The Influence of the Assembly Line Configuration and Reliability Parameter Symmetry on the Key Performance Indicators

Abstract

In the context of the demand for mass customization of products, a trade-off between highly efficient automated systems and flexible manual operators is sought. The linear arrangement of workstations made it possible to divide the process into many simple operations, which increases production efficiency, but also results in an increase in the number of workstations and a significant extension of the line. A human operator is usually treated as a quasi-mechanical object, and a human error is considered, similarly, as a failure of a technical component. However, human behavior is more complex and difficult to predict. A mathematical model of a new production organization is presented, including dividing the traditional production line into shorter sections or replacing the serial assembly line with a U-line with cells. Moreover, the reliability of operator and technical means are distinguished. Work-in-progress inventories are located between line sections to improve system stability. The stability of the assembly line is examined based on the system configuration and probabilistic estimates of human failure. The influence of the symmetry of reliability parameters of people on key performance indicators (KPI (headcount), KPI (surface) and KPI (Overall Equipment Effectiveness) is examined. KPI (solution robustness) and KPI (quality robustness) are also presented in order to evaluate the impact of a disruption on the assembly line performance. New rules for assigning tasks to stations are proposed, taking into account the risk of disruptions in the execution of tasks. For comparison of assembly problems, heuristic methods with newly developed criteria are used. The results show the impact of symmetry/asymmetry on assembly line performance and an asymmetric distribution of manual assembly times that is significantly skewed to the right due to human errors. On the assembly line, the effects of these errors are cumulative and lead to longer assembly times and lower KPIs.

1. Introduction

In the era of rapidly changing customer requirements and short product life cycles, companies are looking for new solutions related to the organization of production. Additionally, the global economic crisis and the breakdown of the supply chain forced many manufacturers to temporarily limit or even suspend production processes. In the context of demand for mass customization of products, assembly line owners are looking for a compromise between highly efficient automated systems and flexible manual operators [1]. The linear arrangement of workstations made it possible to divide the process into many simple operations, which increased production efficiency, but also resulted in an increase in the number of workstations and a significant extension of the line. This highlighted the problem of failure and restarting long production lines after a planned stop or failure.

There are various types of production lines in industry. Their main feature is the serial arrangement of stations in one line, which facilitates the transport of semi-finished products to subsequent stations. The classification of production lines includes [2] continuous and discrete technological lines.

The first assembly line was launched at the Ford plant in 1913 and enabled the mass production of cars [3], which is now considered the beginning of the Second Industrial Revolution. Another classification of assembly balancing problems is proposed by [4]. The classification of assembly line balancing problems includes a number of variants and methods that focus mainly on the case of a single serial line (Single Assembly Line Balancing Problem). General Assembly Line Balancing Problems (GALBP) include Mixed-model assembly line balancing problems (MALBP), U-line balancing problems (UALBP), and other specific types of problems. In the case of other type lines, the effect of symmetry/asymmetry of the inflection point, which is most often in the middle of the line (U-line), is also exhibited, but this is not a necessary condition, e.g., L-type lines. In the case of long assembly lines, there may appear more inflection points (turns), which leads to S-type lines [5].

The U-shaped line arrangement has several advantages over the traditional configuration. Articles [6] present the problem of balancing a U-shaped assembly line. This problem is more complex than the problem of balancing a straight assembly line because tasks can be assigned by moving forward, backward, or in both directions simultaneously in a precedence diagram. The U-line configuration often improves line efficiency compared to traditional lines but creates further complications. The problem of balancing a U-shaped assembly line under uncertainty is rarely studied [7].

The concept of startup generally refers to the period of time from turning on the machine to achieving full functionality. In the case of production lines, one can distinguish [8] start-up regarding the first launch, which requires appropriate technical and organizational preparation of production, setting and calibration of machines, training employees, and checking a trial series of products. Restarting the line after a short stop usually does not pose any problems and does not require emptying the line. However, start-up after a changeover or a longer production break involves emptying and refilling the stations on the line and checking the trial series, which extends the downtime and reduces production efficiency. Thorough maintenance or modernization of production lines, involving the renovation of machines and equipment and the rearmament of stations for the production of a new product, is usually carried out during the holiday season and planned to ensure efficient operation of the line for as long as possible. However, machine failures and human errors, as well as changes in demand or delivery delays, can cause lines to stop more frequently [9].

The objective of the paper is to identify the gaps between the requirements of real configuration problems in assembly lines and state of the art. Practical Assembly Line Balancing (ALB) problems relate to workforce skill and quantity, as well as to production efficiency and stability, space, and cost. The objective is to examine the stability of the assembly line based on the system configuration and probabilistic estimates of component failure. The influence of the symmetry of reliability parameters of machines and system configurations on the adopted average values of key performance indicators is examined.

1.1. Literature Review

In the literature, lines in the stable operation phase are most often analyzed [10]. However, the changeover and start-up phase is often omitted; therefore, the problem of starting an assembly line and the impact of human and machine errors on changes in the pace of work and the stability of the production process are taken into account in the following examples.

According to the Industry 4.0 concept, assembly processes are increasingly performed by machines and robots; however, there are industries and specific products in which manual assembly are widely used [10]. The manual assembly process is associated with a difficulty of assembly [1] and the occurrence of human errors, which cause disruptions in the production process, decrease work efficiency and contribute to quality deficiencies and accidents related to temporary inability to work. Swain and Guttmann [11] define human errors as any element of a set of human actions that exceed a certain limit of acceptability, i.e., operating out of tolerance, where the limits of tolerable performance are defined by the system. Common defects associated with errors in manual assembly processes include loose connections, missing components, installation of incorrect components, improper application of force to fasteners, damage during assembly, and foreign object contamination [12].

Despite academic effort in assembly line balancing, there is a gap between the requirements of real configuration problems and the state of the art [2]. These discrepancies result, among others, from the adoption of certain assumptions and simplifications that facilitate the theoretical description of a given balancing method, but often omit certain technical aspects and human factors [13]. These include assigning an operator to one workplace in accordance with qualifications and assuming constant human performance during work (the so-called mechanistic model of human work). Industrial practice shows that people’s behavior at work is subject to many variable factors (human factors) and is often burdened with errors (human errors—slips, lapses and mistakes), which can disrupt the production process [14]. While, when two or more tasks (stations) are assigned to the same operator, the walking time between the locations has to be considered when estimating the cycle time [6].

