Development of a Simulation Model to Improve the Functioning of Production Processes Using the FlexSim Tool

Abstract

One of the goals of Industry 4.0 is to increase the transparency of the value chain through modern tools in production processes. This article aims to discuss the possibility of increasing the efficiency of a production system by modernizing it with the use of computer modelling tools. This article describes a method for the simulation modelling of a selected production system using the specialized FlexSim 2023 software in a 3D environment. The results and benefits of the practical application of the object-oriented modelling are presented, as well as the possibilities of collecting simulation data used to optimize production processes. The analyses were conducted at a selected production plant in a case study. The research assessed the effectiveness of the existing system and determined the impact of process changes in the event of the introduction of a new design solution. The simulation identified bottlenecks in the material flow. The basis for creating the simulation model was the analysis of the technological process. A simulation model for a real situation was created, and a simulation model was designed to identify and indicate a solution to eliminate the detection of the bottleneck. The problem area identified using visualization in the technological process slowed down the entire production process and contributed to time and economic losses. Thus, the authors confirmed the thesis that the simulation modelling of production systems using the FlexSim program can help eliminate bottlenecks and increase the efficiency of human resource use. At the same time, the use of this tool can lead to increased efficiency, reduced costs and improved sustainability and other performance indicators important for modern production environments as part of the promoted Industry 4.0 idea. A noticeable result of these changes was an increase in production from about 80–90 units. In addition, it was noticed that the condition of the machines preceding the stand changed.

1. Introduction

As observations of production environments indicate, one common phenomenon is the constant pursuit of the continuous improvement of production processes [1]. There is a constant demand for the development of new solutions to improve the efficiency and harmonization of production systems [2]. In particular, this practice has intensified in the era of challenges posed by the increasingly popular idea of Industry 4.0 [3]. In practice, the use of modern optimization tools is expected to lead to an increase in efficiency while reducing costs [4]. When browsing the offers of simulation software manufacturers, it can be assumed that they have very advanced functions and extensive object libraries that enable the very precise construction of the desired model and its actual operation. In the case of production systems, these tools can be used to conduct experiments on existing production lines and to examine the possibility of undertaking optimization and harmonization projects of already operating production lines [5]. With the use of a properly selected tool, it is possible to model these processes without the need to have physical devices constituting their elements. As indicated in the literature on the subject, the obtained results can illustrate the operation of the system over a selected time course, showing its behavior in the event of a failure, and they also enable the analysis of areas defined as problematic [6]. A very common subject of research on functioning production systems is the location of the so-called bottleneck of production processes. In the available literature, many managers and engineers of manufacturing companies are looking for effective methods to eliminate this phenomenon. By addressing this issue, it is possible to streamline production processes and increase their system efficiency while reducing costs. This optimization and harmonization can be achieved with the right simulation tools. Their proper use allows for manufacturing companies to conduct a thorough process analysis and implement beneficial modifications [7]. However, it is worth bearing in mind that using the above-mentioned solution also has disadvantages. The purchase of appropriate software is associated with relatively high financial outlays, especially in the case of detailed models, where creating a correct model can be very time-consuming and cost-consuming [8,9].There is also a risk of making a mistake at the design stage of the model due to a lack of real data, resulting in erroneous results. It is worth noting that there are also very advanced production environments for which it may be impossible to build a correct simulation model [10,11]. However, in most cases, a correct approach to modelling and optimizing production processes based mainly on the use of these tools and real data for the analysis of production systems can bring many systemic benefits in terms of the harmonization and optimization of production. The course and logic of the simulation modelling procedure and its relationship to a real system are shown in Figure 1.

At this stage of consideration, it is important to understand that every manufacturing company may have many sources of waste, e.g., overproduction, defective products, unnecessary inventory, failures, excessive storage, etc. Each of these phenomena has a major impact on the efficiency of the production line and, consequently, on sales revenues. This is an important argument that motivates the use of modelling and simulation tools to eliminate waste from areas at risk. The ideal tool for solving this type of problem seems to be the specialized FlexSim software. FlexSim is an analytical tool used in practice in process design and decision-making [13]. In the FlexSim simulation software, three-dimensional models can be created that map a real system, e.g., a production system.

The considerations presented in this paper focus on the development of a simulation model of the production process of a given product—lighting poles—based on real data obtained from one of the main manufacturers of these structures in Europe. Achieving this goal required the use of the specialized FlexSim software [14]. After preparing the model and analyzing the results obtained, an attempt was made to improve the process by increasing one of the key parameters, i.e., the production efficiency. The research process was used to confirm the hypothesis that the simulation software is an effective tool for investigating potential solutions to improving existing production systems. In addition, the use of computer simulations can lead to a reduction in the time it takes to conduct experiments on production line models. The simulation itself can lead to a reduction in the costs necessary in the process of testing solutions for already functioning systems in the production environment.

