1 Introduction

Expert skills have been analyzed for operators controlling complex systems such as industrial plants and aircraft, aiming at automation and supporting skill development. Extensive studies have attempted to extract cognitive properties specific to expert operators, such as eye movement and motion analysis. For example, eye movement research has shown that expert operators have systematic monitoring strategies even in cognitively demanding situations. However, these approaches have some limitations in investigating expert skills in human–machine systems. As advocated in Industry 4.0, operators are required to work in complex systems with information and communication technologies (Gorecky et al. 2014). Due to these technological advancements, work systems have developed to have socio-technical aspects in which complex interactions with machinery and the surrounding environment play a critical role. It has been emphasized that in socio-technical systems, variabilities constantly occur in daily work as performance fluctuations of machines and human operators and external disturbances (Hollnagel 2012). Socio-technical systems continuously force operators to adapt to and cope with such variabilities to maintain the system’s resilience. Especially in the manufacturing domain, operators’ adaptive aspects can contribute to resilient production against market volatilities and flexible production plans (Johansen and Akay 2022). These adaptive skills of expert operators are challenging to investigate using conventional methods because they are acquired as tacit knowledge.

One of the essential aspects of the adaptive skills of operators to maintain resilient production is how they monitor the target system. According to Hollnagel (2012), resilient performance requires four fundamental competencies—monitoring, anticipating, responding, and learning. Specifically, the monitoring function, linked to non-technical skills like situation awareness, plays a crucial role in enhancing resilience (França et al. 2021). It is important for resilient performance to monitor the situation, identify the changes in the environment, and manage attention allocation even in cognitively demanding situations. With this background, many eye movement studies have shown that skilled operators can adapt their monitoring behavior and attention management strategy in difficult tasks (Tien et al. 2014; Shiferaw et al. 2019). However, although much can be learned from eye movement analysis, the full picture of the expert operator’s attention management strategy has yet to be captured. This is because expert operators acquire these skills as tacit knowledge, which requires an integrated analysis from multiple aspects. This paper pays particular attention to the operator’s attention management strategy in multitasking and takes a multi-perspective approach based on the concept of tacit knowledge. To this end, this study selected a case study that features multitasking, where characteristics of attention distribution are prominently displayed.

For this purpose, this study employs the integrated framework based on the functional structure of tacit knowledge. According to Polanyi (1966), tacit knowledge can be defined as the relationship between proximal and distal terms. Here, the proximal term is the immediate observable experience, while the distal term is the meaning or concept implied from that experience. In order to ensure the proximal perspective, this study analyses eye movements during multitasking. In order to determine what the operators are distally aware of, the operators are interviewed, and their responses are analyzed based on the work domain analysis (WDA). Finally, WDA and the functional resonance analysis method (FRAM) bridge these two perspectives. WDA describes the functional structure of the work and depicts the relationship between proximal and distal terms. In contrast, a simulation study based on FRAM envisions workers’ behavior when variabilities occur in the actual work environment. Here, FRAM is a method that can provide a functional model and envision the behavior of complex socio-technical systems where interactions between components and the environment are crucial. This integrated approach attempted to reveal the attention management aspects of adaptive skills.

This paper uses data obtained from the previous case study conducted by the authors (Yasue and Sawaragi 2022). The previous paper reported the preliminary simulation results of the FRAM model based on eye movement and interview analysis. The present paper expands on these previous results by identifying the resilient characteristics of expert operators, especially in their attention management strategies. Specifically, the current study extends our previous approach considering the nature of tacit knowledge, updates the eye movement analysis method, and adds some new simulation results. This case study has the limitation of having a small number of experimental participants; however, this research attempts to test hypotheses about workers’ attention distribution using a deductive learning approach based on the functional structure of tacit knowledge.

The remaining part of the paper proceeds as follows. Section 2 describes the research background regarding tacit knowledge and the adaptive behavior of human operators. Section 3 introduces FRAM with its historical background. Section 4 explains the methodological framework utilized in this study. Section 5 describes the case study conducted by the authors. Section 6 reports the results. Sections 7 and 8 are discussion and conclusion, respectively.

2 Background

2.1 Tacit knowledge

One of the reasons for the difficulty in extracting adaptive skills from expert operators is that they are acquired as tacit knowledge. This is because adapting to unfamiliar and novel situations is less reproducible and depends on individual situations, making it challenging to describe as unified knowledge. Polanyi (1966) proposed the concept of tacit knowledge, stating that “we can know more than we can tell.” Here, tacit knowledge can be defined based on the relationship between proximal and distal terms. The proximal term is the immediate observable experience, while the distal term is the meaning or concept implied from that experience. This relationship is illustrated by the example of a psychological experiment called the latent cognitive process. In this experiment, the participants were shown a string of letters and given an electric shock only when the specific spelling appeared in it. With repeated trials, participants began anticipating or attempting to avoid the electric shock when the specific spelling linked to the shock appeared. However, post-trial interviews with participants showed they could not explain how they anticipated or attempted to avoid the electric shocks. Polanyi discussed that the relationship between the proximal term—specific spelling—and the distal term—electric shock—could explain this experimental result. Namely, the participants just detected the specific spelling as a result of paying attention to the electric shock. As in this example, people cannot explicitly describe the proximal term itself because they direct their attention to the distal term via the proximal term. This is called the functional structure of tacit knowledge. An integrated approach is needed to examine these proximal and distal terms and their relationships to identify adaptive skills that are tacit knowledge.

2.2 Adaptive behavior of expert operators

The adaptive behavior of human operators to changes in the environment has attracted the attention of researchers. This trend is because as technology advances, the variability and complexity of tasks and the knowledge required to workers have increased in various works. Hatano and Inagaki (1986) defined adaptive and routine expertise as two distinct competencies. While routine expertise stands for the ability to perform routine or repetitive tasks accurately and efficiently, adaptive expertise is the capacity to quickly recover a high level of performance when faced with unfamiliar and novel situations. Based on this concept, relevant factors contributing to the development of adaptive expertise have been studied, mainly in pedagogy. In particular, the effects of learner characteristics, personality factors, task and training characteristics, and the learning environment on adaptive expertise have been investigated (Carbonell et al. 2014). The indicators have also been developed to assess and measure learners’ adaptive expertise (Carbonell et al. 2016). However, how human operators develop these competencies still needs to be clarified. Unless this is clarified, it is difficult to support the development of adaptive expertise. There is a need to investigate the processes by which adaptive expertise is demonstrated from an engineering perspective.