Human Reliability Analysis (HRA) covers a very broad range of topics and is a combination of reliability engineering and human factors research to predict and mitigate errors to ensure safety, reliability and performance [15]. The main goal of HRA is to identify sources of human error and quantify the probability of such errors occurring. Many techniques have been proposed in the literature that arise from the need to quantify human error in dedicated areas such as aerospace, nuclear industry, offshore oil extraction and chemical processing, all of which are safety critical. Reliability engineering tries to predict the overall reliability of a system based on the system configuration and probabilistic estimates of component failure, where the human is usually considered as a quasi-mechanical object and human error is considered the failure of a technical component, but human behavior is individualistic and is difficult to forecast [14].

According to [16], many risk factors during manual assembly processes have to be taken into account. The risk of employee absence, caused by unplanned absence resulting from sick leave and on-demand leave. Risk of employee turnover, caused by the departure of experienced employees and the recruitment of new employees requiring training. Risk of quality errors caused by inexperience of employees. In most cases, it is possible to repair defective products at separate stations, which does not significantly affect the production process. There is also a risk of hidden defects that may only become apparent when the product is used at the customer’s site. Risk of downtime on the production line caused by machine failures, delays in material deliveries, and accidents at work. It is believed that human errors cannot be completely eliminated because they are a natural consequence of human variability [17]. Therefore, during manual assembly, inspection of the final product is required to ensure it is free from defects before it is shipped to the customer. Employees should not send the semi-finished product to the next station if a defect has been noticed. Significant losses in the production process also include startup rejections [18]. These are defective parts produced from start-up until stable production is achieved. They may occur after each start-up of the equipment, but most often during the first start-up and after retooling. Examples include suboptimal changeovers, equipment that requires “warm-up” cycles, or equipment that inherently produces waste upon startup.

A significant gap between the requirements of real configuration problems and the state of the art is that operators can move along the line as well as across it. Kuo et al. [19] noted that operator cycle time should include assembly time and transition time between assembly tasks. Operators can move between stations at normal walking speed or at the same speed as the conveyor along the line, as well as across it. Kuo et al. [20] presents a case study of a bicycle assembly company that developed a mixed integer nonlinear programming model to minimize the total manpower required and the number of job transfers by optimizing cell loading and product sequencing. According to the experimental results, the computation time increases dramatically when the number of products is seven or more. In the case of a cellular organization, all operators must have high qualifications due to the greater scope of tasks performed. However, in the case of a serial assembly line, most operators perform relatively simple tasks that do not require high qualifications, which simplifies the problem of assigning employees to tasks. Koltai et al. [21] provides an example of balancing the bicycle assembly process with labor skills and changes in production volumes. The skills of the workforce have been distinguished into two classes—high skilled (HW) and low skilled workers (LW). The impact of the availability of various employees on the length and capacity of the line was examined. The ALB models presented are deterministic; therefore, they do not account for the variance in task times.

Another paper [22] studies a semi-automatic automotive engine assembly line in which the traditional strategy of using stationary workers in each manual assembly section was replaced by a new strategy of using walking workers. With this approach, both the worker and the engine move simultaneously along the line; each employee is trained in advance to independently perform a series of assembly tasks from start to finish in each manual assembly section. The study showed significant improvement in overall system performance in terms of flexibility, efficiency, responsiveness and reconfigurability using dynamic, flexible and skilled walking workers. Nevertheless, the main problem with this design is that each employee must undergo cross-training to acquire a satisfactory level of skills related to the assignment of assembly tasks. The learning curve describing the total assembly time when a unit of the same type is repeatedly manufactured by a walking worker from the beginning to the end of the line is shortened until a stable state is reached.

Machine failures and human errors make the assembly process unstable. The main problems include failure rate, as the failure of one element can bring the entire assembly line to a standstill. The stability of line operation can be improved to some extent by ensuring adequate stocks of work in progress (WIP—Work in Process) [23]. Another way to improve stability is using a time buffer [24,25]. The time buffer sets the input rate, while the WIP ahead of the bottleneck changes according to stochastic characteristics. The input rate must be periodically updated to accommodate the rate dictated by the bottleneck to prevent infinite WIP. The throughput of the assembly system is maximized by adjusting the time between order arrivals and the size of the WIP buffer of the bottleneck in [26]. A strategy of shutting down the bottleneck and slowing down the operation of non-critical machines to balance the production system is proposed in [27]. Proposed one-piece flow with no WIP buffers reduces costs, saves energy and eliminates waste, but is not robust to disruptions. Three types of buffers are proposed to improve stability: capacity, time and stock buffers [27]. A time buffer is the introduction of a time window into the production plan to protect further production from a downtime caused by a bottleneck disruption. A buffer of constraints (WIP) includes an optimal number of intermediate products (buffer capacity) waiting in front of the bottleneck and protects them from idleness. A time buffer is recommended if a bottleneck disruption is expected.

According to [28], adding a time buffer is a better solution than inventory buffers, as they are not tied to specific parts. In [29], two buffers are proposed between the raw material release stage and the first bottleneck. The time buffer is computed as the sum of the processing and setup times from the first machine to the constraint. Authors [27] propose three types of buffers: constraint, assembly and dispatch buffers to the production system. The assembly buffer is dedicated for the bottleneck with no limited capacity, which is rather theoretical. At the end of the production line, the shipping buffer ensures timely delivery.

Despite academic effort in assembly line balancing, there is a gap between the requirements of real configuration problems and the state of research also in terms of efficiency measurements. To facilitate communication between researchers and practitioners, we provide key performance indicators (KPIs) used in industrial practice [30]. Key performance indicators (KPIs) allow researchers to look at the optimization problem not only from the point of view of line efficiency parameters, but also take into account organizational and financial aspects [31]. KPIs are measures of the effectiveness of activities within a given part of the assembly process or its entirety. Every square meter of the company’s space should generate profit. According to Lean Management, unnecessary warehouse and production space is a waste. Square meters of production or warehouse space are cost carriers in the Activity Based Costing method, which allows for the estimation of unit variable costs of a product. Presented KPI (surface) refers to the number of square meters occupied by the process. KPI (headcount) evaluates the number of employees required for a given part of an assembly process.

Takt time or cycle time of each workstation is a popular indicator used to evaluate the assembly process [19], while Overall Equipment Effectiveness (OEE) [32], solution robustness (SR), and quality robustness (QR) are proposed to evaluate the influence of instability of operation process due to failures or mistakes.

In summary, research challenges have been identified that could contribute to bridging this gap, particularly the speed and time of an operator’s transition between stations is usually overlooked.

Aspects such as randomly variable time of performing tasks by operators, availability and interchangeability of operators when performing tasks, and human errors affecting the quality of products are also omitted in the related literature. Practical ALB problems relate to workforce skill, quantity as well as to production quality, stability, space, and cost.

