Experimental Design

• Example 1.1: Designing and Analyzing a 2^(7-4) Fractional Factorial Design
  Box, Hunter, and Hunter (1978) report the results of a (hypothetical) experiment that nicely demonstrates how to design and analyze a fractional factorial design at two levels. Suppose a person is asked to cycle up a hill on consecutive days. The purpose of the study is to determine the effect of 7 different factors on the speed with which the person can climb the hill. These factors are:
• Example 1.2: Analyzing a 2⁶ Full Factorial
  
• Example 1.3: Analyzing a Botched 2^(7-4) Fractional Factorial Design
  
• Example 2: Designing and Analyzing a 35-Factor Screening Design
  The design and analysis of screening experiments for factors at two levels proceeds in much the same way as you would design and analyze 2(k-p) designs. The difference is that screening designs are specifically constructed to allow for testing of the largest number of main effects with the least number of cases. In this example, we will go through the steps of designing and analyzing such a design.
• Example 3: Analyzing a 3³ Full Factorial
  Box and Draper (1987, page 205) report a study of the behavior of worsted yarn under cycles of repeated loading. (The study was originally conducted by A. Barella and A. Sust for the Technical Committee of the International Wool Textile Organization.) The dependent variable of interest is the number of cycles to failure. Because of large variability in that variable, the log10 transformed dependent variable values were also considered. The data are contained in the data file Textile2.sta. Open this data file:
• Example 4: Designing and Analyzing a 2³3² Experiment
  Connor and Young (in McLean and Anderson, 1984) report an experiment (taken from Youden and Zimmerman, 1936) on various methods of producing tomato plant seedlings prior to transplanting in the field. The experiment is a 2332 factorial design (3 factors at 2 levels, 2 factors at 3 levels). We will first design the experiment, and then analyze the yield (in pounds) as a function of the different factor settings.
• Example 5: Central Composite (Response Surface) Designs
  Box, Hunter, and Hunter (1978, Chapter 15) report a study of the yield of a chemical process. The two factors of interest in that study are the setting of the temperature (variable Degrees) and the amount of Time that the chemical agents are allowed to react. Because you do not expect a simple linear relationship between these factors and the resultant yield, a response surface design is employed.
• Example 6: Latin Square Designs
  Latin square designs are discussed in the Introductory Overview. The design of Latin squares proceeds basically analogously to that of the other designs presented in the previous two examples with a few exceptions that should be self-explanatory. Therefore, the analysis of a Latin square study, specifically the one on the fuel-additives study discussed in the Introductory Overview (from Box, Hunter, and Hunter, 1978, page 247), will be presented in this example.
• Example 7: Taguchi Robust Design Experiment
  This example is based on data presented by Phadke (1989) on the manufacture of polysilicon wafers. It is assumed that you have read the section on Taguchi methods in the Introductory Overview. The purpose of the study was to reduce:
• Example 8.1: Designing and Analyzing a Mixture Experiment
  Cornell (1990a) discusses a simple but typical mixture experiment concerned with the average texture of fish patties. Sandwich patties were made of blends of three types of fish: Mullet, Sheepshead, and Croaker. The dependent variable of interest was Texture, as measured by the force (in grams * 10-3) required to puncture the patty surface. We will first design the experiment as reported by Cornell (1990a, page 9), and then analyze the completed experiment.
• Example 8.2: Designing and Analyzing a Mixture Experiment with Pseudo-Components
  Cornell (1990a, page 41) discusses an experiment involving three ingredients that are used to form bleach for removing grease stains: Bromine, Powder, and diluted HCl. The minimum proportions of each component that must be present in each blend are:
• Example 9.1: Finding Vertex and Centroid Points for a Constrained Region
  
• Example 9.2: Mixture Designs for Components with Upper and Lower Bound Restrictions
  
• Example 10.1: Constructing a Simple D-Optimal Design
  
• Example 10.2: Constructing a Design from Vertex and Centroid Points (Example 9.1, Continued)
  
• Example 11: Constructing a D-Optimal Split Plot Design
  The terminology for split-plot designs arose from their original application in agricultural experiments – a factor that only varies between separate plots of land is called a whole-plot factor (hard-to-change factor), and a factor whose levels vary within each plot is called a subplot factor (easy-to-change factor). Today, split plot experiments are commonly used in industrial and manufacturing experiments.
• Special Topics Example 1 - Simultaneous Optimization of Several Response Variables in a Central Composite (Response Surface) Design
  
• Special Topics Example 2 - Optimization of the Response Variable in a Three-Factor Mixture Experiment
  
• Special Topics Example 3 - Residuals Analysis
  
• Special Topics Example 4 - Box-Cox Transformation of a Dependent Variable
  

Copyright © 2021. Cloud Software Group, Inc. All Rights Reserved.