1. Lecture 9 Last day: 3.2-3.5 Today: Finish last day and start 3.6-3.8, 3.10-3.12 Next day: Assignment #2: Chapter 2: 6, 15 (treat tape speed and laser power as qualitative factors), 27, 30, 32, and 36….DUE Thursday

2. One-at-a-Time Experiments Have discussed the factorial layout for experimentation –all level combinations –m replicates –performed in random order Another obvious strategy is call the “one-factor-at-a-time approach” 1identify the most important factor, 2investigate this factor by itself, keeping other factors fixed, 3decide on optimal level for this factor, and fix it at this level, and 4move on to the next most important factor and repeat 2-3

3. Example: Suppose have 2 factors A and B, each with 2-levels (-1,+1)

4. Comments Disadvantages of the on-factor-at-a-time approach –less efficient than factorial experiments –interactions may cause misleading conclusions –conclusions are less general –may miss optimal settings

5. Assessing Effect Significance For replicated experiments, can use regression to determine important effects Can also use a graphical procedure The graphical procedure can be used for replicated and replicated factorial experiments

6. Normal and Half-Normal Probability Plots Graphical method for assessing which effects are important are based on normal probability plots (a.k.a normal qq-plots) Let be the sorted (from smallest to largest) effect estimates Plot, where represents the cumulative distribution function of the standard normal (N(0,1)) distribution

7. Normal and Half-Normal Probability Plots That is, we plot the quantiles of our sample of effects versus the corresponding quantiles of the standard normal If no effect is important then the sample of effects appear to be a random sample from a normal distribution…we observe: Otherwise:

8. Normal and Half-Normal Probability Plots Why does this work?

9. Normal and Half-Normal Probability Plots Half-Normal Plots

10. Example: Epitaxial Growth Layer Experiment