
Run 12	1.570692765	3.029763143	3.851889431	46.22602128	43.33496
Run 13	1.570692765	2.245458052	3.787120107	46.86160517	43.0671
Run 14	1.570692765	2.954489271	3.849266571	46.7099024	42.85228
Run 15	1.570692765	3.737851832	3.858774743	48.45419133	43.12799
Run 16	1.581749953	3.156681635	3.83976707	48.38107873	43.21746
Run 18	1.581749953	2.245458052	3.777393498	46.96243058	3.65653
Run 19	1.581749953	2.954489271	3.843425933	47.1954662	43.15648
Run 20	1.581749953	3.737851832	3.854375746	48.41697081	42.88908
Run 21	1.410653297	3.156681635	3.959547183	46.26964617	42.23002
Run 22	1.410653297	3.029763143	3.962760529	45.58885002	42.30048
Run 23	1.410653297	2.245458052	3.885955641	45.52305749	42.11189
Run 24	1.410653297	2.954489271	3.953311113	45.75716692	42.30877
Run 25	1.410653297	3.737851832	3.980461552	46.82590727	42.24908

.

4.3.2. Sensitivity Analysis when SMP Changed

Hypothesis 2. 

The safety management process (SMP) is influenced by safety performance (SPF):

$$dSMP/DT=f\left(SPF\right)$$

(3)

Positive safety performance outcomes, such as a decrease in accidents or injuries, can enhance the perception and commitment to safety management within the organisation. For example, when safety performance improves, management may be more inclined to allocate resources towards safety initiatives or reinforce safety policies. This forms a reinforcing loop where improvements in safety performance lead to stronger safety management practices.

Table 16. Hypothesis 2 model distribution.

Distribution	Normal Distribution
Runs	200 (limited runs)
Mean	2
STD	1
Min	1
Max	5

represents its model distribution.

The safety performance frequency appears to be trending upward with time, as indicated by the graph in Figure 11. This indicates that the probability of safety incidents seems to be increasing over several months. The reason for this is that all of the percentile lines (the 50th, 75th, 95th, and 100th) appear to be advancing along the x axis, which represents months. The range of safety performance frequency throughout the 25 simulations is displayed in the shaded area. The darkened area’s width indicates that this variability rises with time. The same applies to Figure 11, Figure 12, Figure 13 and Figure 14.

4.3.3. Sensitivity Analysis when SP Changed

Hypothesis 3. 

Safety Management Process (SMP) influences Safety Performance (SPF):

$$OSPF/DT=f(SMP,SLF)$$

(4)

Effective safety management processes, such as clear safety process design or strong leadership commitment to safety, contribute to a safer work environment and fewer accidents, thereby improving safety performance. This is another reinforcing loop where improvements in safety management lead to better safety performance, reinforcing the importance of effective safety management.

Table 17. Hypothesis 3 model distribution.

Distribution	Normal Distribution
Runs	200 (Limited runs)
Mean	1
STD	1
Min	1
Max	5

represents a model distribution when SP changed. Figure 15, Figure 16, Figure 17 and Figure 18 are the outputs after conducting the sensitivity analysis.

Safety performance metrics including the frequency, extent, and cost of safety incidents were monitored throughout the sensitivity analysis. The model was run for each set of parameter values, and the resulting metrics were recorded and analysed.

The sensitivity analysis revealed several key findings regarding the impact of changes in safety-related factors and safety management processes on safety performance metrics: Frequency of safety incidents: Changes in safety-related factors such as safety training effectiveness and hazard identification had a significant impact on the frequency of safety incidents. Improvements in these factors resulted in lower incident frequencies, while decreases led to higher frequencies.

Extent of safety incidents: Similar trends were observed for the extent of safety incidents. Enhanced safety-related factors and management processes were associated with reduced incident extents, while deterioration led to larger incident extents.

Cost of safety incidents: Changes in safety-related factors and management processes also influenced the cost of safety incidents. Investments in safety training, equipment, and management practices were found to reduce overall safety incident costs, while neglecting these factors led to higher costs due to increased incidents and severity.