From the engineering perspective, adaptation in manual control by human operators has been studied based on control theory. The behavior of human operators controlling vehicles or aircraft has been modeled and analyzed as the human controller involving feedforward and feedback controls (Mcruer and Jex 1967; Mulder et al. 2018). Real-world manual control tasks are converted into simple tasks that can be repeated in the laboratory, and human-in-the-loop experiments have validated the model. In particular, the time-varying adaptive nature of the human controller that can respond to sudden changes in the environment has attracted research interest. For example, adaptations have been studied against the changes in controlled element dynamics (Zaal 2016; Ham et al. 2012) and target signals (van der El et al. 2020). This approach has also incorporated neurophysiological findings in recent years (Mulder et al. 2022). However, these studies still need more than discussions on simple laboratory tasks. It still needs to be clear how skilled operators adapt to environmental changes involving complex interactions between human operators, automated machinery, and the environment, as in real-world tasks. The systemic perspective focusing on the complex interactions in the socio-technical systems is required to overcome this limitation.

Eye movement analysis has been utilized to analyze the monitoring behavior and attention management of skilled expert operators in actual, complex environments. Particularly in aircraft pilots and surgeons, the difference in eye movements between normal and difficult situations or between novice and expert operators have been broadly studied (Tien et al. 2014). For instance, the results of the experiments with aircraft pilots showed that expert pilots’ unified attention management strategy contributes to flight performances (Bruder and Hasse 2019; Jin et al. 2021). Another example from the train operators’ domain showed that expert operators could keep a consistent monitoring strategy rather than the novice group, even when the situation changed (Horiguchi et al. 2015; Sun et al. 2019). Since these differences in eye movements related to the operator’s workload typically manifest in the variation of the gazing points, entropy indicators are often applied (Shiferaw et al. 2019). The entropy indicators derived from eye movement data have been utilized for identifying workers’ skill levels and task complexities (Stasi et al. 2016; Diaz-Piedra et al. 2017, 2019). These studies are useful to compare the adaptation behavior in skilled and novice operators when changing from their usual situation to a cognitively demanding situation. However, although eye movements reflect the operators’ unconscious cognitive features, only the experts’ superficial aspects can be learned. Nevertheless, this approach still does not tell us the mechanism of how skilled operators adapt to changes in their environment. Based on the findings of these analyses of expert operators, a systemic approach is needed that can deal with socio-technical aspects in the field where complex interactions are critical.

3 Functional resonance analysis method (FRAM)

This study used FRAM to capture the functional structure of skilled workers’ tasks; FRAM is one of the methods proposed for resilience engineering (Hollnagel 2012). Resilience engineering is a paradigm of safety management that addresses the system’s complexity and focuses on aspects that balance productivity and safety (Patriarca et al. 2018). There is a growing need to improve system resilience in aviation, air traffic control, medical, nuclear, and industry, where there is a non-negligible interaction between technical, human, and organizational factors. In this context, many studies have utilized FRAM to envision the socio-technical system’s behavior in recent years. The most basic application of FRAM is accident investigation and safety management (Salehi et al. 2021). By modeling and analyzing the target system using this method, it is common to identify safety-critical functions and propose countermeasures to improve resilience based on the FRAM model (Bridges et al. 2018; Buikstra et al. 2020; Ross et al. 2018). Furthermore, FRAM has also been applied to complexity management and socio-technical system analysis where interactions between components play a critical role (Furniss et al. 2016; McNab et al. 2018; Ferreira and Cañas 2019). Recent research has demonstrated that FRAM can develop a comprehensive model for hospital discharge planning, where various activities interact as a socio-technical system, improving its scheduling effectiveness (Salehi et al. 2023). These studies capture the system’s complexity and provide managers with recommendations for improving the system’s safety and efficiency. The domain of application is also expanding, including healthcare (Clay-Williams et al. 2015; McNab et al. 2018), aviation (Carvalho 2011; Sawaragi et al. 2006), maritime (de Vries 2017), and industrial processes (Amorim and Pereira 2015; Gattola et al. 2018; Zheng et al. 2016). In these studies, FRAM is gaining attention as a method for understanding the behavior of complex socio-technical systems as a whole.

One of the trends in this research field is to combine or extend FRAM with other methods. Combinations with other methods are a common approach (Ferreira and Cañas 2019), as FRAM needs to be customized to the target and purpose due to its flexibility. Studies related to the analysis step of building a FRAM model and instantiating for specific scenarios include organizing a hierarchical model with work domain analysis (Patriarca et al. 2017a), developing the application to support model building (Patriarca et al. 2017b), and combining it with formal model verification tools (Yang et al. 2017; Zheng et al. 2016). On the other hand, the step of examining variability propagations in the FRAM model is supported by Monte Carlo simulation (Patriarca et al. 2017c, 2017), analytic hierarchy process (AHP) (Rosa et al. 2015; França et al. 2020), and reinforcement learning (Salehi et al. 2022). However, a unified framework still needs to be created to make it applicable to various domains. In particular, since FRAM models systems at a high level of abstraction, mapping data to reality is a challenge.

Some studies have mentioned the skill aspect of human operators in socio-technical systems. According to the second principle of FRAM, “approximate adjustment,” human operators are constantly required to cope with the variabilities in their daily work to maintain the system’s performance. In this context, the effect of non-technical skills on the variability of daily work is investigated for offshore oil drilling (França et al. 2021; França and Hollnagel 2023). In these studies, the critical aspect related to non-technical skills was identified from the FRAM model, and the countermeasure to enhance the system resilience was proposed. However, previous studies have considered worker skills only as a factor that improves system resilience. In order to clarify the adaptive skills of operators, more attention must be paid to their adaptation process against environmental changes. Yasue and Sawaragi (2022) focused on this aspect and conducted a pilot study of building the FRAM models of the specific work, which requires a high skill level. The current paper extends this pilot study to reveal how skilled workers adapt attention management to changes in the environment based on the functional structure of tacit knowledge.

4 Methods

4.1 Approach overview

This paper focuses on the attention management strategy as one important aspect of adaptive skills. In particular, we focus on multitasking as a typical situation that attention management is crucial. This study took an integrated approach considering the functional structure of tacit knowledge—the relationship between proximal and distal terms—as shown in Fig. 1. In this study, the proximal term corresponds to the information the operator can directly sense, while the distal term refers to the abstract meaning behind the information. The eye movement analysis and the interview analysis take into account the proximal and distal aspects of attention management, respectively. This is because operators are assumed to focus on the abstract function of achieving the task purpose and consequently perceive the information in the environment. This abstract function related to the purpose of the work system is the distal term, and the information resources available to operators are the proximal terms. Thus, the eye movement analysis shows the superficial feature of the operator’s attention management as the proximal aspect. This study utilized an entropy metric derived from eye movement randomness for this purpose. On the other hand, the interview analysis reveals the abstract functions to what the operator’s attention is directed as the distal aspect during the work. For this purpose, the operator’s interview responses were mapped into the functional hierarchy using the work domain analysis (WDA).