1.2. Problem Formulation

Adaptation to changes forces enterprises to introduce new approaches to the organization of production. An example is the electronics industry in Japan, which in the 1990s began to introduce a new organization of production, consisting, among others, of dividing the traditional production line into shorter sections or replacing the line with cellular production, e.g., Seru Seisan [20,33].

It is necessary to evaluate the stability of the assembly system of a new organization by dividing the line into shorter sections and aiding with time buffers or WIP buffers. A trade-off is sought between highly efficient automated systems and flexible manual operators.

The highlight of this paper is listed as follows:

• The problem of balancing a single-product assembly line using new rules for assigning operators to stations, taking into account the risk of task disruptions is considered.
• A search for a trade-off between high-performance automated systems and flexible manual operators through the possibility of automating assembly operations and freeing the employee from the machine or station.
• A human is usually treated as a quasi-mechanical object and human error as a failure of a technical component, but human behavior goes beyond this area and is difficult to predict. Influence of machine failure and human errors are included in the evaluation of the stability of the assembly system. The question is how to describe an operation performed in a bottleneck with manual assembly and possible human errors.
• New KPIs are presented for stability: KPI (OEE), KPI (SR) and KPI (QR). New KPIs are presented for efficiency: KPI (surface) and KPI (headcount).
• The objective is to minimize the number of assembly stations for given assembly operation times and predefined cycle time under human errors. Another objective is to maximize the assembly line efficiency and stability.
• A robust assembly line configuration is searched for by assigning highly skilled workers to a cell separate from the U-shaped line and locating work-in-progress inventories between sections of the line with a high risk of error or failure.

In the second section, a method of reorganizing the assembly line is presented and KPIs are determined. Examples of symmetrical or asymmetrical U-line configurations are presented in Section 3. In the Section, human errors are analyzed during workshops organized for students of Production Engineering for the process of manual assembly of a car model. The results of the experiments indicate that the times of operations executed in the bottleneck should be described by a distribution characterized by skewness and a significant shift to the right. During experiments, the stability of the assembly line is examined based on the system configuration and stochastic parameters, and the results are presented in Section 3.1, Section 3.2 and Section 3.3. In Section 4, the influence of the symmetry of reliability parameters of people on the adopted average values of KPIs is discussed. Final conclusions and plans for further research are presented at the end of the paper.

2. Method of Allocating Human Resources under Conditions of Disruption

The problem of starting a bicycle assembly line is analyzed. The bicycle assembly process involves manual machine operations. One type of product is produced in a given period of time, which involves cyclical changeover, start-up and emptying of the line.

The line start-up time is defined as the period of time from introducing the first semi-finished product to the first station on the line until obtaining the first finished product of good quality. For a balanced line consisting of m workstations and working with a constant takt time t_k and a trial batch, e.g., pieces, with the time to complete and check one-piece t_p, the start-up time T_r is as follows:

$${\mathrm{T}}_{\mathrm{r}}=\mathrm{m}{(\mathrm{t}}_{\mathrm{p}}{\mathrm{n}}_{\mathrm{p}}+{\mathrm{t}}_{\mathrm{k}}1),$$

(1)

A trial series consists of at least one piece, but the time (cycle) of making and checking the first piece t_p is much longer than the standard takt time t_p > t_k.

Increasing the line length usually involves shortening the work cycle, but overall, it increases the line start-up time, which may reach many minutes or hours. The efficiency of the assembly line E is measured by the following relationship:

$$\mathrm{E}={\displaystyle \frac{{\sum }_{\mathrm{i}-1}^{\mathrm{m}}{\mathrm{t}}_{\mathrm{i}}}{\mathrm{m}{\mathrm{T}}_{\mathrm{f}}}}100\mathrm{\%},$$

(2)

where t_i—actual working time of station i, T_f—planned working time including full working shifts, and m—number of assembly stations.

The size of the production batch has a significant impact on the efficiency of the line. Production of small batches is characterized by low efficiency. To achieve high efficiency, a large batch size is required.

KPIs are measures of the effectiveness of activities within a given part of the assembly process or its entirety. Takt time t_k is the first KPI indicator used to evaluate the assembly process:

$$\mathrm{K}\mathrm{P}\mathrm{I}\left(\mathrm{t}\mathrm{a}\mathrm{k}\mathrm{t} \mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e} {\mathrm{t}}_{\mathrm{k}}\right)={\displaystyle \frac{{\mathrm{F}}_{\mathrm{d}}}{{\mathrm{P}}_{\mathrm{d}\mathrm{z}\mathrm{*}}}},$$

(3)

where, P_dz* is number of units produced per shift, and F_d is available working time per shift.

KPI (surface) refers to the number of square meters occupied by the assembly process. It allows for the assessment of the actual use of available space in the company by a given assembly process:

$$\mathrm{K}\mathrm{P}\mathrm{I}\left(\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}\right)={\displaystyle \frac{\mathrm{S}}{\mathrm{X}·{\mathrm{F}}_{\mathrm{d}}·\mathrm{Z}·\mathrm{B}}},$$

(4)

where, X—assumed number of products produced per hour, Z—number of shifts per day, B—number of working days per year, and S—sum of square meters of area used in the process.

The introduction of Work in Process (WIP) buffers consumes additional company space that could be used by another process. The aim of this indicator is to reduce the area used in all production and intermediate processes as much as possible. Each square meter is included in the cost of the plant, which, if not used profitably, is a loss. If there is space in the plant that is not being used in a way that brings financial benefit through the use of value-adding operations in the process, it can be used as profit. For example, by renting it to an external company for their needs, e.g., storage.

Many tasks related to internal logistics or assembly process are not fully automated; human resources are needed; thus, headcount is another one of the three main performance indicators. Headcount means a number of employees required for the completion of a given part of the process. The goal of each department is to design processes so that a number of employees in each part is as small as possible. This reduces costs, but also minimizes the risk of an accident.

$$\mathrm{K}\mathrm{P}\mathrm{I}\left(\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{c}\mathrm{o}\mathrm{u}\mathrm{n}\mathrm{t}\right)={\displaystyle \frac{\mathrm{A}\mathrm{c}\mathrm{t}}{\mathrm{P}\mathrm{e}\mathrm{r}}},$$

(5)

$$\mathrm{A}\mathrm{c}\mathrm{t}=\mathrm{R}·{\mathrm{F}}_{\mathrm{d}}·\mathrm{P}\mathrm{h}$$

(6)

where, Activity Act is the number of parts needed to be processed per shift, performance and, Per is the predefined number of parts that the operator can collect per hour. This number is related to ergonomics and occupational safety requirements. Act is computed by multiplying the number of parts (joints) installed in a product (R), and the number of products assembled per hour (Ph).

