Collision Probability in an In-Line Machines Model

  • Eishi Chiba
  • Tetsuo Asano
  • Takeshi Miura
  • Naoki Katoh
  • Ikuo Mitsuka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6750)


This paper presents a simple model of the manufacturing line which focuses on the performance of collision probability, and a method of application to the manufacture of Flat Panel Displays (FPDs) and semiconductors. We derive an approximate formula of the collision probability. When the processing time follows a normal distribution, we also did simulations to evaluate the exact probabilities and confirm that our approximation approach yields reasonable results compared to the simulated results. Moreover, we simplify our approximate formula of the collision probability. Concretely speaking, we derive a closed form formula when the processing time follows an exponential distribution. Finally, we present an optimization problem with the collision probability and show a method to solve it.


In-line machines model Tact time Collision probability Approximation Closed form Optimization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Eishi Chiba
    • 1
  • Tetsuo Asano
    • 2
  • Takeshi Miura
    • 3
  • Naoki Katoh
    • 4
  • Ikuo Mitsuka
    • 5
  1. 1.Department of Industrial and Systems Engineering, Faculty of Science and EngineeringHosei UniversityTokyoJapan
  2. 2.School of Information ScienceJapan Advanced Institute of Science and TechnologyNomiJapan
  3. 3.Hitachi, Ltd.KawasakiJapan
  4. 4.Department of Architecture and Architectural Engineering, Graduate School of EngineeringKyoto UniversityNishikyoJapan
  5. 5.FEBACS Co., Ltd.Shimogyo-kuJapan

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