Graduate Theses and Dissertations (2019 - present)

Date of Award

5-2026

Document Type

Dissertation

Degree Name

Ph.D.

Department

Systems Engineering

Committee Chair

Sean Walker, Ph.D

Abstract

This research answers three basic questions. First, what are the behaviors (dynamics) of a manufacturing system in the context of system performance? Are these dynamics best described as linear deterministic, periodic, nonlinear deterministic, or stochastic? Second, what are the complexity (chaotic) characteristics of a manufacturing system, namely the maximal Lyapunov exponent, correlation dimension, and Kolmogorov-Sinai entropy? Third, is there a relationship between complexity characteristics and manufacturing system performance? This research involves four high level steps: data analysis, system dynamics analysis, system complexity analysis, and correlation analysis. The data analyzed consists of concrete plant and shipbuilding shop time series performance data. The first step, includes data conditioning, data cleaning, data reduction and, last, time series stationarity testing. The second step includes the method of surrogate data testing for determining the underlying dynamical process as well as Fourier frequency analysis. The third step involves determining the value for each of three complexity measures: maximal Lyapunov exponent, correlation sum and dimension, and Kolmogorov-Sinai entropy. The fourth step investigates whether there is any correlation in the results from the previous two steps. The dynamic analysis of the second step, in general, provided no definitive answer as to the category of dynamics. In most cases the analysis indicated the dynamics could be stochastic or linear deterministic or a combination thereof. Only for one data set was all but the null hypothesis of a stationary linear Gaussian system (linear deterministic) eliminated. The complexity analysis of the third step resulted in values for the maximal Lyapunov exponent, correlation sum and dimension, and Kolmogorov-Sinai entropy. For all data sets, the values of all three of the complexity measures indicated the absence of chaotic behavior. The correlation analysis of the fourth step showed that the strongest correlation exists for correlated noise dynamics and periodic system dynamics. In summary, the use of the complexity measures alone are not reliable for determining a time series’ dynamics. That determination requires the use of multiple techniques and even that approach may give ambiguous result, nor is it useful in predicting or gaining any insights into the performance of the manufacturing system.

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