Project management-related factors (MRF): Changes in management providing opportunities for feedback and reporting on safety issues to workers were found to have a significant impact on safety performance metrics. Improved management practices led to reductions in the frequency, extent, and cost of safety incidents.

Worker-related factors (WRF): Increases in worker comfort in reporting safety concerns and participating in safety activities such as meetings, training, and inspections were associated with improved safety performance metrics. Enhanced worker engagement resulted in fewer safety incidents and lower associated costs.

Site environment-related factors (SRF): Adequate safety practices to prevent slips, trips, and falls were found to be critical for maintaining safety performance metrics. Investments in site safety infrastructure and practices led to reductions in the frequency, extent, and cost of safety incidents.

External-related factors (ERF): Compliance with industry safety regulations and government inspections were identified as important external factors influencing safety performance metrics. Projects that maintained high levels of compliance and underwent regular inspections demonstrated better safety performance outcomes.

Safety management process-related factors (SMP): The design, implementation, evaluation, and improvement of safety processes and systems were found to have a significant impact on safety performance metrics. Projects that effectively managed safety processes and systems experienced lower frequencies, extents, and costs of safety incidents.

The sensitivity analysis results have important implications for decision making and prioritisation of interventions to improve safety climate maturity in construction projects:

Investment in safety training and equipment: The analysis highlights the importance of investing in safety training programs and equipment to reduce the frequency, extent, and cost of safety incidents. Resources allocated to these areas are likely to yield significant returns in terms of improved safety performance.

Enhanced management commitment: Management commitment to safety emerged as a critical factor influencing safety performance metrics. Organisations should prioritise initiatives aimed at fostering a culture of safety and leadership commitment to ensure positive safety outcomes.

Continuous monitoring and improvement: The findings underscore the need for ongoing monitoring and evaluation of safety-related factors and management processes.

5. Discussion

The simulation results provided valuable insights into the factors influencing safety performance in construction projects in Tanzania. First, safety performance for construction projects is not stagnant but grows exponentially [105] with time from the beginning of the project to the end of the project, and the performance parameters decline while safety performance grows, as seen in Figure 19. This differs from the research conducted by Mahmoud, who presented the concept that safety performance in construction projects does not grow exponentially [106].

Second, the safety management process, including commitment to safety as a driving force behind safety climate maturity, is important; therefore, the safety management process is expected to rise exponentially at the beginning of the project [107,108] and to grow steadily as the project execution approaches its end. This strongly signifies that for an effective safety management process, the project will attain a safety maturity climate at the beginning phase of the project because the safety management process will be implemented at a high rate. About monitoring and controlling, safety leading factors and safety initiatives were found to have a significant positive impact on safety performance. This differs totally from the findings established about the safety management process, and they may not rise exponentially at the project’s start, which may be caused by engineers’ obtrusive habits and lack of integrated tools for safety-critical systems.

The patterns or trends in the relationship between SLF, SMP, and the frequency of accidents as shown in Figure 20 and Figure 21 indicate a strong correlation between these factors. This is because of an upward trend in the data points, suggesting that as the SMP and SRF ratings increase, the frequency of incidents might also increase [105,109].

By observing the position of the data points in Figure 22, it can be inferred that there are some potential relationships between the four factors (ERF, MRF, WRF, SMP1) and the extent of the safety performance. The data points for each factor are somewhat scattered, which means there might not be a strong linear correlation between each factor and the safety performance extent. However, there could be some underlying patterns. There might be a few data points that appear farther away from the main cluster for each factor. These could be outliers, representing unique cases where a factor has a significantly different impact on safety performance extent compared to other cases.

Thirdly, the role of the safety management process in safety performance highlights the importance of fostering a culture of safety awareness and participation among workers. Also, the impact of safety leading factors, including site-related factors, work-related factors, management-related factors, and environmental-related factors, on safety climate maturity is demonstrated, with adherence to safety regulations contributing to improved safety performance.

