Learning Curve Model Research Articles

Identification and assessment of regression models of the learning curve 
 for automotive manufacturing

The problem of identification and assessment of the reliability of regression models of the learning curve for the automotive industry is considered. For regression analysis, four learning curve models of a given type are used: Wright's, Stanford-B, Deyong's, and exponential. The parameters of the learning curve models are determined using a nonlinear least squares method. The estimation of the significance and reliability of the regression models is carried out. It is shown that the models of learning curves in the automotive industry are well approximated by the Stanford-B power function.

A new learning curve with fatigue-dependent learning rate

Learning and fatigue are consequences of task repetitiveness and have significant effects on an individual's performance. Despite the importance of the problem at hand, only a few studies have formulated their combined effect in a learning curve context. This paper contributes to this line of research, and unlike other models, proposes a learning curve model with a fatigue level-dependent learning rate. The proposed model has been validated using data from an order-picking task and its predictive ability has also been tested against potential models in the literature. The results show that the proposed learning curve outperforms the other models according to efficiency and balance criteria. The sensitivity analysis indicates the effect of the model's parameters on the selected system's measures and provides some managerial insights.

Projecting the Price of Lithium-Ion NMC Battery Packs Using a Multifactor Learning Curve Model

Renewable energy (RE) utilization is expected to increase in the coming years due to its decreasing costs and the mounting socio-political pressure to decarbonize the world’s energy systems. On the other hand, lithium-ion (Li-ion) batteries are on track to hit the target 100 USD/kWh price in the next decade due to economy of scale and manufacturing process improvements, evident in the rise in Li-ion gigafactories. The forecast of RE and Li-ion technology costs is important for planning RE integration into existing energy systems. Previous cost predictions on Li-ion batteries were conducted using conventional learning curve models based on a single factor, such as either installed capacity or innovation activity. A two-stage learning curve model was recently investigated wherein mineral costs were taken as a factor for material cost to set the floor price, and material cost was a major factor for the battery pack price. However, these models resulted in the overestimation of future prices. In this work, the future prices of Li-ion nickel manganese cobalt oxide (NMC) battery packs - a battery chemistry of choice in the electric vehicle and stationary grid storage markets - were projected up to year 2025 using multi-factor learning curve models. Among the generated models, the two-factor learning curve model has the most realistic and statistically sound results having learning rates of 21.18% for battery demand and 3.0% for innovation. By year 2024, the projected price would fall below the 100 USD/kWh industry benchmark battery pack price, consistent with most market research predictions. Techno-economic case studies on the microgrid applications of the forecasted prices of Li-ion NMC batteries were conducted. Results showed that the decrease in future prices of Li-ion NMC batteries would make 2020 and 2023 the best years to start investing in an optimum (solar photovoltaic + wind + diesel generator + Li-ion NMC) and 100% RE (solar photovoltaic + wind + Li-ion NMC) off-grid energy system, respectively. A hybrid grid-tied (solar photovoltaic + grid + Li-ion NMC) configuration is the best grid-tied energy system under the current net metering policy, with 2020 being the best year to deploy the investment.

Endoscopy for the treatment of posterior ankle impact syndrome: Learning curve

BackgroundThis study aimed to demonstrate our learning curve of endoscopy for the treatment of Posterior Ankle Impact Syndrome (PAIS), assessing the operative time and evolution of the outcomes. MethodsWe conducted a retrospective review of 39 patients submitted to endoscopic treatment by a single surgeon over a period of ten years. We divided the study population into four blocks of ten consecutive patients and compared the mean operative time and outcomes between the four blocks. For the learning curve model, we performed linear regression analysis and logarithmic transformation. ResultsWe found a decrease in the surgery duration over time (P = .0273). All patients had an improvement in the AOFAS Scale (P < .0001), regardless of the group (P = .07). The learning rate was estimated at 83%, indicating a 17% reduction of the operative time as the cumulative cases doubled. ConclusionsThis study showed a decrease in the operative time of the posterior ankle endoscopy over the years, with an estimated learning rate of 83%. The outcomes and incidence of complications showed no relationship with operative time and the number of cases operated. Level of EvidenceLevel IV, case series