Fig. 1
figure 1

Approach overview of this study

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This study adopted a model-constructive approach using WDA and FRAM to integrate these two aspects of tacit knowledge. Both WDA and FRAM describe systems from functional perspectives, leading to combined applications in research. Patriarca et al. proposed a method to develop FRAM models hierarchically based on the Abstraction-Agency framework provided by WDA to address system complexity (Patriarca et al. 2017a). Another study utilized WDA as a preliminary stage in constructing FRAM models for analyzing and improving production systems (Zúñiga et al. 2020). These studies demonstrate that combining WDA and FRAM allows for a comprehensive analysis of systems.

This study combined these two methods to compare Work-as-Imagined and Work-as-Done. Work-as-Imagined represents the behavior envisioned when the system was designed, whereas Work-as-Done corresponds to how the system operates in actual environments. Previous research has used FRAM to compare Work-as-Imagined and Work-as-Done, identifying discrepancies to enhance understanding of system operations (Schutijser et al. 2019; van Dijk et al. 2022) and propose improvements in guidelines and management practices (Clay-Williams et al. 2015; Damen et al. 2021; Tresfon et al. 2022). In this research, WDA was used to organize the fundamental procedures constituting work, and FRAM was utilized to represent characteristics of expert workers that do not appear in basic procedures. The former corresponds to the basic work procedures designed as Work-as-Imagined, and the latter corresponds to Work-as-Done as actually performed by workers on site. The rationale for using these two methods lies in their complementary strengths: WDA is suitable for capturing the overall picture of a system, while FRAM is apt for understanding how variability within the system actually impacts operations. This study aimed to identify the functional structure of tacit knowledge possessed by expert workers by comparing these two aspects.

4.2 Eye movement analysis

This study extracted expert operators’ eye movement features in multitasking to investigate their proximal aspects of attention management. For this purpose, we compared the eye movements of expert and mid-level operators in single-tasking and multitasking. The relative entropy of Shannon’s information theory based on AOI (Area Of Interest) was utilized to show the eye movement features in each condition. AOI is an arbitrary region within the operator’s vision for the statistical analysis of eye movements within that screen (Mao et al. 2021). In our approach, the objects to which the operators’ attention is directed are set as the AOIs. During the work, the operator directs their gazing point to each AOI according to the attention target so that a series of gazing point AOI-to-AOI transitions could be obtained for each single measurement data. When there are n AOIs, the transition pattern between AOIs of a gazing point can be expressed as a probability distribution of \(n(n-1)\) ways. Relative entropy represents how far apart these probability distributions are. Therefore, the relative entropy between the respective gaze measurement data can indicate how similar the gazing point shift patterns are. When the occurrence frequencies of the i-th inter-AOI transition pattern for the two eye movement data are P(i) and Q(i), the relative entropy D can be expressed by Eq. 1.

$$\begin{aligned} D(P||Q) = \sum _{i} P(i) \log _2 \frac{P(i)}{Q(i)} \end{aligned}$$
(1)

This method analyzed expert and mid-level workers’ attention management by comparing how much their eye movement features change in single-task and multitasking.

4.3 Work domain analysis and interview analysis

This study investigated the distal term of attention management by analyzing the interview responses of the workers. A semi-structured format was adopted for this purpose. Semi-structured interviews incorporate characteristics of structured interviews, where question items are predefined, and unstructured interviews, where questions emerge during the conversation, allowing for deeper exploration of topics (Kallio et al. 2016). These characteristics mean that while there is a set guide of open-ended questions, there is also flexibility to delve deeper into specific topics. Such features enable semi-structured interviews to balance consistency among interview participants with acquiring more in-depth responses. Due to these advantages, semi-structured interviews are one of the most commonly used methods for data collection in studies utilizing FRAM (Salehi et al. 2021; Patriarca et al. 2020; Buikstra et al. 2020; Damen et al. 2021). In addition, according to Mori (2013), to elicit deeper layers of tacit knowledge that workers might not be consciously aware of, it is necessary to go beyond basic questions and delve deeper into interviews based on hypothesis testing. Considering these characteristics of interview formats, this study chose semi-structured interviews to maintain consistency while comparing interviews between expert and mid-level workers, yet allowing for in-depth exploration. The basic questionnaire used in the interviews are listed in Appendix A.

Skilled workers are considered to allocate their attention to multitasking by understanding abstract functions such as constraint relations between tasks and the purpose of the system. The relationships between these abstract functions and the observable information resources are described based on the functional structure of the system, e.g., by work domain analysis (WDA). WDA is part of a cognitive work analysis (CWA) framework, a methodology to analyze complex socio-technical systems focusing on human–machine interaction and human work activity (Vicente 1999). CWA contains six top-down steps: work domain analysis, control task analysis, strategies analysis, social organization and cooperation analysis, and worker competencies analysis. This framework is mainly used for the human–machine interface design in complex socio-technical systems, which allows human workers to intuitively operate the system by providing information based on the analysis results. The role of WDA as the first step of this framework is to provide a holistic view of the system as a foundation for designing human–machine interface design. WDA organizes functions involved in the system with a multiple-layer form called Abstraction Hierarchy (AH). AH has five layers: functional purpose, abstract function, generalized function, physical function, and physical form (Vicente 1999). Each layer is more abstract as you go up and more concrete as you go down. Functions assigned in each layer are connected with means-end links. For example, when we focus on the two functions connected with a link, the upper function represents “why” the lower function is conducted, and the lower function represents “how” the upper function is conducted. The overall functional structure of the system can be organized in this way.

Another prominent method for decomposing work into elements is Hierarchical Task Analysis (HTA) (Stanton 2006). HTA is a central approach in ergonomics, known for breaking down tasks into subgoals and organizing them hierarchically. However, while HTA excels in describing task structures, the relationships it describes tend to be confined to whole-part relationships. In this study, we specifically chose WDA because it focuses on the means-end relationships between functions and organizes these functions according to levels of abstraction, which is more suitable for mapping the functional structure of tacit knowledge.

This study visualizes the interview characteristics by mapping typical interview responses onto the functional hierarchy described by WDA. For example, when the worker mentions the purpose of the system, the utterance corresponds to the functional purpose layer. In contrast, when the worker mentions specific devices, it corresponds to the physical function or the physical form layer. In this way, utterances in a conversation can be mapped to functions at each level of abstraction.

In addition, WDA supports building an initial FRAM model by providing a comprehensive view of the target system. Among the functions identified in AH, those relevant to the target work are selected as candidates to constitute the initial FRAM model. The dependencies among those functions are then examined and shown as connections between hexagons. Based on observations and interviews, additional functions may be added to the FRAM model.