To verify the research hypotheses, it was decided to experiment with a production system operating in one of the largest companies in Europe dealing with, among others, the production of lighting poles. After defining the research problem, its implementation and verification of the results obtained were carried out. During the work, the specialized FlexSim software was used, which is a tool for building models and simulating the functioning of systems. The final stage of the research and analysis was to try to improve the process by proposing changes to the bottleneck and examining their impact on the system.

After reviewing the literature from the last 5 years, the authors noticed that researchers had not undertaken the use of simulation tools to optimize and harmonize the production processes of lighting poles. This is a diversified production process, which is why individual methods of approaching this type of project have always been used. This solution is very time-consuming and economically unjustified. Therefore, this article undertook a case study and complements research and analysis of the practical use of FlexSim tools to solve complex problems and design systems of analyzed cases.

This article is divided into the following sections: Section 1 provides an introduction to the topic. Section 2 contains a review of the literature on the development of simulation models for the production process of the analyzed product. Section 3 describes the research methodology used to analyze the production process. Section 4 contains the results of the research and numerical experiment and an extensive commentary on them. Section 5 contains the research conclusions and perspectives for further development for analysis and research on this topic.

2. Literature Review of the Analyzed Problem

In the available literature on process modelling and simulation, many items that explain this issue and indicate its various aspects can be found [15]. Many papers present the application of a particular method or software along with the results obtained by a specific researcher. The first research focused on the theoretical aspects of simulation and modelling. The paper [16] contains definitions of modelling and illustrates the advantages and disadvantages of using this tool to investigate potential solutions. Reference [17] focuses on the issue of model construction. The authors indicate the purpose of modelling, methods of implementation and stages of its preparation [18]. The next analyzed items present the stages of building a simulation model with the use of computer software [19]. This is an extremely important issue because in today’s production environment, this solution is widely used due to the significant complexity of the systems operating in enterprises. In [20], the authors developed one of the most important elements of model building, which is validation. It is of key importance in system analysis because it is used to check the correctness of the implemented project, which translates into the reliability of the results obtained [21]. In addition, this study provides information on the areas of application of simulation modelling and then presents the issue of using this tool in the aspect of production process management [22]. In Ref. [23], simulation models are divided according to their characteristics. Other studies [24] focused on the use of this tool in companies producing a particular product. They present individual production areas in which simulation modelling can be used and describe the stages of production preparation based on simulation models. They describe the methods of analysis of the functioning system through the selection of an appropriate tool and the implications of the results obtained in the real production environment.

In a narrower approach to simulation tools, researchers focus on issues related to the modelling and simulation of production processes themselves. In some articles [6], the authors present the course of the work and the analysis of the results obtained using the ARENA software © 2024 Rockwell Automation [7]. However, reference [8] focuses the authors’ attention on the mathematical aspects of building models. Simulation methods are presented here as well as an experiment illustrating how the results obtained should be considered. Production processes are complex and multi-stage activities, consisting of various tasks and phases [25]. However, the organization of processes in the conditions of dynamic changes occurring in a company’s environment is very difficult and problematic, because in order to maintain the continuity of the production process, work must be properly designed and rationally organized [26]. Another researcher emphasizes that, currently, the availability of new digital technologies shapes the business environment of enterprises and creates new opportunities for development by introducing innovations to the structures within Industry 4.0 [27]. These innovations refer to the possibility of blurring the boundaries between physical and virtual entities [28]. Digitalization is forcing traditional industrial organizations to rethink and develop existing business models [29]. Modelling connections between operations and analyzing real scenarios for a given process, taking into account the internal and external environment of the enterprise, is possible using computer simulations and specialized tools [30]. Solving various technical problems using simulation modelling is effective, and its effectiveness has been confirmed, among others [31], in the research of one of the authors [32]. Other studies [33] show that a properly designed production process can reduce operating costs in a company by up to 50%. The effect of modelling processes, objects and phenomena is to obtain results in the form of temporal dependencies of statistical data [34]. In serial production, simulation modelling can be used to determine the most important parameters that will make the technological process more efficient and effective [35]. Another researcher emphasizes that the modelling of production processes is possible by using computer software to conduct experiments and tests. The author’s research focuses primarily on modelling operations, information visualization and data analysis, thus allowing for the analysis of various scenarios of production activities without the need to disrupt them in reality [36]. Design is conducted by learning and using knowledge about past events. Analysis of available solutions may result from analogous cases or known external potential improvements [37].

