Learning curve constraint cell automaton model for the lean production of CFRP airframe components

  • Tetsuya MorimotoEmail author
  • Satoshi Kobayashi
  • Yosuke Nagao
  • Yutaka Iwahori
Open Access


A new model is proposed for the lean production of carbon fiber reinforced plastic (CFRP) airframes. Our method improves the production rate by determining the ideal human-capital balance and inventory density on the factory line. The proposed model is derived as a two-step process: First, an analytical solution for the learning rate shift with a human-capital ratio is obtained by merging the Wright learning curve model into the Cobb-Douglas production function. Second, the solution is factored by an asymmetric simple exclusion process (ASEP) cell automaton model to assess whether the inventory density negates the theoretical learning effect. Recent moves toward lean production mean that aerospace CFRPs have a limited shelf life, minimizing buffer periods under metastable and stable production in the time discrete ASEP model. The shift from metastable to stable changes the production rate. Combined with the fact that ASEP is known to drastically reduce throughput if the production steps are not harmonized, the shipment probability p at each step becomes less than 1. Therefore, the human learning effect, which can alter the shipment rate, must be controlled so that p=1 at each production step. This paper describes the analytical aspects of the apparent learning rate to determine adequate values for the human and capital resources, and thus harmonize the learning rates of the production steps. The analytical model shows that factory planning dominates the production rate of CFRP aerospace components. The model is applied to Boeing 787 production data, and it is found that a reduction in inventory density could improve the apparent delivery rate up to the maximum of the human potential.


CFRP Airframe component Cell automaton Wolfram rule 184 Asymmetric simple exclusion process (ASEP) Lean production Airframe production Wright learning curve Cobb-Douglas production function Human fraction Man-hour 



Asymmetric Simple Exclusion Process


Cell Automaton


Carbon Fiber Reinforced Plastic


Dream lifter Operations Center


Lean Production Concept


Theory of Constraints


Shipment Probability


Learning Rate


ith Production Factor in Operation


ith Production Factor in Idle


Operational Time of ith Production Factor


Idle Time of ith Production Factor


ith Buffer Factor in Operation


ith Buffer Factor in Idle


Operational Time of ith Buffer Factor


Idle Time of ith Buffer Factor


Throughput Ratio, defined as the throughput

rate of the whole production chain divided by

the rate of each production chain


Work Density, defined as the input rate divided

by the upper bound of throughput


Man-Hours of the N t h Product


Man-Hour Reduction Rate

\(\dot {N}\):

Production Rate at Nth Product


Man-Hours of Human Activities


Man-Hours of Automated Machines


Man-Hour Reduction Rate in the Extreme

Case where the Capital Fraction is 0


Man-Hour Reduction Rate in the Extreme

Case where the Capital Fraction is 1


Adjustment Factor at a Fixed Time


Partial Elasticity of Capital Input


Partial Elasticity of Human Input


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Copyright information

© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Tetsuya Morimoto
    • 1
    Email author
  • Satoshi Kobayashi
    • 2
  • Yosuke Nagao
    • 3
  • Yutaka Iwahori
    • 1
  1. 1.Japan Aerospace Exploration Agency (JAXA)Mitaka-shiJapan
  2. 2.Tokyo Metropolitan UniversityHachioji-shiJapan
  3. 3.Kanagawa Institute of TechnologyAtsugi-shiJapan

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