Investigation and Comparative Analysis of Learning Curve Models on Construction Productivity: The Case of Caisson Fabrication Process

Abstract Learning curves in construction operations analysis is deemed as one of the main factors that determine the variation of on-site productivity and is always taken into account during the planning and estimation stage. This research attempts the assessment of learning curve models’ suitability for the effective analysis of the learning phenomenon for construction operations that are fairly complicated concerning a floating caisson fabrication process for a large-scale marine project, using productivity data. This paper investigates the role of published learning curve models (i.e. Straightline or Wright; Stanford “B”; Cubic; Piecewise or Stepwise; Exponential) by comparing their outcomes through the use of both unit and cumulative productivity data. There are two main research objectives: first, the model best fitting historical productivity data of construction activities that have been completed are investigated, while secondly, an attempt is made to determine which model better predicts future performance. The less actual construction data deviate from each model’s yielded results, the better their suitability. In the case of unit data, the cubic model fits better historical data, while in the case of future predictions, the Stanford “B” model provides better results. Respectively, the Cubic model yields better results when using cumulative data on historical data and the Straight-line model predicts in a more reliable fashion future performance Possible extensions could be developed in the area of future performance predictions, by adopting different data representation techniques (e.g. moving/exponential weighted average) or by including other (non-classic) learning curve models (e.g. DeJong, Knecht, hyperbolic models).

Defect detection method of magnetic disk image based on improved convolutional neural network

This paper proposes an efficient method for defect detection of magnetic disk image based on improved convolutional neural network. We build a model named DiskNet on the basis of VGGNet-19, in which the optimal activation function is selected predictively through a weighted probability learning curve model (WP-Model). First, we use Markov Chain Monte Carlo (MCMC) to infer the predicted value and determine prediction probability. Then, the evaluation point (EP) is determined by the effective information of training curve. In the process of DiskNet training, when the prediction probability is higher than the threshold, the neural network will select the current activation function. If the training epochs exceed the EP and the threshold is not reached, the original activation function will be used. The experimental results show that the accuracy of the proposed method in detecting defects on the magnetic disk image data set is 96.9%.

The Variance Learning Curve

The expansive learning curve literature in Operations Management has established how various facets of prior experience improve average performance. In this paper, we explore how increased cumulative experience affects performance variability, or consistency. We use a two-stage estimation method of a heteroskedastic learning curve model to examine the relationship between experience and performance variability among paramedics at the London Ambulance Service. We find that for paramedics with lower experience, an increase in experience of 500 jobs reduces the variance of task completion time by 8.7%, in addition to improving average completion times by 2.7%. Similar to prior results on the average learning curve, we find a diminishing impact of additional experience on the variance learning curve. We provide an evidence base for how to model the learning benefits of cumulative experience on performance in service systems. Our findings imply that the benefits of learning are substantially underestimated if the consistency effect is ignored. Specifically, our estimates indicate that queue lengths (or wait times) might be overestimated by as much as 4% by ignoring the impact of the variance learning curve in service systems. Furthermore, our results suggest that previously established drivers of productivity should be revisited to examine how they affect consistency, in addition to average performance.

A group learning curve model with motor, cognitive and waste elements

Nowadays, workers, individually or in groups, are continually learning new tasks. The speed at which they learn directly contributes to the success of their firms in competitive markets. Learning curve research has been either on the individual or organizational level. A few papers have developed learning curve models for a group of workers, even fewer that used empirical data for that purpose. However, none of the existing models comprises measurable elements from real industrial tasks. This paper aims to fill this gap in the literature by proposing a bivariate group learning curve model, an aggregation of three learning curves where the number of workers in a group, and the number of repetitions are the independent variables. The dependent variable is the unit assembly time. The three learning curves represent motor, cognitive, and waste per unit assembled. The aggregated learning curve was fitted to experimental data consisting of different group sizes (1 to 4 students/workers), each performing four repetitions, and later compared to two log-linear learning curves, with and without plateauing. The results showed that the aggregated model represented the data the best and that segmenting waste into sub-elements (job familiarization, errors, and group coordination) improved the performance of the model. The parameter values affected by group sizes and repetitions for each task element provided insights that managers could use to improve the performance of their workforce.