At this stage of consideration, it should be emphasized that the production process analyzed by the authors is a complicated one, which may involve many unnecessary or improper activities, leading to production stoppages. Production analysis using a simulation model allows for reducing costs and optimizing the production time. Popular tools for managing and controlling production are known as Manufacturing Execution Systems (MES) [38], which is used in the operational area. However, these systems have significant drawbacks compared to the possibilities of material flow simulation. MES do not allow, for example, production planning or storage based on designated areas, which is important in the process of manufacturing large-size steel structures [39]. Therefore, the identification of complex relationships between material flows in the long term can only be achieved through simulation modelling. FEM allows for short and reasonable process cycle planning whilst only basing the simulation of the material flow on cooperation with MES to optimize production planning [40].

The authors in their works [41,42,43] show how the fourth industrial revolution (Industry 4.0) contributes to the development of the process of the technological and organizational transformation of enterprises, which includes the integration of the value chain, the introduction of new business models and the digitization of products and services. The implementation of these solutions is possible by using new digital technologies and data resources and ensuring communication in the cooperation network of machines, devices and people. The factors driving the transformation towards Industry 4.0 are the increasingly individualized needs of customers and the growing trend of the personalization of products and services. The transformation towards Industry 4.0, according to the authors of works [41,42,43], includes seven stages. The first concerns technological advancement, which takes into account flexible production systems that facilitate quick adaptation to changes in the number or category of products. The next step is to share information about the manufacturing process by people, machines and products. The third phase is about taking into account the principles of the circular economy to fully use raw materials and reduce emissions. The process of the comprehensive implementation of customer expectations towards products, i.e., end-to-end customer-focused engineering, is the fourth stage towards Industry 4.0. Next, it is crucial to focus on people, including using individual differences to strengthen the organization and build a meaningful work environment. The sixth stage, smart manufacturing, involves the use of integrated systems that respond to changing conditions in real time. In this context, storing and sharing large data sets (big data) is of great importance. The final step is an open factory that understands the needs of all participants in the value chain. All these principles make it possible to achieve the most effective production and quality of the final products [44].

In the lighting pole manufacturing industry, material flow simulation should therefore be used as a production planning tool [45]. Through simulation modelling, the authors in [46] analyzed the production process in terms of resource allocation, data collection necessary for decision-making and full capacity utilization [47]. The authors in [48,49,50,51] analyzed the role of the use of simulation modelling in the production of steel structures for large offshore structures. The functionality was presented in a practical example, which allowed us to conclude that simulation modelling contributed to the improvement in the quality of planning in the production of this type of structure.

Modern production systems are very complex and difficult to analyze; therefore, many methods (including mathematical modelling, combinator optimization, Petri net and scenario analysis) are used to solve the above-analyzed problem [52]. Computer simulation methods, especially discrete event simulations (DES), are the most universal and are widely used [53]. There are many DES software tools dedicated to simulating manufacturing processes, such as ARENA, Enterprise Dynamics, FlexSim, Plant Simulation, SIMIO, Witness and others [54]. The main advantage of DES is the ability to conduct many simulation experiments in a short time. Building a simulation model helps in gaining knowledge that can lead to improvements in a real system [55]. The disadvantage of DES is the randomness of some simulation parameters, and it is therefore sometimes difficult to distinguish whether an observation is the result of intersystemic relationships or randomness [56]. Designing complex production systems requires integrating various aspects, including production strategies, system architecture, capacity planning, management techniques, performance assessment, scenario analysis and risk assessment [57]. The beginning of the production system design process is conceptual modelling [58,59,60]. A summary of the most important information from the literature on the subject is presented in

Table 1. Summary of the most important information from the literature regarding the research problem.

Authors	The Most Important Information from the Literature
Toczyńska, 2016 [16]	Avoiding production errors and thus optimizing production requires the use of simulation modelling methods.
Łatuszczyńska, 2015 [21]	Using a simulation model, represent key system features can be represented and data can be collected and used to optimize processes.
Gołda et al., 2015 [23]	A simulation is an imitation of the operation of a real-world process or system over time.
Leminen et al., 2020 [28]	One of the tools that allows for mapping real production and logistics systems in a 3D environment to analyze and optimize their operation based on collected simulation data whilst additionally cooperating with virtual reality technologies is the FlexSim software.
Roháč et al., 2020 [31]	This software can be successfully implemented in the areas of supply, production, warehousing, transport systems and many others.
Qin et al., 2016 [34]	Organizing processes in the conditions of dynamic changes taking place in the enterprise environment is, however, very problematic, because to maintain the continuity of the production process, work must be properly designed and then rationally organized.
Herrmann, 2007 [39]	These innovations refer to the possibility of blurring the boundaries between physical and virtual entities.
Folgado et al., 2024 [42]	Digitalization forces traditional industrial organizations to rethink and develop existing business models.
Akpan and Offodile, 2024 [43]	Modelling of connections between operations and analysis of real scenarios for a given process, taking into account the internal and external environment of the enterprise, is enabled by computer simulation.
Nota et al., 2020 [45]	Solving various technical problems using simulation modeling is effective, and its effectiveness has been confirmed in scientific studies.
Niekurzak et al., 2023 [46]	A properly designed production process can reduce operating costs in a company by up to 50%.
Agarwal and Ojha, 2024 [47]	The effect of modelling processes, objects and phenomena is to obtain resultsin the form of time dependencies of statistical data.
Zamora-Antuñano et al., 2019 [55]	Modelling of manufacturing processes is possible thanks to computer software for conducting experiments and tests. These tools focus primarily on scene modelling, information visualization and data analysis, thus allowing for the analysis of various production operation scenarios without having to interrupt them in reality.
Krenczyk et al., 2019 [53]	Design is conducted by learning and using knowledge about past events. The analysis of available solutions may come from analogous cases or known external potential improvements.
Gola and Wiechetek, 2017 [56]	Popular tools for managing and controlling production are Production Execution Systems (MES), which are used in the operational area.
Veisi et al., 2018 [58]	Thanks to simulation modelling, manufacturing processes can be analyzed in terms of resource allocation, collecting data necessary for decision-making and the full use of the production capacity.

