Innovative Six Sigma Design Using the Eigenvector Dimension-Reduction (EDR) Method

2007 ◽  
Author(s):  
Lee J. Wells ◽  
Byeng D. Youn ◽  
Zhimin Xi
Keyword(s):  
Dimension Reduction ◽  
Six Sigma ◽  
Eigenvector Dimension Reduction

Innovative Six Sigma Design Using the Eigenvector Dimension-Reduction (EDR) Method

2007 ◽  
Author(s):  
Lee J. Wells ◽  
Byeng D. Youn ◽  
Zhimin Xi
Keyword(s):  
Taguchi Method ◽  
Dimension Reduction ◽  
Uncertainty Propagation ◽  
Robust Design Optimization ◽  
Design Parameters ◽  
Quality Engineering ◽  
Control Factors ◽  
Current Design ◽  
Eigenvector Dimension Reduction ◽  
Mean And Variance

This paper presents an innovative approach for quality engineering using the Eigenvector Dimension Reduction (EDR) Method. Currently industry relies heavily upon the use of the Taguchi method and Signal to Noise (S/N) ratios as quality indices. However, some disadvantages of the Taguchi method exist such as, its reliance upon samples occurring at specified levels, results to be valid at only the current design point, and its expensiveness to maintain a certain level of confidence. Recently, it has been shown that the EDR method can accurately provide an analysis of variance, similar to that of the Taguchi method, but is not hindered by the aforementioned drawbacks of the Taguchi method. This is evident because the EDR method is based upon fundamental statistics, where the statistical information for each design parameter is used to estimate the uncertainty propagation through engineering systems. Therefore, the EDR method provides much more extensive capabilities than the Taguchi method, such as the ability to estimate not only mean and standard deviation of the response, but also the skewness and kurtosis. The uniqueness of the EDR method is its ability to generate the probability density function (PDF) of system performances. This capability, known as the probabilistic “what-if” study, provides a visual representation of the effects of the design parameters (e.g., its mean and variance) upon the response. In addition, the probabilistic “what-if” study can be applied across multiple design parameters, allowing the analysis of interactions among control factors. Furthermore, the implementation of the probabilistic “what-if” study provides a basis for performing robust design optimization. Because of these advantages, it is apparent that the EDR method provides an alternative platform of quality engineering to the Taguchi method. For easy execution by field engineers, the proposed platform for quality engineering using the EDR method, known as Quick Quality Quantification (Q3), will be developed as a Microsoft EXCEL add-in.

Bayesian Reliability Based Design Optimization Using Eigenvector Dimension Reduction (EDR) Method

2007 ◽  
Author(s):  
Pingfeng Wang ◽  
Byeng D. Youn ◽  
Lee J. Wells
Keyword(s):  
Dimension Reduction ◽  
Design Optimization ◽  
Engineering Design ◽  
Mean Deviation ◽  
Random Parameters ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Reliability Method ◽  
Practical Engineering ◽  
Eigenvector Dimension Reduction

In the last decade, considerable advances have been made in Reliability-Based Design Optimization (RBDO). It is assumed in RBDO that statistical information of input uncertainties is completely known (aleatory uncertainty), such as a distribution type and its parameters (e.g., mean, deviation). However, this assumption is not valid in practical engineering applications, since the amount of uncertainty data is restricted mainly due to limited resources (e.g., man-power, expense, time). In practical engineering design, most data sets for system uncertainties are insufficiently sampled from unknown statistical distributions, known as epistemic uncertainty. Existing methods in uncertainty based design optimization have difficulty in handling both aleatory and epistemic uncertainties. To tackle design problems engaging both epistemic and aleatory uncertainties, this paper proposes an integration of RBDO with Bayes Theorem, referred to as Bayesian Reliability-Based Design Optimization (Bayesian RBDO). However, when a design problem involves a large number of epistemic variables, Bayesian RBDO becomes extremely expensive. Thus, this paper presents a more efficient and accurate numerical method for reliability method demanded in the process of Bayesian RBDO. It is found that the Eigenvector Dimension Reduction (EDR) Method is a very efficient and accurate method for reliability analysis, since the method takes a sensitivity-free approach with only 2n+1 analyses, where n is the number of aleatory random parameters. One mathematical example and an engineering design example (vehicle suspension system) are used to demonstrate the feasibility of Bayesian RBDO. In Bayesian RBDO using the EDR method, random parameters associated with manufacturing variability are considered as the aleatory random parameters, whereas random parameters associated with the load variability are regarded as the epistemic random parameters. Moreover, a distributed computing system is used for this study.

Predictive Carbon Nanotube Models Using the Eigenvector Dimension Reduction (EDR) Method

2007 ◽  
Author(s):  
Zhimin Xi ◽  
Byeng D. Youn
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotube ◽  
Dimension Reduction ◽  
Topological Defects ◽  
Material Design ◽  
Failure Stress ◽  
Vacancy Defects ◽  
Eigenvector Dimension Reduction ◽  
Parametric Studies ◽  
Nanotube Defects

It has been reported that a carbon nanotube (CNT) is one of the strongest materials with their high failure stress and strain. Moreover, the nanotube has many favorable features, such as high toughness, great flexibility, low density, and so on. This discovery has opened new opportunities in various engineering applications, for example, a nanocomposite material design. However, recent studies have found a substantial discrepancy between computational and experimental material property predictions, in part due to defects in the fabricated nanotubes. It is found that the nanotubes are highly defective in many different formations (e.g., vacancy, dislocation, chemical, and topological defects). Recent parametric studies with vacancy defects have found that the vacancy defects substantially affect mechanical properties of the nanotubes. Given random existence of the nanotube defects, the material properties of the nanotubes can be better understood through statistical modeling of the defects. This paper presents predictive CNT models, which enable to estimate mechanical properties of the CNTs and the nanocomposites under various sources of uncertainties. As the first step, the density and location of vacancy defects will be randomly modeled to predict mechanical properties. It has been reported that the Eigenvector Dimension Reduction (EDR) method performs probability analysis efficiently and accurately. In this paper, Molecular Dynamics (MD) simulation with a modified Morse potential model is integrated with the EDR method to predict the mechanical properties of the CNTs. To demonstrate the feasibility of the predicted model, probabilistic behavior of mechanical properties (e.g., failure stress, failure strain, and toughness) is compared with the precedent experiment results.

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