Pre-Conference Short Course

June 3, 2008
Pyle Center, Madison, Wisconsin

GRAPHICAL ANALYSIS OF DESIGNED EXPERIMENTS
Dr Veronica Czitrom

It’s a source of frustration to statisticians that designed experiments, as useful as they are, aren’t used more extensively. This workshop provides a graphical approach that’s easy to understand even without statistical training.

The concepts are presented with the help of numerous real-life industrial examples. The material will be useful to statisticians trying to present results to customers and students, and to scientists and engineers trying to understand the results of their experiments.

The first example, stripped down to essentials with one observation per run, displays the results using a variability graph, introduces main effects and interactions in an intuitive way, and presents visual t-tests and advantages of DOEs such as hidden replication and “recycling” at its best – every observation is used to estimate several effects.

Another example presents multiple observations and sources of variability (variance components) graphically. A third example presents the results of a fractional factorial robust designed experiment as an array of pictures involving nine variables.


Note:participants with laptops can follow the DOE analysis during the workshop. To do so, download a free trial version of the JMP statistical data analysis software at www.JMP.com, and download the DOE data sets from www.StatsTrain.com.

TABLE OF CONTENTS
Introduction
- Example of 2³ full factorial with one observation per run plus center points: main effects, interactions, hidden replication, visual t-tests, “recycling” to use each observation to estimate several effects, creating a full factorial with pencil and paper using a tree diagram, extension to central composite design if there’s curvature.

Advantages of DOE
- Why DOE works – or why you can study several factors simultaneously
- Advantages of DOEs: they require less resources for the amount of information obtained, provide higher precision, systematically estimate effects
- DOE versus one-factor-at-a-time experiments

Full factorial designs
-Main effects and interactions
-Example of 2³ full factorial for a batch process with multiple observations per run: graphical analysis of raw data and of variance components (graphical analysis avoids more complex ANOVA due to restriction on randomization); DOE eliminated manufacturing bottleneck and increased Cpk from unacceptable 0.86 to excellent 2.12

Fractional factorial designs
-Aliasing
-Example of 2^5-1 fractional factorial robust designed experiment: responses are yield and pictures, the pictures are presented as an array involving nine variables; DOE revealed the failure mechanism causing a drop in yield

INSTRUCTOR
Dr Veronica Czitrom does statistical training and consulting in Asia, Europe and the United States, primarily in the semiconductor industry. She worked as an industrial statistician for Bell Laboratories when it was part of AT&T, for Chartered Semiconductor in Singapore, and as a professor at a couple of universities. She has published technical articles in refereed journals and seven books, and was elected Fellow of the American Statistical Association. She obtained a PhD in Mathematics with concentration in Statistics from the University of Texas at Austin, as well as a BA in Physics and an MS in Engineering from the University of California at Berkeley.
Veronica's Biography can be found via the following link

http://www.statstrain.com/pages/profile.htm