.

When analyzing issues related to the research area described above, it should be emphasized that despite there being a large number of articles on simulation modelling, no analyses were found regarding the use of the FlexSim tool to improve the manufacturing process of a specific product, such as lighting poles. Therefore, it was decided to test the production line model using FlexSim, and then the critical areas were identified, and an experiment was undertaken to improve this process.

3. Material and Methods

3.1. Model Assumptions

The following research program was planned:

• Selection of the production line to be the subject of research,
• Collecting and defining input data necessary to create a simulation model,
• Building a model using the FlexSim software,
• Validation of the created model,
• Conducting a simulation reflecting the implementation of a sample order,
• Analysis of the obtained simulation results,
• Isolation of process bottlenecks,
• Presentation of potential process improvements, specification of implementation cost solutions,
• Conducting simulations using selected improvements,
• Summary of the results obtained,
• Choosing the best solution.

A simulation tool called FlexSim was used for this research. FlexSim is 3D simulation modelling software that transforms existing data into accurate predictions. Customers who use the software are engineers and decision-makers who see potential in processes that can be improved. The FlexSim testing program is available at the University’s laboratory station [61]. It has a perpetual educational license under Academic Classroom LAN. The purchase of a license, depending on the add-ons and library database, costs around EUR 12,000–30,000. Most modern Windows computers meet the minimum FlexSim requirements, i.e., A 64-bit edition of MS Windows 10 2022 version 22H2 under current Microsoft 365 extended support, 8 GB RAM or more, a GPU supporting OpenGL 3.1 or higher, 3 GB free and the latest .NET Framework [62].

The above-mentioned research scheme is intended to allow for the verification of the thesis indicated in the introduction of this work.

3.2. Preparation of the Simulation Model for Research

As part of the research problem, the production process of lighting poles was analyzed in terms of the selected parameter of the unit of time that should be spent on performing individual activities. The first step in building the model was to define the necessary elements and parameters of the analyzed production process. The analyzed production line consisted of the following elements:

• HD-F “Durma” laser cutter,
• Sheet loading, unloading and transport system (part of the cutting machine),
• Pressing the brake of the “Durma” AD-R 30135,
• Integrated system for laser welding of lighting poles (welding cell),
• Cavity cutting station (Fanuc industrial robot),
• Manual (MIG—Metal Inert Gas, MAG—Metal Active Gas) welding machine.

In addition to the above-mentioned machines, the use of human resources was essential. For the efficient operation of the line, the support of at least 5 employees was required to operate the cutting laser, hydraulic press, welding cell and pole foot welding.

A round lighting pole with a length of 4 m was selected as the production object for the relevant analyses. The results of the measurements in the production environment are presented in

Table 2. Average processing time at each stage of the process.

Position	Operation Name	Operating Time [s]
Laser	Table exchange	30
	Sheet metal search	60
	Sheet metal cutting	480
Transfer	Waste collection	130
	Loading + unloading	660
Press brake	Configure	30
	Sheet metal bending	90
	Unlock	30
Welding cell	Snorting	130
	Positioning, fixing	100
	Welding	81.4
	Unlock	30
Transfer	Transport to the next station	55
Cutting station exit from the alcove	Preparation for cutting	90
	Cutting a cavity	230
	Lowering after cutting	120
Pole foot welding station	Preparation for welding	30
	Welding of the column foot	60
	Pulling the bar down	30

Source: own study.

.