Overall Equipment Effectiveness (OEE) is used to evaluate stability of the assembly process. OEE is an indicator that integrates three key aspects of tool and machine performance—availability A, productivity P and quality Q:

$$\mathrm{KPI}\left(\mathrm{OEE}\right)=\mathrm{A}·\mathrm{P}·\mathrm{Q},$$

(7)

$$\mathrm{A}={\displaystyle \frac{\mathrm{r}\mathrm{F}\mathrm{d}}{\mathrm{F}\mathrm{d}}},$$

(8)

$$\mathrm{P}={\displaystyle \frac{\mathrm{r}\mathrm{E}}{\mathrm{E}}},$$

(9)

$$\mathrm{Q}={\displaystyle \frac{\mathrm{r}\mathrm{P}\mathrm{d}\mathrm{z}}{\mathrm{P}\mathrm{d}\mathrm{z}}},$$

(10)

where, rF_d—actual working time, F_d—planned working time, rE—actual efficiency, E—maximum efficiency (theoretical), rP_dz—product compliant with the standard, and P_dz—total quantity of finished products. The higher the value of the OEE, the more stable the assembly system is.

Stability of the assembly process is evaluated by comparing takt time of the assembly line, and the theoretical and actual cycle times of each assembly station. The stability criterion presented below assumes that transport between assembly stations is performed manually and the assembly stations are located in a line within a short distance. The greater the stability of the assembly line, the lower the value of solution robustness (SR). The assembly line consists of a number of stations, i = 1, 2, …, m, and a number of assembled products per shift, j = 1, 2, …, n. To assess the stability index, only disturbances resulting in a violation of takt tk_i are taken into account (Figure 1). Cycle time of each station, C_ij, is determined based on the bottleneck cycle time. An assembly operation performed faster than cycle time is an apparent advantage.

$$\begin{gathered} \mathrm{K}\mathrm{P}\mathrm{I}\left(\mathrm{S}\mathrm{R}\right)=\sum _{\mathrm{i}=1}^{\mathrm{m}}\sum _{\mathrm{j}=1}^{\mathrm{n}}\mathrm{T}\mathrm{T}{\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{i},\mathrm{j}} \\ {\mathrm{T}\mathrm{T}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{i},\mathrm{j}}=\left\{\begin{array}{c}0,\mathrm{if}{\mathrm{C}}_{\mathrm{i},\mathrm{j}}+{\mathrm{M}\mathrm{C}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{i},\mathrm{j}}\le {\mathrm{t}\mathrm{k}}_{\mathrm{i}}\\ \left({\mathrm{C}}_{\mathrm{i},\mathrm{j}}+{\mathrm{M}\mathrm{C}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{i},\mathrm{j}}\right)-{\mathrm{t}\mathrm{k}}_{\mathrm{i}},\mathrm{if}{\mathrm{C}}_{\mathrm{i},\mathrm{j}}+{\mathrm{M}\mathrm{C}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{i},\mathrm{j}}>{\mathrm{t}\mathrm{k}}_{\mathrm{i}}\end{array}\right. \end{gathered}$$

(11)

where, ${\mathrm{T}\mathrm{T}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{i},\mathrm{j}}$—takt time delay in assembling product j at station i, ${\mathrm{M}\mathrm{C}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{i},\mathrm{j}}$—i-th station cycle delay when assembling model (product) j, and ${\mathrm{C}}_{\mathrm{i},\mathrm{j}}$—theoretical cycle time of station i when assembling product j.

$${\mathrm{M}\mathrm{C}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{i},\mathrm{j}}=\left({\mathrm{s}\mathrm{C}}_{\mathrm{i},\mathrm{j}}^{\mathrm{*}}{+\mathrm{C}}_{\mathrm{i},\mathrm{j}}^{\mathrm{*}}\right)-\left({\mathrm{e}\mathrm{C}}_{\mathrm{i},\mathrm{j}-1}+{\mathrm{C}}_{\mathrm{i},\mathrm{j}}\right),$$

(12)

where ${\mathrm{s}\mathrm{C}}_{\mathrm{i},\mathrm{j}-1}^{\mathrm{*}}=\mathrm{m}\mathrm{a}\mathrm{x}\left\{\begin{array}{c}{\mathrm{e}\mathrm{C}}_{\mathrm{i},\mathrm{j}-1}^{\mathrm{*}}\\ {\mathrm{e}\mathrm{C}}_{\mathrm{i}-1,\mathrm{j}}^{\mathrm{*}}\end{array}\right.$. And ${\mathrm{s}\mathrm{C}}_{\mathrm{i},\mathrm{j}}^{\mathrm{*}}$ is the real start time of cycle time of product j at station i, and ${\mathrm{e}\mathrm{C}}_{\mathrm{i},\mathrm{j}}^{\mathrm{*}}$ is the real end time of cycle time of product j at station i.

$$\mathrm{K}\mathrm{P}\mathrm{I}\left(\mathrm{Q}\mathrm{R}\right)=\left|\sum _{\mathrm{j}=1}^{\mathrm{n}}\left(\mathrm{e}{\mathrm{t}\mathrm{k}}_{\mathrm{m},\mathrm{j}}-\left(\mathrm{e}{\mathrm{t}\mathrm{k}}_{\mathrm{m},\mathrm{j}}+\mathrm{T}\mathrm{T}{\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{m},\mathrm{j}}\right)\right)\right|$$

(13)

${\mathrm{e}\mathrm{t}\mathrm{k}}_{\mathrm{m},\mathrm{j}}$ is the real end time of takt time of station m when assembling product j.