4.4 FRAM simulation

Finally, a simulation study based on FRAM was conducted. As a result of the eye movement analysis and interview analysis, the attention management strategies in multitasking depending on the worker’s skill levels were clarified. Based on this result, a FRAM model including all potential functions and dependencies based on WDA was instantiated into two FRAM models of expert and mid-level workers. Because this study focuses on workers’ attention management, the difference between these two instances may appear in the functions related to monitoring the target system. After that, the FRAM simulation was utilized to envision the system’s behavior. It is a simulation method to simulate the functional resonance triggered by variabilities in complex socio-technical systems (Hirose and Sawaragi 2019, 2020). This method was developed to provide quantitative support for FRAM, which was originally qualitative. The variabilities in the system are translated to numerical values based on Common Performance Conditions (CPC), which are the eleven items characterizing the environment surrounding the system (Hollnagel 1998). These values are called CPC scores and range from 0 to 100. Also, performance fluctuations of each function in the FRAM model are expressed by Probability of Action Failure (PAF), which represents how strategically the function is carried out. This method enables simulation of the effect of variability expressed with the specific CPC change on the entire system based on the function interrelations. This simulation method was utilized to investigate the effect of attention management strategies of expert and mid-level operators on work performance when multitasking.

In this simulation method, CPC serves as an indicator of the system’s context and was introduced in the Cognitive Reliability and Error Analysis Method (CREAM), developed as part of second-generation human reliability analysis (Hollnagel 1998). Human reliability analysis originated from investigating human factors in accidents within large-scale systems such as nuclear power plants. While the first-generation human reliability analysis focused primarily on quantifying the probability of human errors, the second-generation recognized the limitations of this approach in complex systems and shifted its emphasis towards analyzing the contexts in which errors occur. As one of the methods proposed under this second-generation framework, CREAM introduced CPC as an indicator of the system’s context. Later, when FRAM was proposed, it advocated representing variability in terms of timing and accuracy instead of using CPC, a practice still employed in many studies today. However, this approach to variability focuses on the fluctuations in function output to focus on functional resonance. In this study, we intentionally adopted CPC, derived from second-generation human reliability analysis, to represent the context of the surrounding environment, which interacts with each function in the FRAM model represented as PAF values. This adoption allowed for the implementation of diverse scenarios corresponding to CPC in the simulation.

4.5 Hypotheses

This section summarizes the relationship between our approach and the functional structure of tacit knowledge, as shown in Fig. 1, and states the hypotheses of this study. In the operators’ multitasking, the individual gazing objects are the proximal terms, and the system’s abstract functions that govern their attention allocation, such as task constraint relations, are the distal terms. The entropy metric derived from the eye movement data sets characterizes the gaze point transition features from the proximal term aspect. On the other hand, mapping the interview conversation using WDA identifies what abstract functions the worker is managing attention based on as a distal term aspect. Based on these two terms, the first hypothesis is that the structured gaze point transition corresponds to the operator’s better understanding of abstract functions in the higher layer in AH. This is because expert workers are assumed to be able to allocate attention systematically based on a good understanding of constraint relations in multitasking. The second hypothesis is that this attention management feature is the critical factor in maintaining work performance in multitasking. The model constructive approach based on FRAM tests this hypothesis by incorporating attention management strategies into the FRAM model and conducting a simulation study assuming multitasking.

5 Case study

5.1 Case study description

This study used the data obtained from the previous case study by the authors (Yasue and Sawaragi 2022). The target was an operation in a steel plate processing line as a case study to investigate the features of expert operators. This process aims to produce flat steel plates from coiled steel strips. The steel plates must be uncoiled from the steel coil, flattened, and cut to predetermined sizes. Figure 2 depicts the outline of this production line. The trimmer and the shear cut the steel plates after the leveler flattens them. The case study focused on a specific operation called the centering operation in this process. This operation aims to control the steel plate’s position at the trimmer to carry out the cutting process accurately. However, the operator can only operate the coil horizontal position in front of the uncoiler, which is more than ten meters away from the trimmer. Because the operator is arranged in front of the uncoiler and cannot directly see the trimmer, a monitor showing the trimmer is installed near the operator. In addition, each type of steel plate has a peculiar process flow between the plate’s entrance site of the uncoiler and the trimming site, and the operator must have the knowledge and experience to deal with them. Due to these conditions, this operation requires a high level of skill.

Fig. 2
figure 2

Overview of the target work (Yasue and Sawaragi 2022)

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We focused on multitasking in this operation to investigate the attention management strategy of expert operators in cognitively demanding situations. Even during the centering operation, another operator brings new coils to be processed by crane at any time. The operator in charge of the centering operation must handle the coil supply by controlling the coil car to catch the coil. This operation is called coil setting operation. Single-tasking is defined as performing only the centering operation, while multitasking is defined as performing the coil-setting operation in addition to in parallel.

5.2 Data collection

This study conducted a comprehensive case study, harnessing the power of both qualitative data from interviews and quantitative data from eye-tracking measurements, to provide a sufficient understanding of the research subject (Yasue and Sawaragi 2022). Figure 3 illustrates the data collection and analysis flow executed in this research. These steps were conducted with the cooperation of Token Machinery Works Co., Ltd. members. Initially, four observational sessions were conducted to understand the content of the target work and plan subsequent experiments. Each session lasted approximately one hour, spread over two months. Based on the outcomes of these observations, the experimental setup for eye-tracking experiments focusing on multitasking in daily work was determined. In addition, this step created a list of base questions for the semi-structured interviews.

Fig. 3
figure 3

Data and analysis flow of the current case study

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As for the eye-tracking experiments, the participants included one expert worker and one mid-level worker, each of whom had worked in the target operation. Measurements were taken over periods that included both single-tasking and multitasking in the daily work. The measurement time was about 40 min per operator. The eye movements were measured using Tobii Pro Glasses 2 (Tobii Pro AB, Danderyd, Sweden) with a sampling rate of 50 Hz.

After the measurements during the operations, this study conducted interviews with the operators. The interview participants were the same two operators participating in eye-tracking experiments. Each interview was conducted one-on-one with each operator. In these interviews, the interviewer and the operator shared a movie. The movie included two synchronized videos: the recording of the operator’s gaze point movement and the video of the bird’s-eye view during the operation. Here, the results of the eye movement measurements were mapped into the operator’s view and converted to a video that recorded the operator’s gaze point movement. The interviewer and the operator shared the video while using a laptop computer. The interviewer posed the listed questions to the workers and delved deeper into the discussion of attention distribution, supported by the shared videos. The interview took about 40 min per operator. The experiments were approved by the Ethics Committee, Graduate School of Engineering, Kyoto University. Before the experiments, the participants were explained the instructions and signed the consent form.

The results of the eye-tracking measurements and interviews were subjected to content analysis that combined qualitative and quantitative data to extract the characteristics of workers’ attention distribution. As described in Sect. 4.2, the eye-tracking results utilized the relative entropy metric to extract features of gaze transitions among workers in each experimental scenario. Additionally, the interview results aimed to differentiate the response characteristics of each worker based on common questions posed to both, as described in Sect. 4.3. These results identified the fundamental work elements and the workers’ attention distribution characteristics. To organize these findings, WDA was conducted to capture the overall picture of the work. This step also described the work-as-imagined model and identified the fundamental functions that constitute the FRAM model. Additionally, based on qualitative analyses of work observations and interview results, this step accepted to deliberately add functions to the FRAM model to represent the workers’ attention distribution characteristics. Finally, the constructed FRAM model and the analysis results were shared with corporate members to verify whether they constituted a valid work-as-done model of the target work. This mixed approach of constructing FRAM models based on multiple data sources, including qualitative data, is also commonly used in other studies (Patriarca et al. 2020; Tian and Caponecchia 2020; Salehi et al. 2021).