A comparison of SMP2 and SMP4 to SMP1 and SMP3 in Figure 23 indicates that they tend to occur at higher rates. This is because compared to SMP1 and SMP3, the data points for SMP2 and SMP4 are generally located higher on the y axis. It is possible to see some variations in the incidence levels of each SMP factor. For instance, it appears that SMP3 occurs at a reasonably high level throughout months 6 and 12, whereas SMP1 occurs at a lesser level during the same months. The data points’ scatter indicates that there are differences in the occurrence levels between the SMP components. Throughout the entire duration, no single SMP factor has the highest or lowest amount of occurrences continuously.

However, the complex interplay between safety climate and safety performance emphasises the need for cultural alignment with safety goals and values [110]. The scenario analysis revealed the potential benefits of interventions such as enhanced safety training programs, improved communication channels, and increased resource allocation to safety initiatives [111]. These interventions, shown in Figure 24, were found to lead to improvements in safety climate and performance, with reductions in safety incidents, accidents, injuries, fatalities, financial losses, and production time loss and with enhanced worker morale.

6. Conclusions

In conclusion, the sensitivity analysis conducted on the system dynamics model provided valuable insights into the factors influencing safety performance metrics in construction projects. By assessing the impact of changes in project management-related factors, worker-related factors, site environment-related factors, external-related factors, and safety management process-related factors, the analysis offers important insights for decision making and intervention prioritisation to improve safety performance.

This research journey, guided by the powerful lens of system dynamics, revealed the complicated relationships that shape the safety climate in Tanzania’s construction industry. It went beyond static snapshots and simulated a dynamic web of factors such as worker comfort, worker involvement in safety activities, inspection by government safety agencies, presence of risk assessment, regular safety reviews, provision of safety feedback, and changes in safety communications by tailoring our model to the Tanzanian context and capturing the unique challenges and opportunities that exist in the East African country’s construction landscape.

The system dynamics model simulation provided valuable insights into the dynamics of safety climate maturity in construction projects in Tanzania. By integrating data-driven insights with dynamic feedback mechanisms, the simulation model offers a powerful tool for understanding and improving safety performance in the construction industry. The findings and recommendations from this study can inform policy decisions and interventions aimed at enhancing safety climate maturity and fostering a culture of safety in construction projects. Based on the findings of the simulation study, the following recommendations are suggested for improving safety performance in construction projects in Tanzania:

• Strengthen management commitment to safety through clear policies, leadership support, and resource allocation;
• Enhance workers’ engagement with safety practices through training programs, communication channels, and participatory initiatives;
• Ensure compliance with safety regulations and standards through regular audits, inspections, and enforcement measures;
• Foster a positive safety climate that values safety, promotes open communication, and encourages continuous improvement.

This study contributes facts on the status of safety climate according to the established SDM model, it introduced a new definition of safety climate (as a product of safety leading factors, safety management process factors, and safety performance factors), and it introduced the SDM model from another analysis method (SmartPLS to Stella) for building construction projects in Tanzania.

This study has several limitations. During simulation, complex, spatially distributed physical processes were difficult for the SDM model to accurately represent. To overcome this constraint, system dynamics can be combined with additional modelling techniques such as the analytical hierarchy process (AHP).

Occasionally, the SD model did not produce quantitative predictions with sufficient accuracy, particularly when describing intricate safety performance categories. A significant amount of data must be calibrated and verified, which can demand a lot of resources.

Conversely, the SDM model aggregates and oversimplifies system representations. High levels of aggregation may not be sufficient to capture important safety management processes, which frequently take place at finer spatial and temporal scales. This restriction can be lessened by beginning with a broad aggregate model and progressively adding more specifics.

However, spatial variability or system elements such as those established by safety lading factors and safety management processes within the modelled system are not explicitly represented by SD models. Although attempts have been made, it is still difficult to include spatial elements in system dynamics modelling. Furthermore, the SDM does not permit the simultaneous examination of multiple scenarios, even though it captures the diversity of changing variable values as has been observed during the simulation of various sensitivity analysis scenarios.

The practical utility of data was limited and depended on another system of collecting and other program/software analysing it (Smart PLS 4 version 4.0.9.6), which may affect the simulation results.

Conclusively, while system dynamics modelling offers significant perspectives on intricate systems, scholars and professionals must acknowledge these constraints and take them into account when utilising this approach in diverse domains.