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Manufacturing-related 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 autocorrelation. 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. [ABSTRACT FROM AUTHOR]

This paper introduces a class of methods called TES (Transform-Expand-Sample) for generating autocorrelated variates with uniform marginals and Markovian structure. TES methods are readily implemented on a computer and have generation complexity comparable to that of the i.i.d, uniform sequence which they transform to an autocorrelated uniform sequence. For any prescribed correlation coefficient p, there is a IES method generating a uniform sequence with the 1-lag autocorrelation rho, and the resultant autocorrelation is monotonic quadratic in two structural TES parameters. A simulation study reveals that TES methods give rise to autocorrelation functions with monotone decreasing as well as oscillating magnitude, bounded by monotone envelopes. The structural parameters were found to control the "amplitude" and "frequency" of the resultant autocorrelation function. A third parameter can be used to transform a TES sequence into more continuous-looking versions and to control the skewness of sample path cycles. [ABSTRACT FROM AUTHOR]

Temporal shaping of time series is the activity of deriving a time series model with a prescribed marginal distribution and some sample path characteristics. Starting with an empirical sample path, one often computes from it an empirical histogram (a step-function density) and empirical autocorrelation function. The corresponding cumulative distribution function is piecewise linear, and so is the inverse distribution function. The so-called inversion method uses the latter to generate the corresponding distribution from a uniform random variable on [0,1), histograms being a special case. This paper shows how to manipulate the inverse histogram and an underlying marginally uniform process, so as to “shape” the model sample paths in an attempt to match the qualitative nature of the empirical sample paths, while maintaining a guaranteed match of the empirical marginal distribution. It proposes a new approach to temporal shaping of time series and identifies a number of operations on a piecewise-linear inverse histogram function, which leave the marginal distribution invariant. For cyclical processes with a prescribed marginal distribution and a prescribed cycle profile, one can also use these transformations to generate sample paths which “conform” to the profile. This approach also improves the ability to approximate the empirical autocorrelation function. [ABSTRACT FROM AUTHOR]