Collision Probability in an In-Line Equipment Model under Erlang Distribution

Eishi CHIBA  Hiroshi FUJIWARA  Yoshiyuki SEKIGUCHI  Toshihide IBARAKI  

IEICE TRANSACTIONS on Information and Systems   Vol.E96-D   No.3   pp.400-407
Publication Date: 2013/03/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E96.D.400
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science — New Trends in Algorithms and Theory of Computation —)
stochastic model,  collision probability,  Erlang distribution,  closed form,  approximation,  

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Flat Panel Displays (FPDs) are manufactured using many pieces of different processing equipment arranged sequentially in a line. Although the constant inter-arrival time (i.e., the tact time) of glass substrates in the line should be kept as short as possible, the collision probability between glass substrates increases as tact time decreases. Since the glass substrate is expensive and fragile, collisions should be avoided. In this paper, we derive a closed form formula of the approximate collision probability for a model, in which the processing time on each piece of equipment is assumed to follow Erlang distribution. We also compare some numerical results of the closed form and computer simulation results of the collision probability.