The generation of random families of parts for manufacturing systems simulation

Abstract

This paper provides a method for a manufacturing systems designer to generate the processing times of random families of parts from expert predictions or descriptions for the purposes of systems simulation. This approach is especially useful in circumstances in which it is not possible to collect data on parts' processing times or in which the family of parts to be produced is not currently realized, but is based on longer term market analysis and technological forecasts.

Appropriate marginal distributions on processing times are provided by use of the inverse transformation method. The correlation structure between machines and between parts is also modelled from the expert data in order to provide samples from the random matrix representing the processing times of the various parts on different machines. This is difficult in general, since it is necessary to provide samples from a random matrix whose row vectors and columns vectors have independent correlation structures.

The difficulties of providing samples with representative correlation matrices amongst both machines and parts are resolved by using an approximation method for intermachine correlations along with some assumptions concerning the nature of manufacture in a modern multi-product environment.