Quality engineering applications on single and multiple nonlinear profiles

Abstract

Profile analysis has drawn attention in quality engineering applications due to the growing use of sensors and information technologies. Unlike the conventional quality characteristics of interest, a profile is formed functionally dependent on one or more explanatory variables. A single profile may contain hundred or thousand data points. The conventional charting tools cannot handle such high dimensional datasets. In this dissertation, six unsolved issues are investigated. First, Chang and Yadama’s method (2010) shows competitive results in nonlinear profile monitoring. However, the effectiveness of removing noise from given nonlinear profile by using B-splines fitting with and without wavelet transformation is unclear. Second, many researches dealt with profile analysis problem considering whether profile shape change only or variance change only. Those methods cannot identify whether the process is out-of-control due to mean or variance shift. Third, methods dealing with detecting profile shape change always assume that a gold standard profile exists. The existing profile shape change detecting methods are hard to be implemented directly. Fourth, multiple nonlinear profiles situation may exist in real world applications, so that conventional single profile analysis methods may result in high false alarm rate when dealing multiple profile scenario. Fifth, Multiple nonlinear profiles situation may be also happened in designs of experiment. In a conventional experimental design, the response variable is usually considered a single value or a vector. The conventional approach cannot deal with when the format of the response factor as multiple nonlinear profiles. Finally, profile fault diagnosis is an important step after detecting out-of-control signal. However, current approaches will lead to large number of combinations if the number of sections is too large. The organization of this dissertation is as following. Chapter 1 introduce the profile analysis, current solutions, and challenges; Chapter 2 to Chapter 4 explore the unsolved challenges in single profile analysis; Chapter 5 and Chapter 6 investigate multiple profiles issues in profile monitoring analysis and experimental design method. Chapter 7 proposed a novel high-dimensional diagnosis control chart to diagnose the cause of out-of-control signal via visualization aid. Finally, Chapter 8 summarizes the achievements and contributions of this research.