Variance of the output as a function of time: production line dynamics

Article Abstract:

Markovian models of discrete materials flow production systems were studied, particularly the transient properties of a production line. Specifically, mean and variance of the number of parts produced in a given time period conditioned on an arbitrary initial condition were determined by applying a Markov reward model. Closed-form expression for the variance of the output from a single unreliable station was derived to demonstrate the process. Then, variance of the output from a general two-station production line with a finite buffer was determined through a set of recursive equations that take advantage of the special structure of the probability matrix.

Assembly-line methods, Assembly lines

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On the M/G/1 machine interference model with spares

Article Abstract:

A recursive technique is used to calculate the steady state probability distribution of the number of down machines at arbitrary time epoch of a machine interference problem with spares. Several system performance indicators such as average number of down machines, average waiting time for repair, average number of spare machines, average number of operating machines, machine availability and operator utilization were determined for several repair time distributions.

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Analysis of a synchronization station for the performance evaluation of a kanban system with a general arrival process of demands

Article Abstract:

The analytical process of determining the performance of a kanban system manufacturing a single part type when the demands for the finished product arrive in a single unit according to a Poisson process, is extended to the case where demands arrive according to a general process. A matrix-geometric solution is suggested to resolve a quasi-birth-and-death process with an infinite number of states and with a very regular structure.

Just in time inventory systems, Just in time systems

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