A group learning curve model with motor, cognitive and waste elements
Introduction
Manufacturing firms have increasingly been using workers in groups on the floor level (Lantz et al., 2015, Moreland et al., 2002). Working in groups is the practice, especially at the final assembly stage of large and complex products (Martignago et al., 2017, Yazgan et al., 2011). Lack of coordination and conflicts that might arise between group members impede their performance. Resolving those issues before initiating work, results in better worker utilization and, subsequently, group performance (Yilmaz & Yilmaz, 2016). Product customization is the trend for many manufacturing firms. Frequent changes in product design and production processes are the norm in work environments like those, requiring workers to adapt to them, and learn new tasks as they do through learning-by-doing (Letmathe & Rößler, 2019, Tilindis and Kleiza, 2017, Uzumeri and Nembhard, 1998). In such an environment, it is usually uncommon to have clear instructions on how to perform tasks effectively and efficiently. Other examples include rush orders (Engström, Jonsson, & Johansson, 1996) and rework (Badiru, 1995). Additionally, the number of workers assigned to a task may exceed the optimum, and group coordination becomes more complicated. All the above studies emphasize the importance of group learning, and further, its predictability by utilizing learning curve models.
The question about what affects learning has captured the attention of numerous researchers in various fields. The purpose has been to mathematically model learning as a function of known variables. Manufacturers produce products, typically, in lots. They have been using cumulative production, independent variable, as a proxy for measuring experience, which also has been the traditional approach for modelling the learning curve (Glock et al., 2019, Jaber, 2011, Yelle, 1979). There has been a debate in the literature, whether cumulative production, alone, appropriately represents learning. Some researchers have suggested learning to be time-dependent; others have stated that cumulative production overstates its persistence (Jaber & Sikström, 2004), while few have argued that having it alone underrepresents the learning data. However, none has proposed excluding it (Jaber & Sikström, 2004). The most commonly used univariate model is the Wright (1936) learning curve, henceforth WLC (Jaber, 2011). It has been popular among managers as it is easy to use; i.e., it could be transformed into a straight line once plotted on a log-log paper, and shown to fit many data sets well. However, it has a fundamental drawback as its results are not meaningful when learning ceases; i.e., it enters a plateau. Thus, this drawback has been an appropriate starting point for further developments of learning curve models (Jaber, 2011), ones that represent empirically gathered data better. The earliest along this road is the de Jong’s model (1957), henceforth DJLC, who introduced a plateauing parameter that represents the minimum processing time, which is similar to the plateau model of Baloff (1971). Readers may refer to Glock et al. (2019) for a list of learning curves with plateauing. There has not been a consensus on what causes plateauing. Researchers have associated it with different causes (e.g., Jaber and Guiffrida, 2004, Peltokorpi and Niemi, 2019a, Yelle, 1979). Some researchers have modelled learning curves as bivariate or multivariate models (Badiru, 1992). For example, using a 4-year empirical data from an electronics manufacturing plant, Badiru (1995) presented a learning curve with cost per unit as the dependent variable and production level, the number of workers, downtime, and rework as the independent variables.
Thus, besides the numerical presentation of learning, industrial learning curves aim to show where improvement is needed. In this context, Yelle (1979) and Dutton and Thomas (1984) concluded that the factors underlying the learning curve are not well understood. Thomas and Yiakoumis (1987) continued with the same line of research and introduced a concept of the factor model for construction productivity. The model considers a learning curve for a crew of workers performing repetitive tasks. It states that many random factors disturb the work environment and, subsequently, crew performance. The study advocated that aggregating the factors that cause disturbance and representing them mathematically in one learning curve could result in an ideal model. Dar-El et al., 1995, Jaber and Glock, 2013, who combined motor and cognitive elements, and Jaber and Guiffrida (2004), who included the additional time to rework defective items, are examples of aggregated learning curves for individual performance.