For the numerical example, we assume that the assembly line consists of two stations, m = 2, and three products are assembled, n = 3 (Figure 1). The cycle time of assembly stations, C_i,j, is 15 min, and takt time of the assembly line is 20 min. The second operation of the second product j = 2 was disrupted and cycle time C_1,2 was equal to 25 min (Figure 1b). The question is, what are solution robustness and quality robustness indicators? First, the effect of the disturbance on each machine cycle is measured using MCdelay_i,j for each product. Next, the effect of the disturbance on takt time is measured using TTdelay_i,j:

$$\begin{gathered} {\mathrm{M}\mathrm{C}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{1,1}}=\left(0+15\right)-\left(0+15\right)=0,{\mathrm{T}\mathrm{T}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{1,1}}=15+0\le 20\to 0, \\ {\mathrm{M}\mathrm{C}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{1,2}}=\left(15+25\right)-\left(15+15\right)=10,{\mathrm{T}\mathrm{T}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{1,2}}=15+10\ge 20\to 25-20=5, \\ {\mathrm{M}\mathrm{C}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{1,3}}=\left(40+15\right)-\left(30+15\right)=10,{\mathrm{T}\mathrm{T}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{1,3}}=15+10\ge 20\to 25-20=5, \\ {\mathrm{M}\mathrm{C}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{2,1}}=\left(20+15\right)-\left(20+15\right)=0,{\mathrm{T}\mathrm{T}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{2,1}}=15+0\le 20\to 0, \\ {\mathrm{M}\mathrm{C}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{2,2}}=\left(40+15\right)-\left(35+15\right)=5,{\mathrm{T}\mathrm{T}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{2,2}}=15+5\le 20\to 0, \\ {\mathrm{M}\mathrm{C}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{2,3}}=\left(55+15\right)-\left(50+15\right)=5.{\mathrm{T}\mathrm{T}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{2,3}}=15+5\le 20\to 0, \end{gathered}$$

Finally, solution robustness is $\mathrm{K}\mathrm{P}\mathrm{I}\left(\mathrm{S}\mathrm{R}\right)=5+5=10.$ Quality robustness is computed only for the final station for each product, ${\mathrm{q}}_{\mathrm{m},\mathrm{j}}=\mathrm{e}{\mathrm{t}\mathrm{k}}_{\mathrm{m},\mathrm{j}}-\left(\mathrm{e}{\mathrm{t}\mathrm{k}}_{\mathrm{m},\mathrm{j}}+\mathrm{T}\mathrm{T}{\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}}_{\mathrm{m},\mathrm{j}}\right)$:

$${\mathrm{q}}_{\mathrm{2,1}}=40-\left(40+0\right)=0,{\mathrm{q}}_{\mathrm{2,2}}=40-\left(40+0\right)=0,{\mathrm{q}}_{\mathrm{2,3}}=40-\left(40+0\right)=0$$

$\mathrm{K}\mathrm{P}\mathrm{I}\left(\mathrm{Q}\mathrm{R}\right)=0$ means that the disturbance has no effect on on-time assembly. Tasks and workers are allocated to workstations in order to minimize KPIs: SR, QR, headcount, surface and maximize OEE.

Organizational solutions are proposed to improve indicators. Employees are assigned to assembly stations according to the line reorganization algorithm:

• Carrying out the initial balancing of the assembly line using the selected method.
• Symmetrical or asymmetrical U-shaped organization of stations.
• Selection of station s to be eliminated (usually the first, last or least loaded machine) or designated for joint service.
• Selection of p subsequent workload-relieving stations, r = i + 1, i + 2, …, i + p, for i = 1, …, m − p, $\mathrm{r}\ne \mathrm{s}$, located on the opposite side to the station being eliminated (symmetrically, so that the distance covered by employees is as short as possible). The selected stations may be located before or after the bottleneck.
• Performing various combinations of workload relief and workload addition at selected stations under the condition that $\mathrm{r}\ne \mathrm{s}$ and $\mathrm{r}\ne \mathrm{b}\mathrm{o}\mathrm{t}\mathrm{t}\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{k}$.

  5.1

  Offloading p selected stations—Shifting back the first/initial operations of a given station to the previous station. Operation shifts are performed within the line takt limits using the backward offloading rule, maintaining the required ordering relations (described by a graph or matrix). Moving forward the last operation(s) of a given station to the next station.

  5.2

  Adding workload to p selected stations—Division of tasks from station s into p sub-tasks so that the sum of the workload of station r and subtask p does not exceed the takt time. Adding workload to selected stations with subtasks and eliminating station s. Employees handling additional operations can move between stations.

• Division of the line into cells depending on the organization of employee work (one-way flow, two-way flow). Introduction of WIP buffer or buffer time between cells and after the bottleneck.

Let us analyze the example of a bicycle assembly line and the allocation of tasks to assembly stations obtained using the SALAP-1 method [21] (Figure 2a). The line pre-balanced using the SALAP-1 method is organized in a U-shape (Figure 2b). The first station is eliminated, s = 1. Three (p = 3) end stations are selected in order to release the load r = 8, 9, 10. Operations 26 and 27 are moved back, from station 8 to 7. The cycle time of station 7 is 90s. Division of tasks from station i = 1 into three subtasks: the first set is operations 1 and 2, the second set is operations 3 and 4, and the third set is operations 5 and 10. The condition is met that the sum of the workload of stations r = 8, 9, 10 and the set p = 1, 2, 3, respectively, do not exceed the takt time. Adding workload to selected stations with subtasks allowed for the elimination of the first station.

Employees serving more than one station are often more highly qualified, and the probability of making an error is increased. The more tasks there are in takt time, the more likely human error is. Moreover, working under stress (maximum workload) may also generate errors. Therefore, in the case of bottleneck management, it is recommended to use quality improvement solutions, such as poka-yoke or automation. Employee reliability can be described by an exponential distribution and employee performance can be modeled with lognormal distribution [29]. It is necessary to examine the impact of the proposed assembly line improvement and optimization methods on KPIs: SR, QR, headcount, surface, OEE and efficiency. It is necessary to check the correctness of the line reorganization assumptions; the FlexSim program is used for this purpose.

3. Numerical Example and Results

Tasks and precedence relations of the bicycle assembly process are presented in the matrix of constraints $\mathrm{M}\mathrm{P}={\mathrm{p}}_{\mathrm{j},\mathrm{k}}$ (

Table 1. The matrix of the relationships between joints of the bicycle.

pj,k	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
1
2	1
3		1
4		1
5		1
6		1
7			1
8				1
9
10
11					1
12									1	1	1
13
14												1
15													1
16														1
17	1
18		1
19								1								1
20							1		1		1
21				1	1							1			1		1
22						1	1										1	1	1
23																				1	1	1
24																							1
25																								1
26																									1
27																										1
28																											1
29																												1
30																													1
31																														1

). The MP matrix represents the relationships between the successive joints n_j and n_k. Value p_j,k = 1 means that joint n_j takes precedence over n_k.

Balanced assembly line flow with capacity of stations (red line—takt time, yellow line—minimum cycle time) with low-skilled workers dedicated to the stations (Figure 2a) is achieved using the SALAP-1 method. The method is compared to the reorganized line using the method presented in the previous section which assumes the possibility of using highly qualified workers who are able to serve a number of stations. Highly qualified workers are dedicated to the stations 8, 9 and 10 in the case study in the first variant presented in (Figure 2b). Operations assigned to stations according to the SALAP-1 and reorganization method are presented in

Table 2. Operation assigned to stations according to the SALAP-1 and reorganization method.