Cost reduction or electricity penetration: Government R&D-induced PV development and future policy schemes

Government policies and investments in photovoltaic (PV) research and development (R&D) have contributed to the rapid development of a PV industry through technology push in most countries over the past decade. It is worth investigating the effectiveness of investment-drive R&D policies at a global level, particularly how they work in reducing the costs of PV technologies. This study constructs a learning curve model to assess the performance of PV R&D policies in China, Germany, the United States and Japan. Market information—for example, PV module production, PV installation and PV technology improvement—is utilised to analyse how these policies take effect. The results show that PV R&D investments are efficient in decreasing the production costs of PV modules, which positively affects the development of PV module markets. However, weak PV technology conditions (including conversion efficiency, reliability) and low PV electricity penetration levels have resulted in surpluses in PV module markets, as well as PV electricity curtailment around the world. It is suggested that future R&D policies should contribute more to improving conversion efficiencies (the structure of technology push power) and grid integration technologies (demand pull power) for PV systems.

The effect of switching renewable energy support systems on grid parity for photovoltaics: Analysis using a learning curve model

Renewable energy electricity, such as photovoltaic (PV) power generation, has the benefits of strengthening energy security, addressing climate change, reducing air pollution, etc., but there are some impediments to deployment of renewable energy electricity: higher costs than fossil fuels, intermittent energy production, site constraints, etc. Korea changed its renewable energy electricity support systems from feed-in tariff (FIT) to a renewable portfolio standard (RPS) in 2012. This study evaluates FIT versus RPS in terms of the time to reach grid parity for PVs. Using a learning curve model, we calculate the learning rate of PV power generation during the FIT and RPS periods. We find that the PV learning rate during the RPS period was 18.44%, much higher than that during the FIT period, −0.28%, and R2 is 0.9861 and 0.7346 in the RPS and FIT periods, respectively. Using the calculated learning rate in the RPS period, we also predict that grid parity for PVs is expected in 2025 in Korea.

Global Spatio-Temporal Attention for Action Recognition Based on 3D Human Skeleton Data

The human skeleton joints captured by RGB-D camera are widely used in action recognition for its robust and comprehensive 3D information. Presently, most action recognition methods based on skeleton joints treat all skeletal joints with the same importance spatially and temporally. However, the contributions of skeletal joints vary significantly. Hence, a GL-LSTM+Diff model is proposed to improve the recognition of human actions. A global spatial attention (GSA) model is proposed to express the different weights for different skeletal joints to provide precise spatial information for human action recognition. The accumulative learning curve (ALC) model is introduced to highlight which frames contribute most to the final decision making by giving varying temporal weights to each intermediate accumulated learning results. By integrating the proposed GSA (for spatial information) and ALC (for temporal processing) models into the LSTM framework and taking the human skeletal joints as inputs, a global spatio-temporal action recognition framework (GL-LSTM) is constructed to recognize human actions. Diff is introduced as the preprocessing method to enhance the dynamic of the features, thus to get distinguishable features in deep learning. Rigorous experiments on the largest dataset NTU RGB+D and the common small dataset SBU show that the algorithm proposed in this paper outperforms other state-of-the-art methods.

A novel virtual resource pricing policy based on game model in federated clouds

In recent years, more and more cloud providers are unified together to form a federated cloud market, where a suitable pricing strategy plays a key role to help they attracting more users. However, many existing pricing policies can not deal with the competition between different cloud providers. In this study, we take efforts on the resource pricing policy in federated cloud market. To obtain an optimal pricing scheme among multiple IaaS providers (ISPs), we firstly use the learning curve model to model the production supply behaviours of ISPs, and then we use a standard Markov decision process to describe the pricing game model and present an efficient algorithm to solve this game model in a distributed manner. The proposed pricing model has been fully investigated and evaluated in a real-world federated cloud platform, and the results indicate that it can significantly improve the profits of ISPs comparing to several existing pricing mechanisms.