Alongside individual learning, group learning has received growing attention. Argote, Gruenfeld, and Naquin (2001, p.370) defined group learning as “the activities through which individuals acquire, share and combine knowledge through experience with one another.” Leavitt (1951) experimented on how knowledge sharing occurs among group members. The experiment consisted of a hundred students divided into groups of five, with each group member receiving a card having five symbols. The group’s task was to find which symbols appeared on all cards. The members were allowed to write messages and send them according to a communication pattern. Leavitt (1951) showed that not all communication patterns used were effective. Few researchers have expanded upon Leavitt’s experiment to explore the effects of group organization (Guetzkow & Simon, 1955) and planning (Shure, Rogers, Larsen, & Tassone, 1962). They showed that the WLC model describes well the performance of novice groups when learning tasks (Baloff & Becker, 1968). The above experimental studies on group learning did not consider varying group sizes. However, they improved our understanding of the dynamics of the transfer of knowledge among group members, implicitly linked to group size. In practice, the number of coordination links increases with increasing the group size, making a group inefficient (Steiner, 1972).
As per the group learning definition (Argote et al., 2001, p.370), many group learning curve models considered the transfer of knowledge as an additional measure to cumulative production or the number of repetitions (Glock and Jaber, 2014, Ingram and Simons, 2002, Méndez-Vázquez, 2019, Ryu et al., 2005, Wilson et al., 2007). Glock and Jaber (2014) proposed a group learning curve model that has two components, one describing individual learning and the other the transfer of knowledge among the group members. Furthermore, two factors in their model impact the success of knowledge transfer. The first is knowledge compatibility, and the second is the willingness of group members to share and absorb it among themselves. According to the prevailing theory, the model of Glock and Jaber (2014) assumes an increasing delay in the transfer of knowledge as a function of increasing group size. A group learning curve is formed by aggregating the learning curves of the individuals in a group (e.g., the sum of all WLCs), which happens when knowledge of the members is neither compatible nor transferable. Knowledge incompatibility and the unwillingness to share it impede its transfer. Their proposed model fitted experimental group learning data rather well. They also compared the fits to a model that was an aggregation of individual learning curves and their model outperformed it. However, the data sets fitted to models do not consider varying group sizes.
The model of Méndez-Vázquez (2019) is the only model that differentiates the effect of process loss from that of knowledge transfer in a group. Process loss occurs when the group’s actual performance falls below potential because of coordination, motivation and relational processes between group members. Using the data from Peltokorpi and Niemi (2019a), the process loss parameter was estimated and assumes a fixed value, which increases with group size. Méndez-Vázquez (2019) tested various scenarios (degrees, percentages) of knowledge transfer and process loss and used the developed model for simulation and optimization purposes. For future research, she suggested the development of mathematical models with the effect of knowledge transfer derived from experimental data.
Camm and Womer (1987) developed a bivariate model that has the production rate as the dependent variable and crew size and the number of repetitions as the independent variables. They estimated the model using empirical production data. They did not fit the model to data as they have not mentioned so in their article. The model of Camm and Womer (1987), to the authors’ knowledge, is the only one of its form in the literature.
The paper at hand considers a group task that is divisible into sub-tasks as per Steiner (1972), with group performance being the additive and interactive efforts of individuals in a group (Witte & Davis, 2013). Previous experimental studies for such assembly tasks (e.g., Peltokorpi and Niemi, 2019a, Sando et al., 2011, Staats et al., 2012, Ryall et al., 2004) verify the diminishing returns in output with increasing group size, in line with the hypothesis of Steiner (1972, p.96). The group learning curve models in the literature associate diminishing returns in output to either delay in the transfer of knowledge (e.g., Glock & Jaber, 2014), process loss (Méndez-Vázquez, 2019) or overmanning (Camm & Womer, 1987), i.e., having more workers on a task than its optimal group size. However, the above models have not been fitted to empirical data containing varying group sizes. More importantly, there is a lack of group learning curve models comprising of measurable elements from real industrial tasks. By aggregating, for example, different waste elements into a learning curve would provide insights for managers on how to improve working and speed up learning.