6 Results

6.1 Attention management features

6.1.1 Eye movement analysis results

The relative entropy based on eye movements was adopted to visualize the monitoring behavior difference between single-tasking and multitasking of expert and mid-level workers. This measure indicates how different the probability distribution of transitions from one AOI to another is between the two eye movement data sets. The relative entropy between the four ways in the single-tasking and multitasking cases for expert and mid-level workers was calculated and mapped using multidimensional scaling (Cox and Cox 2008). As indicated by Eq. 1, calculating relative entropy requires the gaze transition patterns between AOIs, P and Q, from two measurement data sets. This study computed the relative entropy for six combinations: from (Expert worker, Single-task) to (Expert worker, Multitask), from (Mid-level worker, Single-task) to (Mid-level worker, Multitask), from (Expert worker, Single-task) to (Mid-level worker, Single-task), from (Expert worker, Multitask) to (Mid-level worker, Multitask), from (Expert worker, Single-task) to (Mid-level worker, Multitask), and from (Expert worker, Multitask) to (Mid-level worker, Single-task). As a baseline, the relative entropy to a uniform probability distribution of AOI transitions was calculated for these four measurement data sets. Figure 4 visualizes the relative entropy of each data pair as a pseudometric distance using multidimensional scaling. In this graph, the greater the distance between two data points, the more significantly their associated gaze movement characteristics differ.

Fig. 4
figure 4

Visualization of the differences in the monitoring behavior using relative entropy and multi-dimension scaling

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This graph was generated using multidimensional scaling, and thus, the X–Y–Z axes require interpretation based on the underlying data. The X-axis corresponds to the shift in gaze movement characteristics from single-tasking to multitasking among the mid-level worker. As values on the X-axis increase, the gaze movements approach a more random pattern, suggesting an increase in the complexity of eye movements. The Y-axis, on the other hand, corresponds to changes in the gaze movement characteristics of the expert worker, reflecting shifts in attention distribution strategies due to the introduction of new coils. The Z-axis implies that the gaze movement characteristics represented are consistent across all measurements, suggesting they are standard features of eye movements acquired by the workers, regardless of skill level or task scenario. The relative entropy from single-tasking to multitasking for the expert worker was about 1.14; for the mid-level worker, it was about 3.35. This means that the expert worker showed less change in the probability distribution of the inter-AOI transition pattern than the mid-level worker.

Table 1 shows the calculated relative entropy from the anchor to each eye movement data.

Table 1 Relative entropy from the anchor (uniform distribution) to each eye-tracking data
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This metric indicates that the smaller the value, the closer the gaze transitions between AOIs in the measurement data were to be random. The random gaze point transitions imply that attention management becomes opportunistic, as attention is distracted by various events in front of them. In contrast, the structured gaze point transitions correspond to systematic attention management in which the worker knows where to look next. For both of the workers, gaze point transitions approached randomness when multitasking. This fact suggests that multitasking made attention management opportunistic. In addition, the gaze point transitions of the mid-level worker significantly fluctuated when transitioning from single-tasking to multitasking, whereas the change was relatively small for the expert worker. These results show that the expert worker could relatively maintain the systematic attention management represented by the structured gaze point transitions.

6.1.2 Interview analysis results

Differences in the characteristics of the interview responses between the expert and the mid-level participants were analyzed. We focused on the part of the interview conversation that related to multitasking in centering and coil-setting operations. The results showed that answers replied with more abstract words are features of the expert participants. For example, when asked what they were conscious of during multitasking, the expert operator referred to the temporal relationship between centering and coil setting and the constraints of each other, whereas the mid-level operator focused only on the individual objects by mentioning the information resources they had to look at during each task. Similarly to the other questions, the expert operator was characterized by the answers relating to abstract relationships between elements and the purpose of the system as a whole, whereas the mid-level operator was characterized by the answers that focused only on individual concrete elements.

WDA was conducted to visualize these features of interview responses. This method builds an overall picture of the target operation as a series of chained functions based on the interviews. Figure 5 shows the AH of the target operation, showing the functional structure of the system.

Fig. 5
figure 5

Characteristics of expert’s and mid-level’s answers mapped to AH (modified from Yasue and Sawaragi (2022))

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The top hierarchy of the functional purpose places efficiency and product quality as objectives to be achieved in this work. The second layer of the abstract function describes the fundamental rules that cover the process, such as the flow balance and steel plate dynamics. Parts representing the general steps of the work process were placed at the level of the general function. In addition, substeps of the general functions were placed in the physical function layer. Finally, specific devices for conducting physical operations were placed in the physical form layer. Connections between functions represent the means–ends relationships between those components. The functional structure of this target work was obtained in this way.

Figure 5 illustrates the results of mapping the differences in response characteristics between expert and mid-level workers in individual semi-structured interviews. Questions common to both interviews regarding multitasking strategies related to functions such as Coil setting and Centering within the general function layer are enclosed in squares. The typical response patterns seen in experts are visualized in red, while those typical for mid-level workers are shown in blue. The expert operator typically responded to the neutral question about multitasking by focusing on the abstract relationships between elements and the purpose of the whole system. This corresponds to the transition to higher levels of the abstraction hierarchy. Because the connections between functions represent means–ends links in AH, the upper transitions show that the expert workers know why the process is performed. In contrast, the mid-level typically responded to the neutral question by focusing only on individual concrete elements. This corresponds to exploring lower levels of the hierarchy of abstraction. The interview analysis showed that experts could carry out tasks with an awareness of the relationships between components and the purpose of the whole system, even when multitasking.

6.1.3 Brief summary of expert attention management features

The following characteristics of expert operators were identified based on the eye movement and interview analysis results.

  • The relative entropy from the anchor characterized how close to random the gaze point transition in each condition was. This index showed how consistently the operators could allocate their attention within the constraints of multitasking. The results showed that expert operators could maintain their attention management strategy even when multitasking. In contrast, the mid-level operators’ attention management strategy became opportunistic.

  • The interview analysis showed that expert operators were aware of the abstract relationships between elements in the system. In contrast, mid-level operators focused only on individual elements.

These results support the first hypothesis of this study that structured gaze point transitions correspond to a better understanding of the system’s abstract functions. The expert operator could associate the task constraints, distal terms, with each gazing object, proximal terms, so that gaze point transitions remained structured when multitasking. In contrast, the mid-level was not fully aware of the system’s abstract functions, so their attention was diverted by multitasking, and the gaze point behaved randomly. Thus, the expert operator could maintain systematic attention management in multitasking because of a better understanding of the system’s abstract functions.