When a laser is used, 4 pieces of sheet metal with the given dimensions are obtained from one sheet. Therefore, for analysis, it was decided to divide the working time on this machine by 4 to obtain the processing time of one piece of product. After determining the implementation times of the individual process stages, it was decided to introduce information about all the events causing the operation of the individual machines to stop in the model. For this purpose, an analysis was performed using prediction tools.

Among the many possible disruptions to the production process, an undoubtedly harmful phenomenon is the failure of the machines carrying out their production processes. Each defect causes the device to be excluded for a certain period. In the case of not very complicated damage, this time may range from a few to several minutes (repair by employees of the maintenance department). However, in the event of a serious fault, the machine’s downtime may reach one or even several days (need to call the service center or order a damaged component or part). The fault causes an inability to perform a technological operation on a given machine, as well as a loss of smoothness of subsequent operations resulting from the technological route. This situation also affects the remaining tasks in the schedule. To conduct the presented research, it was necessary to collect historical data on failures and defects. The source of this data was service books for technological machines constituting part of the company’s machinery. The books contained information on all activities carried out on 12 machines by employees of the maintenance department. However, data on failures were selected for research, and inspections (annual and periodic) were carried out (

Table 3. Summary of data on the failure rate of technological machines in 2017.

1	2	3	4	5	6	7	8	9	10	11
Machine	Failure _1	Time_1	Failure _2	Time_2	Time_12	Complete_1	Complete_2	Previous	Time_Review < 90	Next
Machine 1	0	365	0	365	0	0	0	0	0	0
Machine 2	1	10	1	74	64	1	1	0	0	0
Machine 3	1	199	0	365	166	1	0	0	1	1
Machine 4	0	365	0	365	0	0	0	0	0	0
Machine 5	1	77	1	246	169	1	1	0	0	0
Machine 6	1	170	1	213	42	1	1	0	0	0
Machine 7	1	247	1	266	19	1	1	0	1	1
Machine 8	1	73	1	231	158	1	1	0	0	0
Machine 9	0	365	0	365	0	0	0	0	0	0
Machine 10	1	220	0	365	145	1	0	0	0	0
Machine 11	1	67	1	260	193	1	1	0	0	0
Machine 12	1	3	1	45	42	1	1	0	0	0

Source: own study.

).

Because most failure cases were recorded in 2017, data from this period were used for the analysis. The acquisition and appropriate processing of historical data allowed for their implementation in the STATISTICA 13.1 StatSoft Polska system. The collected data were saved in the form of a table using the appropriate variables:

−

Failure_1 and Failure_2—variables informing about a failure (value “1”) or its absence (value “0”),

−

Time_1 and Time_2—variables defining the number of days from the beginning of the observation to the occurrence of the event,

−

Time_12—variable defining the time between the first and second failure,

−

Complete_1 and Complete_2—variables informing about the observation status (complete—“1”, abscissa—“0”),

−

Previous—a variable defining whether the failure was related to the previous failure (“1”—yes, “0”—no),

−

Time_review < 90—variable indicating whether the fault occurred within 90 days of an inspection (“1”—yes, “0”—no),

−

Next—a variable informing about subsequent failures (“1”—further failures occurred, “0”—no further failures).

Presenting the data in this form made it possible to perform research using the tools available in the Survival Analysis module of the STATISTICA package (version 12). The basic tool for duration analysis is mortality tables. This technique belongs to the group of the oldest methods of analyzing duration data. For each interval, the number of complete and censored observations is determined. Based on these data, the number of cases at risk, the proportion of cases failing or the proportion of cases surviving were calculated (

Table 4. Survival tables for cases from 2017.

Compartment	Initial Range	Midpoint	Compartment Widths	Number Incoming Observations	Number Truncated Observations	Number of Threats	Number of Deaths	Proportionality Deaths	Proportionality Experiences	Cumulative Probability of Survival	Probability Density	Hazard Rate
L.Initial_1	0.000	13.035	26.071	14	0	14.000	3	0.214	0.785	1.00	0.008	0.009
L.Initial_2	26.071	39.107	26.071	11	0	11.000	0	0.045	0.954	0.758	0.001	0.001
L.Initial_3	52.142	55.178	26.071	11	0	11.000	3	0.274	0.724	0.750	0.007	0.012
L.Initial_4	78.214	91.250	26.071	8	0	8.000	0	0.062	0.935	0.545	0.001	0.002
L.Initial_5	104.285	117.321	26.071	8	0	8.000	0	0.062	0.935	0.511	0.002	0.002
L.Initial_6	130.357	143.392	26.071	8	0	8.000	0	0.062	0.935	0.479	0.004	0.005
L.Initial_7	156.428	169.464	26.071	8	0	8.000	1	0.125	0.875	0.441	0.002	0.012
L.Initial_8	182.500	195.535	26.071	7	0	7.000	2	0.284	0.714	0.391	0.002	0.008
L.Initial_9	208.574	221.607	26.071	5	0	5.000	1	0.200	0.800	0.280	0.001	0.008
L.Initial_10	234.642	247.678	26.071	4	0	4.000	1	0.250	0.750	0.224	0.000	0.010
L.Initial_11	260.714	273.750	26.071	3	0	3.000	0	0.167	0.833	0.165	0.000	0.006
L.Initial_12	286.785	299.821	26.071	3	0	3.000	0	0.167	0.833	0.140	0.000	0.006

Source: own study.