This paper, therefore, addresses this research gap by proposing a bivariate group learning curve model, an aggregation of the motor, cognitive and waste elements. This study achieves this goal by conducting additional analysis of the data in Peltokorpi and Niemi, 2019a, Peltokorpi and Niemi, 2019b. The experiment of Peltokorpi and Niemi (2019a) consisted of assembling a product whose components came from real industrial products. Students as surrogates for workers did the assembly, including the work assignment and management. The conductor of the experiment has not instructed them on how to. They measured the time it took to assemble the product by a worker and a group of workers of sizes 2, 3, and 4 for four consecutive repetitions. The results first showed that, for novice workers, assembly time decreases, and learning occurs rapidly through repetition. The learning data for each group size fitted De Jong (1957) model almost perfectly, suggesting that learning plateaus. Second, productivity per worker decreased smoothly as a function of increasing group size, according to the hypothesis from Steiner (1972, p.96). Peltokorpi and Niemi (2019b) conducted a further analysis of the data to gain insights into the factors affecting group performance. More precisely, by using a video-based activity analysis the assembly time was broken down into the following elements: (1) value-added time (refers to part installation), (2) necessary movements, (3) time used to read instructions, and (4) waste (comprising different types of inefficiencies at work). The results showed that much of the time for assembling the product for the first time contained reading instructions and waste due to inexperience. This further causes productivity losses with larger groups at first repetitions. Idleness that large groups experience negatively affects performance in later repetitions. This observation was due to a lack of meaningful tasks and working space for several workers at the end of processing.
Data from the aforementioned experiment is the first to account for the size of a group and the number of repetitions as independent variables. By utilizing this data, the present paper shows the following contributions:
- 1.
The paper develops a bivariate group learning curve aggregated from three task elements: motor, cognitive, and waste. This model contributes to current literature that lacks group learning curve models comprising of measurable elements of real industrial tasks.
- 2.
The developed aggregated model represents the data better than two non-aggregated models derived from literature. The parameter values for the effects of group size and repetition for each task element over the entire learning period provide insights that managers could use to improve the performance of their workforce.
The rest of the paper is structured as follows. Section 2 provides a background to the learning curves that are relevant to this study. Section 3 presents the group learning experiment. Section 4 develops five bivariate group learning curve models: three aggregated models and two non-aggregated log-linear models. The developed models are fitted to experimental data, and their results are compared. The parameter values of the models are analyzed to gain insights into the effects of group size and the number of repetitions on different elements of assembly work. Section 5 presents the conclusions and provides aspects for further research.
Section snippets
Background to learning curves
Learning is a natural phenomenon where human performance improves each time he/she repeats a task or activity (Glock et al., 2019, Jaber, 2011). Task repetition reduces the time to recall procedural information (Dar-El et al., 1995), improves familiarity with a product and process (Peltokorpi & Niemi, 2019b), and eliminates inefficiencies (i.e., errors and unnecessary and faulty activities and movements). Numerous learning curve models aim to represent empirically gathered learning data, and
Experiment on group learning
This section briefly describes the experiment conducted by Peltokorpi and Niemi (2019a). It starts with the product structure and assembly steps, followed by an overview of the participants, the assembly procedure, and the experimental data, respectively.
A group learning curve model
In this section, five group learning curve models are developed and fitted, in the next subsection, to the experimental data of Table 1, Table 2. This is followed by two subsections that provide additional analysis of the values of the learning curve parameters and a comparison of the models, respectively.
Conclusions
This paper developed an aggregated bivariate group learning curve model of motor, cognitive and waste elements. The number of workers in a group, and the number of repetitions are the independent variables for each bivariate model. The dependent variable is the time per unit to assemble a unit. Each of the bivariate models contributed a fraction to the time per unit. The fits of the developed models were tested using the empirical data of Peltokorpi and Niemi, 2019a, Peltokorpi and Niemi, 2019b
CRediT authorship contribution statement
Jaakko Peltokorpi: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Resources, Data curation, Writing - original draft, Writing - review & editing, Visualization, Project administration, Funding acquisition. Mohamad Y. Jaber: Methodology, Software, Validation, Resources, Writing - review & editing, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The research of Dr Jaakko Peltokorpi was funded by a grant (no. 201800421) from KAUTE – The Finnish Science Foundation for Technology and Economics. He also thanks Ryerson University for the in-kind support.
Mohamad Y. Jaber thanks the Social Sciences and Humanities Research Council (SSHRC) of Canada (no. 435-2020-0628) for supporting his research.
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