Application of Learning Curves in Operations Management Decisions

In the time of industry 4.0 and big data, methods which are based on the collection and the processing of a large amount of data in order to support managerial decisions have outstanding significance. The learning curve theory pertains to these methods. The purpose of this paper is to explore some application possibilities of the classical learning curve in manufacturing and service operations. The learning effect assumes that as the quantity of units manufactured increases, the time needed to produce an individual unit decreases. The function describing this phenomenon is the learning curve. Various learning curves have been developed and applied in the area of production economics and much research studies the significance of the learning effect in management decisions. This study summarizes the main learning curve models and demonstrates how learning can be considered in three classical areas of operations management. First, the calculation of economic manufacturing quantity in the presence of learning is studied. Next, the effect of learning in break-even analysis and assembly line balancing is explored. The results show that with the consideration of the learning effect, calculations become more complex and require greater efforts, but the application of the learning curve concept can provide valuable insight both at operational and strategic levels.

The grid parity analysis of onshore wind power in China: A system cost perspective

The grid parity of wind generation has drawn increasing attention owing to the serious subsidy funding shortages in China, but scientific evidences for the grid parity feasibility are still not sufficient, because most studies have neglected the additional balancing cost and grid-connection cost caused by the wind generation. We hence develop an integrated methodology to analyze the grid parity of onshore wind generation from a system cost perspective, coupling a system generation cost model, a grid parity index model and a learning curve model. Key findings are summarized as follows: (1) The average system cost of wind generation declined from 0.84 yuan/kWh in 2006 to 0.57 yuan/kWh in 2017. Guangdong has the highest system cost, while Xinjiang costs the least. (2) The traditional LCOE approach underestimates the wind generation cost by about 15%, resulting in biased conclusions regarding the grid parity. (3) All the provincial grid parity indexes have values more than 1, indicating that the current grid parity of wind generation is impractical. (4) The national average grid parity time of wind generation are forecasted to be 2021, 2023 and 2026 when the on-grid coal generation prices are 0.50 yuan/kWh, 0.45 yuan/kWh and 0.40 yuan/kWh, respectively.

Innovation modelling and multi-factor learning in wind energy technology

Learning curves are frequently cited to justify the subsidization of new technologies to facilitate market competitiveness. The main literature has focused on improving the specification of the basic learning curve model by augmenting it to control for technological development measured by public R&D expenditures. In addition to employing R&D expenditures, the purpose of this paper is to assess the robustness of an augmented multi-factor learning curve model by estimating learning rates in a panel framework utilising patent data on relevant wind power technologies in Germany, Denmark, Spain and the UK. Results indicate that both innovation proxies are qualitatively identical and generate consistent learning estimates. The paper also aims at exploring the presence of unit roots in learning curves and alerts to the possibility of spurious estimations. Renewable energy policy guided by learning curve estimates should therefore be implemented with caution.

A system dynamics modeling on wind grid parity in China

Abstract Renewable energy is growing quickly in China due to subsidies, but the short-term subsidies cannot maintain long-term stable development of the wind power industry. With increasing environmental risks, it is imperative to achieve wind power grid parity which is the base for market-driven development. But when and how to achieve wind power grid parity is a question worth studying. In this paper, a system dynamics model for studying wind power grid parity is established by combining economic growth theory, logistic learning curve model. The results show that it is difficult to achieve wind grid parity under the current situation (high cost, low utilization hours and serious curtailment), and wind power price will break through 0.4 CNY/kWh in 2023 and should be stable at 0.3 CNY/kWh in 2025. However, wind power grid parity may be reached in 2020 by linked with green certificate trading. Finally, policy implications on how to reduce corporate taxation, improve operational efficiency of wind power and link with green certificate trading can are proposed.

