The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs Developed by Don Edwards, John Grego and James Lynch Center for Reliability and Quality Sciences Department of Statistics University of South Carolina

Part I.3 The Essentials of 2-Cubed Designs Methodology Methodology –Cube Plots – Estimating Main Effects – Estimating Interactions (Interaction Tables and Graphs) Statistical Significance: When is an Effect “Real”? Statistical Significance: When is an Effect “Real”? An Example With Interactions An Example With Interactions A U-Do-It Case Study A U-Do-It Case Study Replication Replication Rope Pull Exercise Rope Pull Exercise

Replication Why? Average values have less variability as the number of things you average increases Average values have less variability as the number of things you average increases –Estimated effects will be reliably closer to true effects –More of the mid-sized and small effects will be distinguishable from error –Data from replicated experiments can be used to estimate the amount of variability in the process (This allows more formal test for “real” effects—ANOVA). –Data from replicated experiments can be used to determine not only which factors affect the mean of the process, but which factors affect the variability of the process.

Replication Analysis of a Replicated 2 3 Replication means repeating the entire set of 8 runs, but (for the analysis as described below), the entire collection of runs should be done in random order (be it 16, or 24, or 48, etc. runs); if you want to do them in complete sets of 8, you should analyze the results in blocks—explained later). Replication means repeating the entire set of 8 runs, but (for the analysis as described below), the entire collection of runs should be done in random order (be it 16, or 24, or 48, etc. runs); if you want to do them in complete sets of 8, you should analyze the results in blocks—explained later). For our analysis, you can reduce the data to averages over each of the 8 treatment combinations; use these averages as your “y’s” in the rest of the analysis. For our analysis, you can reduce the data to averages over each of the 8 treatment combinations; use these averages as your “y’s” in the rest of the analysis. –Discussion of shortcomings of this approach to follow Effects plot, interaction plots, and EMR calculations are done as before using these estimated effects. Effects plot, interaction plots, and EMR calculations are done as before using these estimated effects. Replication Example to Follow!

U-Do-It Exercise Rope Pull Study* with Replication Purpose of the Design Purpose of the Design –Test Hose to Determine the Effect of Several Factors on an Important Quality Hosiery Characteristic, Rope Pull –Response y = Upper Boot Rope Pull (in inches) Factors: Factors: –A: Vacuum level (Lo, Hi) –B: Needle Type (EX, GB) –C: Upper Boot Speed (1000,1200) Two Replicates of the Full 2 3 Were Performed * Empirical basis for this data was motivated by a much larger study performed by the developers at Sara Lee Hosiery Two Replicates of the Full 2 3 Were Performed * Empirical basis for this data was motivated by a much larger study performed by the developers at Sara Lee Hosiery Purpose of the Design Purpose of the Design –Test Hose to Determine the Effect of Several Factors on an Important Quality Hosiery Characteristic, Rope Pull –Response y = Upper Boot Rope Pull (in inches) Factors: Factors: –A: Vacuum level (Lo, Hi) –B: Needle Type (EX, GB) –C: Upper Boot Speed (1000,1200) Two Replicates of the Full 2 3 Were Performed * Empirical basis for this data was motivated by a much larger study performed by the developers at Sara Lee Hosiery Two Replicates of the Full 2 3 Were Performed * Empirical basis for this data was motivated by a much larger study performed by the developers at Sara Lee Hosiery

U-Do-It Exercise Rope Pull Study - Experimental Report Form

U-Do-It Exercise Rope Pull Study - The Analysis To do: Analyze the data. This should include... To do: Analyze the data. This should include... –Fill in the table on the next slide. –Analyze the averages in Minitab:  Create a 3-factor 2-level design, enter the averages as a response variable; compute factor effects and construct a normal probability plot of the effects.  If appropriate, graph interaction plots.  Compute EMR using only the significant terms To do: Analyze the data. This should include... To do: Analyze the data. This should include... –Fill in the table on the next slide. –Analyze the averages in Minitab:  Create a 3-factor 2-level design, enter the averages as a response variable; compute factor effects and construct a normal probability plot of the effects.  If appropriate, graph interaction plots.  Compute EMR using only the significant terms

U-Do-It Exercise Rope Pull Study - The Analysis