).

The summary of data in the above form allows for the analysis of failure rates in specific time intervals. Another parameter worth noting is the hazard rate. It is defined as the probability per unit of time that a case that has survived to the beginning of a given interval will fail in that interval. This indicator increases its value in intervals where the number of failures increases, so observing its variability may be a good element in predicting future events. Compiling data in the form of survival tables is the basic element of creating probability charts. This process involves fitting the theoretical distribution of failures over time to empirical data. In this way, life expectancy function graphs (Figure 2) and probability density distributions (Figure 3) can be obtained. Because the Weibull distribution is a distribution quite often used in analyses related to failure rates, such a distribution was chosen when generating the charts. The estimation is based on three different estimation procedures—least squares and two weighted least squares methods.

Analyzing the obtained estimation results, it should be stated that in the case of the observations from 2017, the approximate distribution charts overlapped to a significant extent with the empirical distributions. In the case of the estimated distributions for the observations from 2017, it should be stated that the procedures used gave very similar results. Nevertheless, the distribution matching tool allows us to illustrate, to some extent, the nature of the analyzed failures.

In the case of estimating the probability density curves, we also observed that for the data from 2017, various approximation methods took a similar shape. It should be noted that the obtained graph has a typical shape of the probability density function of the Weibull distribution. Based on the results obtained, it was possible to determine the shape parameter, which is one of the parameters of the fitted distribution.

In the subsequent part of this study, the survival function was estimated directly from continuous survival times using the Kaplan–Meier method. Each interval then contained exactly one event. The survival function is defined as the product of successive probabilities from the intervals [62]:

$$S_n\left(t\right)={\displaystyle \prod }_{t_j\le t}\left(1-{\displaystyle \frac{d_j}{r_j}}\right)$$

(1)

where:

• $S_n\left(t\right)$—estimated survival function,
• ${\displaystyle \prod }_{t_j\le t}$—product symbol,
• $d_j$—number of events in the period $t_j,$
• $r_j$—number exposed per period $t_j$.

The results of the estimation of the survival function for the examined empirical data are presented in Figure 4.

By analyzing the above data, we can determine the value of the survival function in a specific time interval. For example, around 140–170 days of work, the survival rate was 90%. Analyzing the graphs of the tested samples, it should be concluded that the occurrence of the second and subsequent failures significantly affected the probability of survival. Its value dropped below 0.5 already within 100 days, while for machines experiencing only 1 failure, it remained at the level of 0.7 even up to the 220th day. This is valuable information that allows for the identification of machines that potentially pose a threat to the smooth operation of the production process. Selected statistical tests were used to examine the statistical significance of the analyzed data. The results of the significance tests are presented in

Table 5. Results of significance tests—2017.

Comparing Trials: Occurrence or absence of failure #2
Test name	Level of significance p
F Coxa	0.001
T. Coxa–Mantela	0.004
log-rank	0.004
Comparing trials: Occurrence of subsequent failures.
Test name	Level of significance p
F Coxa	0.04
T. Coxa–Mantela	0.07
log-rank	0.1

Source: own study.

.

Analyzing the above results of the significance tests, it should be stated that in the case of comparing the tests concerning failure no. 2, all the tests showed that the results obtained were statistically significant (p < 0.05). Unfortunately, when comparing the samples in terms of subsequent failures, the significance level in the case of the two tests was above p = 0.05, which means that it cannot be concluded that the presented differences were statistically significant. The results of comparing the tests allowed us to conclude that both the occurrence of a second failure and the number of days that pass from the inspection to the occurrence of the failure have a significant impact on the course of the survival function. Machines that have only had one failure are more likely to survive than those that have failed again. Similarly, machines whose fault occurrence time is longer than 90 days from the last inspection are characterized by higher survival function values than those where the fault occurred within 90 days of inspection.

Moreover, before building the simulation model in FlexSim software, it was decided to make the following assumptions:

• The line is open on weekdays from 6:00 a.m. to 4:00 p.m. and closed at other times and on Saturdays and Sundays,
• Sheet metal and finished column feet are available in sufficient quantities to process the order,
• The finished poles are loaded for transport one at a time,
• Each machine has an assigned operator who is responsible for operating it,
• Each operator is assigned to one machine,
• Orders are placed for one type of product, so there is no need to change the equipment,
• Orders are fixed and accepted every Monday (150 pcs.) and Wednesday (200 pcs.).