A two-factor learning model for private sector industrial firms

ABSTRACT The Cobb–Douglas form of the two-factor learning curve model has been the conventional choice in empirical studies of the relative importance of R&D versus capacity expansion for cost reduction in energy technologies. Most empirical studies have focused on the role of public R&D in the context of renewable energy technologies. In this study, we provide a rationale for considering a different model formulation of the tradeoff between R&D and production capacity expansion when studying technology development in the private sector and we compare it to the conventional Cobb–Douglas model. We then apply our model formulation to a particular emerging technology case study.

La curva de aprendizaje y su contribución al desempeño del talento humano en las organizaciones: una revisión teórica

Este documento presenta una revisión sobre el concepto de curva de aprendizaje, sus orígenes, modelos y principales aplicaciones. Se realizó una investigación documental, para la cual se consultaron bases de datos especializadas, abordando los principales autores y los aspectos característicos de cada modelo. Los hallazgos indican la importancia del estudio de las curvas de aprendizaje, tanto a nivel individual, grupal y organizacional. Estas últimas pueden ser fuente para la toma de decisión en las empresas, ya que los distintos modelos de curva de aprendizaje pueden brindar información, referente a: metas de producción, evaluación de rendimientos, estimación de mano de obra, optimización de precios y costos, para crear ventajas competitivas. Los trabajos revisados destacan el beneficio de las curvas de aprendizaje en temas como: la planeación, la capacitación y el control de procesos. Se concluye que las curvas de aprendizaje, si bien iniciaron en la industria de la aviación, se han difundido a diversos sectores industriales, con la aportación de nuevos modelos matemáticos para su estimación.

Heterogeneities in energy technological learning: Evidence from the U.S. electricity industry

While the role of organizational learning in improving firm performance is well documented, there are still questions on what drives technological learning. This is evident in the electricity industry where the growth of renewable energy technologies has been pervasive. Vicarious learning contributes to the adoption of emerging technologies through successful inter-firm knowledge sharing and transfer. However, there is hesitation to adoption that characterizes vicarious learning especially in the context of intra-firm learning. This paper investigates the differences in knowledge acquisition within and across electricity firms in the U.S. The learning curve model is applied to a longitudinal study of 5573 plants belonging to 1542 U.S. electricity firms between 1998 and 2010. This study finds: (i) The capacity growth of the solar photovoltaic technology is positively associated with intra-firm knowledge acquisition; (ii) The effect of financial incentives on the adoption of solar and wind technologies is higher under inter-firm learning; (iii) The higher the stringency of policy mandates, the more varied is the progress on technological change across technologies; (iv) Knowledge sharing between firms are higher for wind technology than for solar technology. These findings combine to show disparities in the learning trends of technologies across and within firms’ boundaries.

Competence in and Learning Curve for Pediatric Renal Transplant Using Cumulative Sum Analyses.

We assessed achievement of competence in pediatric renal transplant by developing a learning curve model for consecutive operations performed by a single surgeon. We retrospectively evaluated pediatric renal transplant cases performed by an index pediatric urologist during his first 15 years of being the primary transplant surgeon at our institution. Case characteristics, operative time and surgical complications within 30 days postoperatively were assessed and compared to those of a reference senior surgeon. To generate a learning curve plot, we performed a cumulative sum analysis to evaluate the evolution of operative times and surgical complications. During 15 years 55 pediatric renal transplants (17%) were performed by the index surgeon and 78 (24%) by the senior surgeon. Total operative time was shorter for the index surgeon (226 vs 252 minutes, p = 0.006), while ischemia time was longer (40 vs 30 minutes, p = 0.001). The 30-day surgical complication rates were similar (32.7% and 35.9%, p = 0.853). The learning curve showed that the complication rates and operative times did not increase following the 17th case. Ureteroureterostomy has been more commonly performed for ureteral anastomosis (p = 0.048) and longer warm ischemia time has been noted after reaching the peak of the learning curve (p = 0.003). We determined that technical skills for pediatric renal transplant can be achieved after the 17th case. We propose that a dedicated team with a pediatric urologist who has an interest in performing pediatric renal transplant secure more cases than the case volume determined in our study within the first few years of practice to maintain proficiency.