6.2 FRAM model construction and instantiation

For the FRAM model building, the functions of the target process were selected, referring to WDA. Figure 6 shows the basic FRAM model focusing on the multitask of centering and coil-setting operations.

Fig. 6
figure 6

The basic FRAM model of the target work (Yasue and Sawaragi 2022)

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The operator mainly monitors the components corresponding to the physical form, such as the strip edge gap between the coil and the laser marker, the side-guide monitor, the trimmer monitor, and the new coil to be processed. Using this monitoring information, the operator sets the target position of the steel plate based on the estimation and controls the steel plate position by manipulating the lever. In parallel with this centering operation, the position of the coil car is controlled to receive the new coil brought in by another operator. In addition, the attention distribution function was added to the model. This additional function “Distribute the attention” was not identified in WDA but was added to the FRAM model to represent the attention distribution characteristics of expert workers based on work observations and insights from past research. It was explicitly identified through the observation that the most significant differences in performance between expert and mid-level workers occur during multitasking. This observation aligns with the conclusions of Sect. 6.1.3, which analyzed gaze movements during single-task and multitask scenarios. These findings are supported by previous insights on adaptive expertise, which, as discussed in Sect. 2.2, corresponds to the ability to manage unforeseen situations flexibly. For adaptive expertise to be effective, it is known that metacognitive abilities to manage one’s cognitive processes are crucial (Brown 1988; Bransford et al. 2000). The function “Distribute the attention” in Fig. 7 integrates several monitoring functions and adjusts the focus of attention according to changes in multitasking situations, embodying the characteristics of metacognition. By adding this function related to metacognition, it is possible to represent the strategic attention distribution characteristics of experts in multitasking, as revealed through gaze movement analysis and interview analysis. Thus, this additional function was introduced based on work observations and past insights on adaptive expertise.

The functions are grouped into three categories: the monitoring group, shown in blue; the estimating group, shown in green; and the responding group, shown in red. These three groups correspond to the four capacities required for resilience: monitoring, estimating, responding, and learning (Hollnagel 2017). Learning is omitted due to the different time scales. This functional grouping can be associated with the situation awareness theory. Situation awareness theory describes human decision-making as a process involving three stages: Perception, Comprehension, and Projection (Endsley 1995). These are followed by the steps of Decision and Action, which are performed cyclically to make decisions in response to the surrounding environment. Our analytical approach involves mapping these stages to the three functional groups in Fig. 5 of the FRAM model. Specifically, the situation awareness steps correspond to the Monitoring group, the subsequent Decision step to the Estimating group, and the final Action step to the Responding group. This study primarily focuses on the Monitoring group corresponding to the situation awareness steps, given its emphasis on worker attention distribution. However, as situation awareness involves the integrated execution of Decision and Action steps, the functions in the Estimating and Responding groups in this FRAM model are also represented as interacting with each other. Adopting this approach makes it possible to analyze work performance from a systemic perspective of the entire work process.

The grouping of these functions is also related to the Abstraction-Decomposition framework, a form of representation in WDA that describes the system along abstraction and decomposition axes. As introduced in Sect. 4.3, the axis of abstraction unfolds functions regarding means–end relationships, whereas the decomposition axis expands the system regarding part–whole relationships. It is common in WDA to grasp the system’s structure through these two axes. Patriarca et al. (2017a) proposed a method for representing the structure of complex systems systemically by combining an extended abstraction–agency framework with FRAM. This method organizes each agent’s functions according to levels of abstraction, thus enabling the visualization of the complex system’s overall structure. While the FRAM model in this current study groups functions not by the agent but by the cognitive processes of an individual worker, it similarly categorizes functions within the FRAM model, facilitating the analysis of which functions are crucial.

The basic FRAM model was instantiated according to the operators’ attention management strategy. Figure 7 shows the two instances of the FRAM model of the expert and mid-level operators.

Fig. 7
figure 7

Instantiation of the FRAM model based on the monitoring behaviors of the operators (modified from Yasue and Sawaragi (2022))

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All functions and connections were activated in the FRAM model instance of the expert operator. The connections from the output of the “Distribute the attention” to the other four monitoring functions colored in blue indicate that expert operators can distribute their attention based on the consistent attention management strategy even when multitasking. The feedback from the “Monitor...” functions to the “Distribute the attention” indicate that expert operators plan the attention allocation based on the relationships between components in the work domain. In contrast, the connections between functions shown in dotted lines were deleted in the FRAM model instance of the mid-level operator. The deactivated connections indicate that mid-level operators cannot maintain the attention management strategy and behave opportunistically in multitasking. These models represent differences in attention allocation features in multitasking, depending on the skill.

6.3 Simulation study

This study conducted a simulation study to investigate how attention management strategies affect work performance in multitasking. The attention management strategies are clarified through the eye movement and interview analysis and incorporated into the FRAM model structure, as shown in Fig. 7. The FRAM models show the difference between expert and mid-level operators in attention allocation features. This simulation study aims to show how this difference contributes to the operator’s resilient performance in multitasking. The simulation scenario and the settings are as follows.

Scenario: The operator was conducting the centering operation as a single-tasking in daily operation. Then, a new coil to be processed next was carried into the process by the other operator. The operator conducting the centering operation had to receive this new coil by controlling the coil car in parallel with the ongoing main task. Because the timing of the new coils being brought in cannot be controlled, multitasking was required at this moment. The operator faced multitasking in the centering and coil-setting operation.

The settings were established as follows to implement this scenario in the simulation. As described in the Methods section, the simulation method involves two variables: PAF corresponding to the state of each function and CPC representing the context surrounding the system, with defined interactions between them. Variability specified in the scenario is introduced into the simulation as changes in CPC scores, allowing for investigating how variability propagates through the system based on the coupling relationships between functions. In the coupling between functions, one side always leads to output, with the function providing this output referred to as the upstream function and the function receiving this output called the downstream function. It is generally calculated that variability propagates from the upstream function to the downstream function. As a result, the PAF values of each function at each simulation timestep are obtained.

Settings: The multitasking situation triggered by the new coil arrival corresponds to the “Number of goals,” which is one of the CPC scores defining the surrounding situation in this simulation method. Thus, the CPC score of the “Number of goals” was set from 100 to 0 at the simulation time 0 to implement this variability. How these fluctuations propagate to the functions comprising the work is simulated.

Figure 8a and b shows the simulation results.

