Chapter 8 – Fractional Factorial Designs (Montgomery DOE)

SAS implementations of the examples presented in Chapter 8: Fractional Factorial Designs from Douglas C. Montgomery's Design and Analysis of Experiments.

Overview

This repository contains SAS code for reproducing and studying the examples in Chapter 8 of Montgomery's textbook. The programs demonstrate the construction, analysis, and interpretation of fractional factorial experiments using SAS.

The repository is intended for:

• Students taking a Design of Experiments (DOE) course
• Instructors preparing lecture materials and demonstrations
• Researchers learning fractional factorial designs in SAS
• Anyone interested in reproducing textbook examples and understanding their implementation

Topics Covered

The examples in this repository cover:

• Two-level fractional factorial designs
• Design generation using PROC FACTEX
• Design resolution and defining relations
• Alias structures and confounding
• Estimation of main and interaction effects
• Half-normal plots for effect screening
• Model fitting using PROC GLM
• Residual analysis and model diagnostics
• Blocking and replicated experiments

Repository Structure

The code includes implementations of the following textbook examples:

Example	Topics
Example 8-1	Basic fractional factorial design and effect estimation
Example 8-2	Half-normal plots and residual diagnostics
Example 8-3	Generator relations and defining contrasts
Example 8-4	Resolution IV designs and confounding
Example 8-6	Blocking and effect screening
Example 8-7	Fractional factorial analysis and effect estimation

Software Requirements

• SAS 9.4 or later
• Base SAS
• SAS/STAT

The examples make extensive use of:

• PROC FACTEX
• PROC GLM
• PROC SQL
• PROC PLOT
• PROC GPLOT
• PROC UNIVARIATE

Running the Examples

1. Open SAS.

2. Load the .sas file from this repository.

3. Execute the program.

4. Review the generated:

   • Experimental designs
   • Alias structures
   • Estimated effects
   • Half-normal plots
   • Residual plots
   • Probability plots

Learning Objectives

After working through these examples, you should be able to:

• Generate fractional factorial designs in SAS
• Determine the resolution of a design
• Interpret aliasing and confounding structures
• Estimate and screen important effects
• Construct and interpret half-normal plots
• Fit reduced models and assess model assumptions

Reference

Montgomery, D. C. Design and Analysis of Experiments. John Wiley & Sons.

Disclaimer

This repository is an educational resource created for learning and teaching purposes. All examples and datasets originate from the textbook and are implemented in SAS to facilitate understanding of fractional factorial designs and their analysis.