Collision probability in an in-line machines model

  • Authors:

  • Eishi Chiba;Tetsuo Asano;Takeshi Miura;Naoki Katoh;Ikuo Mitsuka

  • Affiliations:

  • Department of Industrial and Systems Engineering, Faculty of Science and Engineering, Hosei University, Tokyo, Japan;School of Information Science, Japan Advanced Institute of Science and Technology, Nomi, Japan;Hitachi, Ltd., Kawasaki, Japan;Department of Architecture and Architectural Engineering, Graduate School of Engineering, Kyoto University, Kyoto, Japan;FEBACS Co., Ltd., Kyoto, Japan

  • Venue:
  • Transactions on computational science XIII
  • Year:
  • 2011

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Abstract

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.