slide1
Download
Skip this Video
Download Presentation
Analyzing Supersaturated Designs Using Biased Estimation

Loading in 2 Seconds...

play fullscreen
1 / 26

Analyzing Supersaturated Designs Using Biased Estimation - PowerPoint PPT Presentation


  • 139 Views
  • Uploaded on

FAMU-FSU College of Engineering, Department of Industrial Engineering. Analyzing Supersaturated Designs Using Biased Estimation. QPRC 2003 By Adnan Bashir and James Simpson. May 23,2003. FAMU-FSU College of Engineering, Department of Industrial Engineering. Outline. Introduction

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Analyzing Supersaturated Designs Using Biased Estimation' - ilyssa


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

FAMU-FSU College of Engineering, Department of Industrial Engineering

Analyzing Supersaturated Designs Using Biased Estimation

QPRC 2003ByAdnan Bashir andJames Simpson

May 23,2003

outline

FAMU-FSU College of Engineering, Department of Industrial Engineering

Outline
  • Introduction
  • Motivation example
  • Research objectives
  • Proposed analysis method
    • Multicollinearity & ridge
    • Best subset model
    • Simulated case studies
    • Example
    • Results
  • Conclusion & recommendations
  • Future research
introduction

FAMU-FSU College of Engineering, Department of Industrial Engineering

Introduction
  • Many studies and experiments contain a large number of variables
  • Fewer variables are significant
  • Which are those few factors? How do we find those factors?
  • Screening experiments (Design & Analysis) are used to find those important factors
  • Several methods & techniques (Design & Analysis) are available to screen
slide4

Motivation exampleComposites Production

FAMU-FSU College of Engineering, Department of Industrial Engineering

Raw Materials

INPUTS (Factors)

Resin Flow Rate (x1)

Type of Resin (x2)

Gate Location (x3)

Fiber Weave (x4)

Mold Complexity (x5)

Fiber Weight (x6)

Curing Type (x7)

Pressure (x8)

OUTPUTS

(Responses)

Fiber Permeability

Product Quality

Tensile Strength

Process

Noise

slide5

Motivation example (continued)

FAMU-FSU College of Engineering, Department of Industrial Engineering

Response y = Tensile strength

Each experiment costs $500, requires 8 hours, budget $3,000 (6 experiments)

1: High level

-1: Low level

  • Supersaturated Designs: number of factors m ≥ number of runs n
  • Columns are not Orthogonal
research objectives

FAMU-FSU College of Engineering, Department of Industrial Engineering

Research Objectives
  • Propose an efficient technique to screen the important factors in an experiment with fewer number of runs
    • Construct improved supersaturated designs
    • Develop an accurate, reliable and efficient technique to analyze supersaturated designs
analysis of ssds current methods

FAMU-FSU College of Engineering, Department of Industrial Engineering

Analysis of SSDs – Current Methods
  • Stepwise regression, most commonly used
    • Lin (1993, 1995), Wang (1995), Nguyen (1996)
  • All possible regressions
    • Abraham, Chipman, and Vijayan (1999)
  • Bayesian method
    • Box and Meyer (1993)

Investigated techniques

  • Principle components, partial least squares and flexible regression methods (MARS & CART)
analysis of ssds proposed method

FAMU-FSU College of Engineering, Department of Industrial Engineering

Analysis of SSDs – Proposed Method
  • Modified best subset via ridge regression (MBS-RR)
    • Ridge regression for multicollinearity
    • Best subset for variable selection in each model
    • Criterion based selection to identify best model
ridge regression motivation

FAMU-FSU College of Engineering, Department of Industrial Engineering

Ridge Regression Motivation

Ordinary Least Squares

Ridge Regression

Consider adding k > 0 to each diagonal of X*\'X* , say k = 0.1

Consider a centered, scaled matrix, X*

ridge regression

FAMU-FSU College of Engineering, Department of Industrial Engineering

Ridge Regression
  • Ridge regression estimates

where k is referred to as a

shrinkage parameter

  • Thus,

Geometric interpretation of ridge regression

ridge regression continued shrinkage parameter

FAMU-FSU College of Engineering, Department of Industrial Engineering

Ridge Regression, (continued)Shrinkage parameter
  • Hoerl and Kennard (1975) suggest
  • where p is number of parameter
  • are found from the least squares solution
shrinkage parameter ridge trace

FAMU-FSU College of Engineering, Department of Industrial Engineering

Shrinkage ParameterRidge Trace

Ridge trace for nine regressors (Adapted from Montgomery, Peck, & Vining; 2001)

proposed analysis method

FAMU-FSU College of Engineering, Department of Industrial Engineering

Proposed Analysis Method

Read X, Y

Cont’d.

Select the best 1-factor model

By OLS (k=0)

Calculate k, and find the best

2-factor model by all possible subsets

Adding 1 factor at a time to the best

2-factor model, from the remaining

variables to get the best 3-factor model

proposed analysis method1

FAMU-FSU College of Engineering, Department of Industrial Engineering

Proposed Analysis Method

Is the stopping

rule satisfied?

Yes

No

Adding 1 factor at a time to the best

3-factor model, from the remaining

variables to get the best 4-factor model

Yes

Is the stopping

rule satisfied?

No

Adding 1 factor at a time to the best

7-factor model, from the remaining

variables to get the best 8-factor model

Final Model with

Min. Cp

method comparison monte carlo simulation design of experiments

FAMU-FSU College of Engineering, Department of Industrial Engineering

Method Comparison-Monte CarloSimulation & Design of Experiments

Factors considered in the simulation study

III Fractional Factorial Design Matrix

analysis method comparison

FAMU-FSU College of Engineering, Department of Industrial Engineering

Analysis Method Comparison
  • The performance measures, Type I and Type II errors
summary results

FAMU-FSU College of Engineering, Department of Industrial Engineering

Summary Results

A: No. of runs

B: No. of factors

C: Multicollinearity

D: Error variance

E: No. of Sig. factors

conclusions recommendations

FAMU-FSU College of Engineering, Department of Industrial Engineering

Conclusions & Recommendations

SSDs Analysis: Best Subset Ridge Regression

  • Use ridge regression estimation
  • Best subset variable selection method outperforms stepwise regression
future research

FAMU-FSU College of Engineering, Department of Industrial Engineering

Future Research

Analyzing SSDs

  • Multiple criteria in selecting the best model
  • All possible subset, 3 factor model
  • Streamline program code
  • Real-life case studies
  • Genetic algorithm for variable selection
acknowledgement

FAMU-FSU College of Engineering, Department of Industrial Engineering

Acknowledgement
  • Dr. Carroll Croarkin, chair of selection committee for Mary G. Natrella
  • Selection Committee for Mary G. Natrella Scholarship
  • Dr. Simpson, Supervisor
ad