No Station	Salap-1	Workload of Station [s]	Reorganization 1	Workload of Station [s]
1	1, 2, 3, 4, 5, 10	90	-	-
2	6, 7, 9, 11, 17	88	6, 7, 9, 11, 17	88
3	13, 15, 20	65	13, 15, 20	65
4	12, 14, 18	84	12, 14, 18	84
5	8, 16, 19, 21	65	8, 16, 19, 21	65
6	22, 23, 24	75	22, 23, 24	75
7	25	70	25, 26, 27	90
8	26, 27, 28	55	1, 2, 28	79
9	29, 30	65	3, 4, 29, 30	85
10	31	50	5, 10, 31	76

.

Takt time is determined by the bottleneck—7th station (Figure 2b). Assembly stations operate in cycle times from 65 to 90 s. The total cycle time of the process is the sum of Σt_i = 707 s. The matrix of assembly operation times of the bicycle joints is presented in

Table 3. The matrix of assembly operation times of the bicycle joints.

Assembly Operation Times
No	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31
tj [s]	21	23	10	10	10	10	10	10	30	16	14	50	10	10	20	20	24	24	10	35	25	10	15	50	70	10	10	35	15	50	50

.

The objective is to compare two variants (Figure 2a,b) of the bicycle assembly line in order to achieve better value of selected KPIs: SR, QR, headcount, surface, OEE and efficiency. The objective is to build a robust assembly line. In the presented model, the reliability of the operator and the technical means is distinguished. WIP inventories or time buffers are located between line sections (cells) to improve system stability. The stability of the assembly line is examined based on system configuration and probabilistic estimates of component failure. The influence of the symmetry of reliability parameters of machines and employees on the adopted average values of KPIs is examined.

The planned production volume results from the daily demand of Pdz’s customer for products, which is 300 pieces per shift. The required (theoretical) takt time results from the available working time fund (F_d) for a shift of 8 h each with a break of 30 min:

$${\mathrm{t}}_{\mathrm{k}}\le {\displaystyle \frac{{\mathrm{F}}_{\mathrm{d}}}{{\mathrm{P}}_{\mathrm{d}\mathrm{z}}}}={\displaystyle \frac{\left(8-0.5\right)}{300}}=1.5\min ,$$

(14)

The average operating time t_k is assumed to be 1.5 min and start-up time is 15 min. Therefore, in the first shift, only 290 pieces can be achieved, as the system starts from an empty state. In the second shift, the full productivity of 300 pieces can be achieved.

The efficiency is related to the number of operators and workstations and is approximately 73.6% for 10 workstations and 81.8% for 9 workstations.

$$\mathrm{E}={\displaystyle \frac{300\times 707}{10\times 28800}}\times 100\mathrm{\%}=73.64\mathrm{\%},$$

(15)

average operating time t_k is assumed to be 1.5 min and start-up time is 15 min. Therefore, in the first shift, only 290 pieces are assembled, achieving an efficiency of approximately 80%.

$$\mathrm{E}={\displaystyle \frac{300\times 707}{9\times 28800}}\times 100\%=81.83\%,$$

(16)

However, in practice, a high variability of operators’ work is observed, and the measured work cycle is often much longer than the assumed average value due to various human errors causing a loss of work pace at various positions.

3.1. Impact of Reduced Number of Stations on KPI

In order to verify the developed algorithm, two variants of the bicycle assembly line (Figure 2a,b) are modelled in FlexSim (Figure 3a,b) for data from Table 2. In the U line, three cells with walking operators were created in order to balance the beginning and ending operations.

FlexSim 2023 provides software to model, simulate, analyze, and 3D visualize any system in manufacturing, material handling, and warehousing, using Discrete Event Simulation (DES) method [34]. It uses predefined objects for many production resources, as well as a parametric human operator model that can be arranged to simulate a real process.

Initially, we assume that operators are assigned to one workstation and do not have to move, because they have all components and tools within their immediate reach (Golden Zone) [35]. One work shift lasts 8 h and includes a 30 min rest break for employees. The transport between stations is carried out using a conveyor that moves products at a speed of 1 m/s. In this case breakdowns and quality losses were omitted.

The subject of the work is a cuboid with the dimensions of a bicycle. The occupied area (the visualization excludes component warehouses at the terminals, but the area for them is included) equals 26 × 5 = 130 m² for the first variant SALAP-1 and 15 × 8 = 120 m² after reorganization (second U-line variant). A total of 288 pieces per shift were obtained for both variants after the first shift (when starting from the empty state), and 296 pieces after the second shift with stable system conditions. The results are the same due to the takt times being the same. In the second variant, the bottleneck is moved from station 1 to station 7; therefore, a queue is created in the buffer (Queue20). In the first variant, the bottleneck is at the entrance to the system.

A summary of simulation results for the startup of an empty system after the first shift is showed in (Figure 4a). For the 2nd shift, the model without operators (LineB0) runs in a stable way and the production can be increased by nine pieces. However, after adding walking operators (LineB1), a decrease in the average workload of stations and employees (Figure 4b) is observed and the obtained production is lowered to 211 pieces only. This problem is caused by the walking time and the reserve of time being too small. Especially walking operator 36A which is overloaded; therefore, a bottleneck is created at the beginning of the line.

Changing from a serial line to a U-line allows for a more even balance of operations and reduces the number of stations and employees by one, which increases work efficiency. In order to evaluate the results, the OEE metric can be used.

