Discrete Event Models for Flexible Manufacturing Cells

Abstract

A manufacturing system includes a set of machines performing different operations, linked by a material handling system. A major consideration in designing a manufacturing system is its availability. When a machine or any other hardware component of the system fails, the system reconfiguration is often less than perfect. It is shown that, if these imperfections constitute even a very small percent of all possible system faults, the availability of the system may be considerably reduced. The system availability is computed as the sum of probabilities of the system operational states. A state is operational when its performance is better than a threshold value. In order to calculate the availability of a manufacturing system, its states (each corresponding to an acceptable system level) are determined. A system level is acceptable when its production capacity is satisfied. To analyze the system with failure/repair process, Markov models are often used. As a manufacturing system includes a large number of components with failure/repair processes, the system-level Markov model becomes computationally intractable. In this paper, a decomposition approach for the analysis of manufacturing systems is decomposed in manufacturing cells. A Markov chain is constructed and solved for each cell i to determine the probability of at least Ni operational machines at time t. Ni satisfies the production capacity requirement of machine cell i. The probability is determined so that the material handling carriers provide the service required between Ni operational machines in machine cell i, and Ni+1 operational machines in machine cell i+1. The number i=1,...,n at time t, where n is the number of machine cells in the decomposed system. Production lines are sets of machines arranged so as to produce a finished product or a component of a product. Machines are typically unreliable and experience random breakdowns, which lead to unscheduled downtime and production losses. Breakdown of a machine affects all other machines in the system, causing blockage of those upstream and starvation of those downstream. To minimize such perturbations, finite buffers separate the machines. The empty space of buffers protects against blockage and the full space against starvation. Thus, production lines may be modeled as sets of machines and buffers connected according to a certain topology. From a system theoretic perspective, production 2