The case for modeling correlation in manufacturing systems

Manufacturing-related models have traditionally made independence assumptions on associated stochastic processes in order to achieve tractability of analytical models and simplify Monte Carlo models. This paper aims to alert users to potential deleterious implications stemming from unfounded independence assumptions in traditional stochastic models of manufacturing systems. Specifically, it demonstrates the dramatic impact that appreciable autocorrelations can have on manufacturing performance measures through a preliminary study of prediction errors incurred in ignoring dependence. To this end, the study compared performance measures of common manufacturing models with renewal components to their autocorrelated counterparts, drawn from the TES (Transform-Expand-Sample) class. TES models constitute a versatile class of stochastic processes, designed to capture empirical distributions and autocorrelations, simultaneously, and as such, are suitable for both Monte Carlo simulation and analytical modeling of autocorrelated time series. A brief overview of simple TES processes and their generation algorithms is also included.