Availability is reduced by a rest break of 30 min per 8 h.

$$\mathrm{A}={\displaystyle \frac{\mathrm{r}\mathrm{F}\mathrm{d}}{\mathrm{F}\mathrm{d}}}={\displaystyle \frac{8-0.5}{8}}=0.9375$$

(17)

Performance is reduced by a speed loss during transport; therefore, actual production of 296 pieces is smaller than the theoretical production of 300 products.

$$\mathrm{P}={\displaystyle \frac{\mathrm{r}\mathrm{E}}{\mathrm{E}}}={\displaystyle \frac{296}{300}}=0.9867$$

(18)

Quality is assumed as Q = 1. The resultant KPI (OEE) can be calculated from Equation (7)

$$\mathrm{KPI}\left(\mathrm{OEE}\right)=\mathrm{A}·\mathrm{P}·\mathrm{Q}=0.9375·0.9867·1=0.92503$$

(19)

As OEE-related constraints are taken into account in the model, the resulting production and utilization of stations (especially at the bottleneck) corresponds to the OEE indicator. Slight differences are a result of the rounding of the number of products to full pieces. The maximal production Pmax in ideal conditions is equal to 320 pieces; therefore,

$$\mathrm{KPI}\left(\mathrm{OEE}\right)={\displaystyle \frac{\mathrm{P}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}{\mathrm{P}\mathrm{m}\mathrm{a}\mathrm{x}}}={\displaystyle \frac{296}{320}}=0.925$$

(20)

However, the walking operators caused a loss of work speed in this case. The realistic OEE is much lower than expected.

$$\mathrm{KPI}\left(\mathrm{OEE}\right)={\displaystyle \frac{\mathrm{P}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}{\mathrm{P}\mathrm{m}\mathrm{a}\mathrm{x}}}={\displaystyle \frac{211}{320}}=0.659$$

(21)

Verification has shown that in such a case, the walking operators would be too overloaded, and this is not a recommended solution for ergonomic reasons.

3.2. Impact of Reduced Takt Time on KPI

In order to check the possibility of increasing the production volume, a second case study was analyzed that requires the reduction of the takt time and division of work into a larger number of workstations. The shortest takt time is equal to 70s, as this is a time of the indivisible activity nr 25. Data obtained after rebalancing is presented in

Table 4. Operation assigned after the reorganization method.

No Station	Reorganization 2	Workload of Station [s]
1	1, 2, 17	68
2	3, 4, 5, 6, 18	64
3	9, 13, 15	60
4	7, 8, 11, 20	69
5	10, 12	66
6	14	10
7	16, 19, 21, 22	65
8	23, 24	65
9	25	70
10	26, 27, 28, 29	70
11	30	50
12	31	50

.

The reorganized line has 12 workstations, including activity nr 14, which is unassignable to neighboring workstations. However, the last two operators are not fully loaded, and they can be changed into walking operators. The model of the modified line is presented in Figure 5.

The results of stable production after the second shift are presented in Figure 6. Variant A shows the state of the line with stationary operators and variant B shows the state using walking operators. In this case, the walking operators have enough time reserve to freely move between the workstations.

The maximal production (Pmax) in ideal conditions is equal to 411 pieces in this case; therefore,

$$\mathrm{KPI}\left(\mathrm{OEE}\right)={\displaystyle \frac{\mathrm{P}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}{\mathrm{P}\mathrm{m}\mathrm{a}\mathrm{x}}}={\displaystyle \frac{378}{411}}=0.9197$$

(22)

There was a slight decrease in OEE due to Waiting for Operators and a slight difference of the utilization of the bottleneck (92.04%) is due to rounding the OEE to full units.

This example shows the possibility of rebalancing the assembly line into a U-line, which gives more opportunities to reorganize the production. Simulation enables a verification of the solution obtained by the proposed method.

3.3. Impact of Stochastic Parameters on KPI

During production planning, fixed (determined) process times are usually used, which facilitates production planning and scheduling. This results from the adopted methods of working time standardization, such as Time Measurement Methods [36] or time study, where average values of the set working time are determined for normal working conditions. In practice, however, there is a great deal of variability in human behavior during assembly, which manifests itself in fluctuations in work pace, human errors causing process delays or product quality defects. There is also a high employee turnover, which means that new employees have low qualifications and gain experience only after some time [26].

Due to the considerable number of variable factors, modeling human performance is difficult and causes simulation results to often deviate from reality [37]. However, the use of stochastic parameters in manual processes significantly complicates the model and makes the analysis of results difficult [38].

In modeling, the human is treated as a quasi-mechanical object that should behave like a machine. In this case, human reliability can be described using reliability parameters used in machines, such as MTBF (mean time between failures) and MTTR (mean time to repair). We assume that a sick and absent employee can be replaced but the machine requires repair. The exponential distribution or Weibull distribution is most often used to describe machine reliability [38,39,40]. Taking into account typical human failures and errors [41], the short-term human failure rate during one shift can be described by the exponential distribution and the parameters MTBF = 8 h and MTTR = 5 min. [14].

Human errors have a major impact on product quality. The distribution of quality is most often described as a symmetric normal distribution with a standard deviation, since, according to the central limit theorem (CLT), the sum of many independent random variables converges to a normal distribution (unless systematic errors are present). Quality levels are described as the Sigma standard deviation from the mean, e.g., according to the Six Sigma method from −6 Sigma to +6 Sigma, which corresponds to about three defects per million [42]. For manual processes, a level of ±3 Sigma is assumed, which corresponds to approximately 99.73% of quality products and about three defects per thousand cases (Figure 7).

The assembly process time also varies significantly due to changes in the work pace of operators due to fatigue, errors and mistakes. There are three types of active human errors [9,41]: slips and lapses—made inadvertently by experienced operators during routine tasks; Mistakes—decisions subsequently found to be wrong, though the maker believed them to be correct at the time; and violations—deliberate deviations from rules for safe operation of equipment. In serial systems such as an assembly line, delays in executing bottleneck operations are cumulative and cannot be made up during normal working hours (or overtime).

To determine the impact of stochastic parameters on KPIs, let us analyze a case study of car model assembly. Workshops were organized for students of Production Engineering, during which the process of manual assembly of a car model was carried out (Figure 8). The model consists of 138 parts and requires some manual skills.

During the workshops, different configurations of the production system were analyzed from cellular production to the assembly line. The final assembly line consists of 12 assembly stations, as well as a buffers and an inspection station. After initial training of the students, the operation time was measured using the time study method. The average operation times are presented in

Table 5. Average processing times of assembly operations.

No	Operation	Processing Time [s]	Processing Time [min]
1	Assembly 1	110	01:50
2	Assembly 2	75	01:15
3	Assembly 3	67	01:07
4	Assembly 4	64	01:04
5	Assembly 5	67	01:07
6	Assembly 6	94	01:34
7	Assembly 7	97	01:37
8	Assembly 8	131	02:11
9	Assembly 9	110	01:50
10	Assembly 10	104	01:44
11	Assembly 11	74	01:14
12	Assembly 12	67	01:07
13	Inspection	90	01:30

. The summary of statistical parameters for operation 8 (bottleneck) is presented in

Table 6. Statistical characteristics of assembly operations no. 8.

No	Data Characteristic	Value
1	Number of observations	48
2	Minimum observation	120
3	Maximum observation	171
4	Mean	131.17
5	Median	126.5
6	Variance	163.63
7	Coefficient of variation	0.09752
8	Skewness	1.7891

.

