FAMU-FSU College of Engineering,  Department of Industrial Engineering
This presentation is the property of its rightful owner.
Sponsored Links
1 / 26

Analyzing Supersaturated Designs Using Biased Estimation PowerPoint PPT Presentation


  • 84 Views
  • Uploaded on
  • Presentation posted in: General

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

Download Presentation

Analyzing Supersaturated Designs Using Biased Estimation

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


Analyzing supersaturated designs using biased estimation

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


Analyzing supersaturated designs using biased estimation

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


Analyzing supersaturated designs using biased estimation

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


Selecting the best model

FAMU-FSU College of Engineering, Department of Industrial Engineering

Selecting the Best Model

Where diff: user defined tolerance

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


Case studies with corresponding models

FAMU-FSU College of Engineering, Department of Industrial Engineering

Case Studies with Corresponding Models


Method comparison results type i errors

FAMU-FSU College of Engineering, Department of Industrial Engineering

Method Comparison Results, Type I errors


Method comparison results type ii errors

FAMU-FSU College of Engineering, Department of Industrial Engineering

Method Comparison Results, Type II errors


Factors contributing to method performance type ii errors

FAMU-FSU College of Engineering, Department of Industrial Engineering

Factors Contributing to Method PerformanceType II Errors

Stepwise Method

var


Factors contributing to method performance type ii errors1

FAMU-FSU College of Engineering, Department of Industrial Engineering

Factors Contributing to Method PerformanceType II Errors

Proposed Method

var


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


  • Login