Fig. 8
figure 8

Simulation results based on FRAM. (a) Simulation result of expert operator in multitasking [8]. (b) Simulation result of mid-level operator in multitasking [8]

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The horizontal axis shows the simulation time. The vertical axis shows the logarithm of PAF, which corresponds to how safe the functions in the FRAM model are conducted. For example, when the graph remains at a low level, it means that the function is conducted safely or strategically. In contrast, an increase in the graph represents the high probability of dysfunction. Thus, this simulation method allows us to investigate what state each function settles into after fluctuations are imposed on the FRAM model. In both cases of the expert and the mid-level operators, the log(PAF) of the functions increased after the variability occurred at the simulation time 0. These increases represent that the shift to multitasking significantly affected the cognitive functions comprising the target operation. After this increase, the functions recovered to the normal status in the case of the expert operator, while they remained at the relatively dangerous status in the mid-level case. This trend of the mid-level operator indicates that the FRAM functions continued to have a high probability of malfunctioning. In contrast, in the case of the expert operator, the FRAM model can recover from the temporary hazardous conditions and perform multitasking stably.

These results support this study’s second hypothesis that the attention management strategies represented by the FRAM models had a critical role in maintaining work performance in multitasking. The difference between the FRAM model instances that produced this result was whether the attention management function was active. This difference corresponds to the first hypothesis, the relationship between proximal and distal terms for the operators. That is, the expert operator understood the abstract relationships in the system and was, therefore, able to allocate attention effectively even when multitasking. This feature was expressed by the active “Distribute the attention” function, which centrally managed the other monitoring functions in the FRAM model. Thus, the attention management strategies of the expert operator identified based on the structure of proximal and distal terms were critical for the work performance in multitasking.

7 Discussion

7.1 Attention management in multitasking

This study investigated attention management strategies considering the functional structure of tacit knowledge. Attention management strategies are an important aspect of clarifying the adaptive expertise of skilled workers. In particular, we focused on multitasking as a typical situation that attention management is crucial in manufacturing worksites. Because operators acquire attention management as tacit knowledge, the approach considering its structure—the relationship between proximal and distal terms—was needed. This study applied eye movement and interview analysis for the proximal and distal aspects. By combining these two perspectives, we investigated which abstract function the operators were aware of and, consequently, what their attention management strategies were.

The eye movement analysis examined how the operators allocated their attention to the surrounding information resources as the proximal term. The relative entropy showed how the attention management features changed in single-tasking and multitasking for expert and mid-level operators. In addition, the relative entropy from a uniform probability distribution of inter-AOI gaze point transitions showed how structured or random the eye movements are under each condition. As a result, the mid-level operator’s gaze point transitions significantly approached randomly in multitasking. In contrast, the expert operator’s gaze point transitions remained relatively structured in the same situation. These results showed that the expert operator could maintain attention management in multitasking while the mid-level operator’s monitoring behavior became opportunistic.

The interview analysis investigated what abstract functions the operators are aware of during work as the distal term. For this purpose, the typical responses of the expert and the mid-level operators were mapped onto the functional hierarchy of WDA. As a result, the expert operator focused on the task constraint relations and the system’s objective, which correspond to the upper layer of the abstraction hierarchy. In contrast, the mid-level operator only focused on the individual components, corresponding to the abstraction hierarchy’s lower layer. These results showed that the expert operator was aware of abstract functions in multitasking while the mid-level operator was occupied with focusing on individual elements.

These two analyses indicated that the attention management strategy can be described under the functional structure of tacit knowledge—the relationship between the proximal and distal terms. The gazing objects to which attention was allocated was the proximal term, and the abstract relations between components were the distal term. The expert operator could associate task constraint relations with individual gazing objects, allowing them to maintain systematic attention allocation even when multitasking. In contrast, the mid-level operator’s attention was more opportunistic, just reacting to changes in individual objects in multitasking without fully understanding the system’s abstract functions. These results confirmed the first hypothesis that structured gaze point transitions correspond to a better understanding the system’s abstract function. This finding is consistent with the previous studies. Chanijani et al. (2016) indicated that experts have low gaze entropy with a systematic attention management strategy because they understand where to look during the task, while novices hunt information by aimlessly browsing the display. Horiguchi et al. (2015) reported that experienced train operators could better maintain gaze point movement patterns than novices when the situation changed. Similar to these studies, the present study shows expert workers’ attention management characteristics in cognitively demanding situations.

7.2 Integrated analysis with WDA and FRAM

In order to integrate proximal and distal aspects, this study employed a model constructive approach using WDA and FRAM. While WDA organized the overall picture of work from the Work-as-Imagined perspective using an abstraction hierarchy, FRAM incorporated attention distribution features to the model and provided a Work-as-Done perspective, examining the impacts when multitasking occurs.

WDA showed that the two tasks in multitasking—centering and coil-setting operation—shared the system’s objective of quality and efficiency. Also, these two tasks have several connections to specific devices in the lower layer, so the operator must allocate attention to these components. Thus, the abstraction hierarchy of WDA can interpret as the relationships between observable proximal terms at the lower layer and distal terms, which are important for task management, at the upper layer. However, this only shows the static relationship between the two. In order to clarify how this relationship is demonstrated in actual work, we need a method to examine the system’s behavior dynamically.

We conducted a simulation study with a multitasking scenario based on the FRAM model instances reflecting the operators’ attention management strategies. In this study, the simulation output assessed the impact of variability on the FRAM models of expert and mid-level workers using PAF. The PAF value quantifies the control modes defined in CREAM—strategic, tactical, opportunistic, and scrambled—using membership functions and is an indicator for evaluating functional safety. In our research, this metric corresponded to how successfully each function within the FRAM model was performed, and it was used to evaluate work performance when variability was introduced. The FRAM models constructed in this study mostly correspond to the cognitive processes of the workers; therefore, an increase in the PAF of these functions is considered to correlate with an increase in the mental workload of the workers. It is well-known that a high mental workload can impede working memory, decision-making, and situation awareness, negatively affecting safety behavior and performance and increasing the risk of accidents (Chenarboo et al. 2022; Longo et al. 2022). Thus, the analysis in this study is also considered to contribute to safety management.

This simulation study was based on the second hypothesis that the expert’s attention management strategy is critical to resilient work performance in multitasking. The expert operator’s attention management strategy was expressed by the “Distribute the attention” function. This function centrally manages the attention among the other monitoring functions, which are proximal terms, based on their abstract relationships, which are distal terms. The simulation results showed that the FRAM model with the expert’s attention management strategy recovered the performance after the variability of multitasking. In contrast, the mid-level’s FRAM model remained likely to be dysfunctional. These results indicate that the attention management strategy of the expert operator contributes to resilient work performance. In addition, the expert’s FRAM model had a perceptual action cycle that involved monitoring, estimating, responding, and then monitoring again. This structure in the FRAM model may correspond to the resilience of the expert operator to adapt to changes in the environment and maintain their performance.

Our approach investigated the attention management strategy in multitasking, considering the functional structure of tacit knowledge. Since these skills related to the adaptive behavior of workers are tacit knowledge, a multifaceted approach not limited to gaze analysis is necessary. Following this idea, this study considered proximal and distal aspects using eye movement and interview analysis. Furthermore, the model constructive approach described this relationship using FRAM and enabled us to clarify how this feature contributes to work performance.