The obtained distribution is characterized by skewness and a significant shift to the right. This phenomenon is due to the fact that a certain number of operations are affected by human errors causing longer assembly times (e.g., searching for a lost screw). In traditional timing, measurement values that are too far apart are discarded. In this case, an attempt is made to fit a statistical distribution to the data using the ExpertFit program. The results are presented in Figure 9.

The best fit was obtained for the lognormal distribution. The distribution parameters were then used in FlexSim to model the assembly process taking into account human errors. The developed S-shaped assembly line model is shown in Figure 10.

In the second version of the model, stochastic process parameters were used, including the variability of assembly times according to the lognormal distribution (location = 119.1, scale = 7.18, shape = 1.1), operator errors MTBFh = 8 h and MTTR = 5 min, and the quality distribution of 95% of good products (for low skill operators). The obtained simulation results are presented in Figure 11.

The model with random parameters is characterized by a significant scatter of results. The replication plot for the production of good quality products in a series of 30 replications is presented in Figure 12. The statistical summary of the obtained results is presented in

Table 7. Results of simulation experiments for model with stochastic parameters.

Performance	Mean (95% Confidence Interval) [Pieces]	Sample Std Dev	Min	Max
OK production	180.00 ± 1.36	3.65	172.00	189.00
NOK production	9.100 ± 0.997	2.670	4.00	15.00
Max WIP	6.933 ± 1.176	3.151	3.00	16.00

.

The maximal production Pmax in ideal conditions is equal to 219 pieces in this case; therefore, the theoretical OEE for a deterministic model is equal to the following:

$$\mathrm{KPI}\left(\mathrm{OEE}\right)={\displaystyle \frac{\mathrm{P}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}{\mathrm{P}\mathrm{m}\mathrm{a}\mathrm{x}}}={\displaystyle \frac{198}{219}}=0.9041$$

(23)

However, the more realistic value was obtained by the stochastic model as follows:

$$\mathrm{KPI}\left(\mathrm{OEE}\right)={\displaystyle \frac{\mathrm{P}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}{\mathrm{P}\mathrm{m}\mathrm{a}\mathrm{x}}}={\displaystyle \frac{180}{219}}=0.8219$$

(24)

There was a significant decrease in OEE compared to previous examples due to stochastic human factors. The model with stochastic parameters reflects the course of real assembly processes much better. The obtained results show the influence of variable human factors on the decrease in the efficiency of the assembly process and the increase in work in process (WIP) and explains why the actual production often deviates from the planned one. During the workshops, it was also not possible to achieve the planned production capacity of 27 pieces per hour due to human errors and delays as well as a significant number of quality defects. Therefore, employee training is necessary and only after some time do they gain more experience, which translates into increased assembly efficiency.

4. Discussion

The U-shaped arrangement of workstations enabled more efficient assignment of operations to workstations (

Table 8. Summary of the most important KPIs.

KPI	Salap-1	Symmetric U-Line	Asymmetric U-Line	Deterministic S-Line	Stochastic S-Line
OEE	0.925	0.925	0.9197	0.9041	0.8219
Surface [m2]	130	120	114	120	120
Headcount	10	9	11	13	13
Takt time [s]	90	90	70	131	150
Throughput [pieces/h]	40	40	51.4	27.5	24

). The OEE value is equal for linear organization and U-line reorganization due to the bottleneck workload, and the takt time is 90 s in both cases. Surface is reduced by 10 square meters, while Headcount by 1 employee. Surface and Headcount reduction means additional profits from renting out production space and delegating the worker to external clients or allocating the saved resources to other processes.

Taking into account the movement times of operators resulted in a loss of work speed in this case (Section 3.1 and Section 3.2, Table 8). OEE = 0.659 is unacceptable. The symmetric U-line and asymmetric U-line approaches that take into account employee movement, allow for achieving reliable KPI values. The asymmetric U-line shape with 11 workers and 11 stations allows for an acceptable OEE = 0.91. Although the number of employees is higher, the Surface is reduced to 114 square meters. The manager can decide whether the additional production space is available for rent as well as if the higher throughput compensates for the need to hire two additional workers. However, the variants presented above assumed constant times for assembly operations and did not take into account any possible disruptions.

When comparing KPIs for the deterministic and stochastic models, taking into account the variance of the bottleneck operation time due to human errors, a significant decrease in OEE from 0.9 to 0.82 was again observed (Section 3.3, Table 8). The model with stochastic parameters reflects the course of real assembly processes much better. The obtained results show the influence of variable human factors on the decrease in the efficiency of the assembly process and the increase in WIP.

Human errors were analyzed during workshops organized for students of Production Engineering for the process of manual assembly of a car model. The results of experiments indicate that the times of operations executed in the bottleneck should be described by a log-normal distribution characterized by skewness and a significant shift to the right.

Due to the large volume of the paper, a trade-off between high-performance automated systems and flexible manual operators will be presented in the future. In this paper, the benefits of freeing the employee from the machine or station were outlined. Future research directions include developing a reorganization algorithm using the selected artificial intelligence method and modeling a digital twin of an assembly line with human operators.

5. Conclusions

The objective of the paper was to identify gaps between the requirements of real configuration problems in assembly lines and state of the art. Practical ALB problems should take into account workforce skill and quantity as well as production efficiency and stability, space and cost. Assembly operator travel times as well as employee errors resulted in a loss of KPIs and need to be taken into account in the optimization process. This paper analyzes the system configuration in the symmetric, asymmetric U-line and S-line, as well as the variance of operation times performed in the bottleneck described by the lognormal distribution. The impact of employee reliability parameters and different system configurations on key performance indicators was investigated.

Despite the scientific trails linking science and practice, some shortcomings are noted, especially in the assembly line evaluation process. Practical assembly problems are usually more multi-criteria; however, most authors focus on single-criterion problems [44]. Authors developing models that address multiple performance objectives are more practical in today’s manufacturing environment. In [45], four objectives are taken into account to be minimized: cycle time, number of workstations, workload variance, and workstation idle time. However, when addressing management interests, the following key performance indicators should be considered: KPI (headcount), KPI (surface) and KPI (Overall Equipment Effectiveness). KPI (solution robustness) and KPI (quality robustness), developed in the paper can be used interchangeably with KPI (OEE) for evaluating the efficiency, performance and quality under disruption. Among the presented KPIs, only KPI (OEE) is known from the literature [32]. KPI (headcount), KPI (surface) and KPI (OEE) are practical indicators known in automotive industries. KPIs are used to evaluate solutions for improvement and optimization methods and are individually developed for the case of a factory, line, cell or station.