Based on the above data and the assumptions made, a simulation model was built in the FlexSim program. The following data and objects were used for this purpose:

• Source, i.e., the order generator; the arrival times of individual orders were introduced by importing an Excel spreadsheet. This element was also selected to reflect the composition of the column feet, which are delivered from the workshop once a week in the amount of 500 pieces. Figure 5 shows the program window with the characteristics of the order generator.
• A queue, reflecting the composition of the sheet metal. As a result of accepting the order, sheets appear in this place, which is an input element for processing at subsequent stations. It is assumed that the stack can hold a maximum of 500 sheets.
• A processor equivalent to a laser cutting machine, a press brake, a welding cell and a cavity cutting station. For each station, the processing time, the time between failures and the repair time of the device are specified. Figure 6 shows windows from the FlexSim program with information about one of the machines.
• A connector, corresponding to the welding station of the column foot. As with the previous machines, the processing time of the product was determined, and the “join” operation was fixed so that the final product was a pole with a foot.
• A sink, which is a place to store finished products.
• Operators, assigned one to each machine,
• A transporter, transporting finished products to the field for shipment.

Figure 7 shows the diagram of the built model.

The finished products are transported for shipment by a forklift. The logic of its operation is based on the time of completion of the last operation of the production process. Figure 8 shows the process of transporting finished products.

To maintain the logic and consistency of the analyses, the line operating time was also determined. For this purpose, information about the hours when the system will perform scheduled operations on particular days of the week was entered into the model. Figure 9 shows the program window reflecting this aspect of the model.

Once the simulation model was built in FlexSim, the validation process began. For this purpose, a simulation of the implementation of a historical order carried out by a production plant was carried out. Then, the actual lead time of the production order was compared with the result obtained with the specialized FlexSim software. After the model was validated, the production line was analyzed in terms of the assessment of the achieved efficiency of individual production sections. For this purpose, a simulation covering a 365-day system operation cycle was carried out based on the previously adopted assumptions.

4. Results and Discussion

4.1. Simulation Results

After entering the data into the model and taking into account the previously adopted assumptions, the simulation of the production line operation was carried out. Figure 10 presents the data generated with the FlexSim program, which illustrate the individual characteristics of the individual production stages and thus the percentage share of the use of the selected machines in the analyzed production process.

By analyzing the presented data, a so-called bottleneck located on the cavity cutting section was identified. For about 86% of the simulation time, the station performed operations on the product. For the rest of the time, the machine waited for the failure to be repaired at the previous stations to resume production. In addition, it was noted that the column foot welding station was idle most of the time (only about 24% of the simulation time was spent by the machine working on product finishing). The second section stage that attention was paid to was the welding cell. Its operation reduced the efficiency of the press brake, which spent most of its time in the simulation waiting for the possibility of transferring the machined product to the next stage of production.

Another area of analysis was the number of products that could be produced during one shift with the current system functioning. Figure 11 shows an analysis of the daily output of poles over a year.

The data analysis indicated that the production line was capable of producing about 80 pieces of product per day. Due to failures and different repair times of individual machine sections, this value was not fixed for all days. After examining the “for shipment” field, it was determined that in the simulated time (365 days), the line produced 18,200 lighting poles.

In addition, the influence of the sheet metal composition state section was studied. Figure 12 shows a chart reflecting the execution of orders throughout the year.

The analysis of the presented data confirmed that the sheet metal storage section could meet the demand for the manufactured product. All of the above values were considered as the initial state to which the results of the next simulation will be compared.

4.2. The Concept of Changes in the Production Process—Analysis and Evaluation

The cavity cutting station of the analyzed semi-finished product was identified as a bottleneck of the analyzed line. The residence time of the semi-finished product in this section slowed down the entire system and reduced the production capacity. Due to the large area of the production hall, it was possible to introduce a second nest-cutting station into the system. The concept of the changes assumed the purchase of a second Fanuc robot and the involvement of an additional employee.

To assess whether the presented solution would improve the process and to what extent the individual parameters of the system would change, it was decided to use the FlexSim software and modify the original model of the system. The following changes were made to the base model:

• A station for cutting out recess No. 2 with the same processing time as station No. 1 was added,
• A second operator of the cutting machine was introduced,
• The logic of selecting the position for the excision of the cavity due to availability was established,
• A queue in front of the foot welding station was added.

After making these changes, the model shown in Figure 13 was obtained.

The next step was to simulate the modified system. As with the original model, the duration of the experiment was set at 365 days. Figure 14 shows the daily production of products, Figure 15 shows the graphs showing the use of machines in the analyzed production line and Figure 16 shows the sheet metal composition in the new conceptual model.