7.3 Analyzing skills using FRAM

These results of FRAM can relate to the theory of situation awareness. Endsley (1995) has proposed a theoretical model of situation awareness with three levels to describe human decision-making. The first level is the perception of individual elements in the current situation. The second level is comprehending the current situation by integrating relevant individual components. The third level is the projection of future status based on the current system status and future goals. This study confirms that the target work can be described by following these levels. At the first level, the operator perceives the individual information, such as the display of the trimming process and the reference laser line. The operator integrates that information at the second level to build an overall comprehension of the current process, including the steel plate status. Finally, the operator projects the future steel plate condition as it moves through the process and operates adequately. These levels possibly correspond to the FRAM model of the target work, as shown in Fig. 6. The four monitoring functions allocated at the center of the FRAM model represent the first “perception” level; the “Distribute the attention” function corresponds to the second “comprehension” level; and finally, the “projection” results are passed on to the estimating group of the FRAM model. Because the critical factor of the expert’s FRAM model was the active “Distribute the attention” function, the performance difference of the operators may be characterized by the second “comprehension” level.

This study utilized FRAM to investigate the adaptive aspect of expert operators who work in socio-technical systems. This application partly differs from the typical use of FRAM in previous studies. Much of the FRAM research has focused on identifying safety-critical functions of large-scale complex systems and proposing countermeasures to improve resilience (Carvalho 2011; Salehi et al. 2021). In contrast, our approach dares to focus on the specific operators in the system and to model their adaptive behavior using FRAM. However, this study confirms that our approach matches the research objectives. In the resilience engineering approach, workers in socio-technical systems must continuously adapt to the variabilities in their daily work. This feature is the second principle of resilience engineering, “approximate adjustments.” This aspect is precisely the skill required of expert manufacturing workers. FRAM based on resilience engineering has shown to be a suitable method to investigate this in the present study. The results further suggested that our approach has contributed to elucidating the adaptive skill mechanics through modeling and simulation, which were previously difficult to verbalize as tacit knowledge. In addition, the proposed framework can be applied to other work in socio-technical systems. Note that the methods for extracting features of expert operators are not limited to eye movement and interview analysis but must be selected appropriately.

The case study conducted in this research to reveal the attention distribution characteristics of workers was limited to one expert and one mid-level worker as participants. This study adopted a deductive learning approach to overcome this limitation. Generally, an approach that extracts common features from quantitative data and statistical analyses corresponds to inductive learning, which identifies patterns from a large amount of training data. In contrast, deductive learning is an approach that extracts targeted concepts from a small number of cases based on established rules and logical reasoning. Notably, the method of developing abstract knowledge representations based on actual specific cases is called Explanation-Based Learning (EBL) (Mitchell et al. 1986). In EBL, the initial step involves constructing a causal model that extracts only the parts relevant to learning from the training instances. In this step, domain-specific knowledge, pre-established in the system as domain theory, is used to integrate fragmentary information manifested in the descriptions of the training instances. The output of this step is a causal model equipped with a structure that explains the training instances, generally represented in a tree structure. At this stage, information from the training instances that do not align with the target concept is discarded and not included in the explanation structure. In the next step, the causal model extracted from the training instances is generalized into an explanation structure encompassing other instances where the same interpretation applies. Here, constants at each node of the tree structure are replaced with variables to represent generally applicable concepts. Through these steps, it is possible to identify the explanatory structure from a few instances. Recently, research based on EBL has expanded to analyses of the learning processes in infants, demonstrating its growing scope (Baillargeon and DeJong 2017). For more detailed information, please refer to the relevant literature (Dejong and Mooney 1986).

The approach based on FRAM in this study can be interpreted in line with EBL. Initially, the EBL step of discarding non-relevant features from the training instances to create a model corresponds to the phase in which the FRAM model is constructed from the case study of worker performance. In this step, based on the results of the Work Domain Analysis, which includes domain-specific knowledge, we extracted only the functions related to attention distribution in multitasking, which is the focus of this study, to construct the FRAM model. The construction of the FRAM model in this study aligns with the first step of EBL, which involves creating a causal model by extracting only the information relevant to the target concept from various information in the training instances. Furthermore, the simulation study step in this research is analogous to generalizing the causal model derived from a single instance. In this step, our study differentiated the models of expert and mid-level workers in the FRAM model construction phase above and compared the simulation results to identify crucial functional structures in tacit knowledge. Thus, the simulation study in this research corresponds to identifying generalizable variables and constants from the constructed causal model. As outlined above, the methodology used in this study, which focuses on the overall structure of tacit knowledge, is consistent with EBL based on a limited number of instances. This study believes it has gained substantial insights even with few participants by adopting such a deductive learning approach.

7.4 Limitations and future work

The current research has some limitations. First, since FRAM models the target work at an abstract level, it is challenging to correspond to simulation results and actual data. It is necessary to overcome this point to validate the FRAM model further. Second, the present research had a limited number of experiment participants. Assembling a large number of skilled personnel for a particular task is often fraught with difficulties. In the case study of this research, there were inherently few workers engaged in the task under analysis, and it was impossible to recruit additional participants for the same work. The issue of skill transfer is pronounced in smaller enterprises where resources are relatively limited, making it difficult to avoid this problem. This study adopted a deductive learning approach that extracts explanatory structures from a limited number of cases, responding to this aspect. However, it is anticipated that further insights can be gained by combining this with an inductive learning approach based on a larger sample size. Future work will also examine the features of expert workers in other subjects and determine whether there are common attributes. Third, WDA and FRAM currently need more objectivity in building a model. An objective and systematic method of carrying out these procedures must be developed. Finally, the present study employed a static FRAM model for analyzing adaptive behavior. The FRAM model should dynamically change over time as workers transform their practices in response to environmental changes. FRAM needs to be further extended to investigate this feature.

8 Conclusion

This study aimed to investigate the attention management strategies of expert operators in multitasking. This expert’s feature is crucial to adaptively cope with daily work variabilities and maintain a resilient work performance. For this purpose, this study utilized the framework based on the functional structure of tacit knowledge. The data from a case study focusing on the steel plate processing operator was applied. First, the eye movement and interview analysis was conducted to clarify the proximal and distal aspects of the target work. The results showed that the expert operator could maintain attention management systematically in multitasking by understanding the abstract relations in the system. Then, the model constructive approach based on WDA and FRAM was taken. The identified attention management strategies were incorporated into the FRAM model structure. The simulation study showed that the expert’s attention management strategy contributed to the resilient work performance in multitasking. In the data collection process conducted in this study, there was a limitation due to the small number of participants; however, this study took a deductive learning approach, and it was possible to test hypotheses based on the relationship between the proximal and distal terms of tacit knowledge through a multifaceted approach centered on FRAM. It was shown that the integrated approach based on the concept of tacit knowledge is useful and applicable to manufacturing works.