After analyzing the data from the conceptual model, it was found that:

• The maximum daily production of the final product increased to about 90 pieces,
• An increase in the phenomenon of inactivity was observed in the selected sections, which resulted from the faster execution of accepted orders,
• The introduction of a second cavity-cutting station eliminated the bottleneck phenomenon at this stage,
• In the remaining sections, it was found that the machines were used to the same extent, but the blocking time of these devices was shortened,
• The stock level of sheet metal was more likely to reach a coefficient of 0.

Based on observations of both the original production line and the conceptual one, it was found that the introduction of an additional welding station resulted in an increase in production efficiency compared to the original model of the production line. A noticeable result of these changes was an increase in production from about 80–90 units. In addition, it was noticed that the condition of the machines preceding the stand had changed. In the case of welding, the percentage of time during which equipment was blocked and waiting for the possibility of transferring the semi-finished product to the next stages of the production process was significantly reduced.

5. Conclusions

Observations of production environments indicate that many companies are currently implementing the idea of Industry 4.0 [63]. This process builds the belief that the implementation of related solutions will allow for significant efficiency improvements, cost reductions, optimization and the harmonization of production processes on the way to sustainable development. One of the key solutions to achieve this success seems to be the use of simulation modelling and the use of specialized tools such as FlexSim to diagnose the entire production system or its selected components [64].

There is no doubt that simulation modelling enables the optimization of product flow and, consequently, the full use of available resources. This effect is possible by conducting simulation experiments on the production line without the need to stop production [54]. The case of using a simulation on the example of the selected good analyzed in this article certainly confirmed how complicated modern production processes can be. In a way, it indicates how many factors affect the difficulties in proper production planning and how important it is to reduce unnecessary activities to optimize production.

Based on the presented research, the following conclusions were formulated:

• Simulation models can be used to identify adverse phenomena occurring in the area of production processes. They reflect the functioning of systems in a production environment, which are subjected to all kinds of analyses. With their help, it is possible to test the validity of the proposed conceptual and model solutions without the need to make actual changes to the production system and without incurring significant financial outlays.
• Tools such as FlexSim contain extensive libraries of 3D objects. This makes it possible to faithfully reproduce the analyzed process—the production line. This allows for the construction of detailed models of production systems, the conducting of experiments and the analysis of the achieved results. It is important to emphasize that advanced algorithms together with statistical tools enable the mapping of the natural variability of the process. Thanks to these tools, it is also possible to analyze a large number of alternative scenarios to find a solution, thus confirming the validity of strategic decisions, finding the optimal solution from hundreds of possibilities or even creating the best production plan. In addition, these programs have the function of integration with other tools (e.g., Microsoft 365 Excel 2016 or © 2024 Autodesk Inc. CAD—Computer-Aided Design—software).
• The use of the FlexSim software made it possible to propose solutions that could bring positive effects to the existing production line without incurring additional costs. Furthermore, the tool used significantly reduced the time spent on research and development. The simulation of the system allowed for the 365-day life cycle of the modified line to be analyzed in one day, which is an extremely short time compared to the period during which the data were obtained.
• According to the authors, the FlexSim modelling and simulation tool can also be used to create new production lines. At the same time, it provides a solid foundation supporting the digital transformation of Industry 4.0. This software allows for the analysis of project costs and potential profits from production. This makes it possible to decide whether to start or reject a project of building a production line without incurring additional costs.

Thus, the authors postulate that in the era of growing interest in the idea of Industry 4.0, it is worth considering investing in simulation software, especially in the case of corporations that can use it in many areas and branches of a given group. Furthermore, simulation software can not only improve individual internal processes but also harmonize the coordination of the entire supply chain. The benefits of simulation will then also be noticeable in other links in the production chain. The authors agree with the statement promoted by other researchers that the possibilities offered by simulations are certainly worth considering and will probably become a standard as part of the Industry 4.0 idea [65]. The business sphere should recognize that simulations offer great opportunities to create new processes and systems and even to design entire supply chains and improve their operation, regardless of the complexity of the process [66].

Although the presented considerations do not exhaust the entire topic, they were intended to draw attention to the modelling and optimization of production processes in a real production environment as part of the idea of Industry 4.0 [67]. Undoubtedly, increasing efficiency and reducing production costs are serious challenges that cannot be successfully achieved without breakthrough changes in production paradigms and the underlying technologies and applications. According to the authors, appropriate tools, such as those discussed in this article, have the potential to play a significant role in this process of evolution from Industry 4.0 to Industry 5.0 [68,69] in key areas such as simulation, system integration, autonomous systems, cloud computing, augmented reality, big data and data analysis [70].