Lecture 7

1 / 18

# Lecture 7 - PowerPoint PPT Presentation

Lecture 7. Last day: 2.6 and 2.7 Today: 2.8 and begin 3.1-3.2 Next day: 3.3-3.5 Assignment #2: Chapter 2: 6, 15 (treat tape speed and laser power as qualitative factors), 27, 30, 32, and 36. Balanced Incomplete Block Designs. Sometimes cannot run all treatments in each block

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Lecture 7' - jayden

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Lecture 7
• Last day: 2.6 and 2.7
• Today: 2.8 and begin 3.1-3.2
• Next day: 3.3-3.5
• Assignment #2: Chapter 2: 6, 15 (treat tape speed and laser power as qualitative factors), 27, 30, 32, and 36
Balanced Incomplete Block Designs
• Sometimes cannot run all treatments in each block
• That is, block size is smaller than the number of treatments
• Instead, run sets of treatments in each block
Example (2.31)
• Experiment is run on a resistor mounted on a ceramic plate to study the impact of 4 geometrical shapes of resistor on the current noise
• Factor is resistor shape, with 4 levels (A-D)
• Only 3 resistors can be mounted on a plate
• If 4 runs of the of the plate are to be made, how would you run the experiment?
Balanced Incomplete Block Design
• Situation:
• have b blocks
• each block is of size k
• there are t treatments (k<t)
• each treatment is run r times
• Design is incomplete because blocks do not contain each treatment
• Design is balanced because each pair of treatments appear together the same number of times
Analysis
• The analysis of a BIBD is slightly more complicated than a RCB design
• Not all treatments are compared within a block
• Can use the extra sum of squares principle (page 16-17) to help with the analysis
Extra Sum of Squares Principle
• Suppose have 2 models, M1 and M2, where the first model is a special case of the second
• Can use the residual sum of squares from each model to form an F-test
Analysis of a BIBD
• Model I:
• Model II:
• Hypothesis:
• F-test:
• Similar to other cases, can do parameter estimation using the typical constraints
• Can also do multiple comparisons
Example (2.31)
• Experiment is run on a resistor mounted on a ceramic plate to study the impact of 4 geometrical shapes of resistor on the current noise
• Factor is resistor shape, with 4 levels (A-D)
• Only 3 resistors can be mounted on a plate
• If 4 runs of the of the plate are to be made, how would you run the experiment?
Model I:
• Model II:
• Hypothesis:
• F-test:
Chapter 3 - Full Factorial Experiments at 2-Levels
• Often wish to investigate impact of several (k) factors
• If each factor has ri levels, then there are possible treatments
• To keep run-size of the experiment small, often run experiments with factors with only 2-levels
• An experiment with k factors, each with 2 levels, is called a 2k full factorial design
• Can only estimate linear effects!
Example - Epitaxial Layer Growth
• In IC fabrication, grow an epitaxial layer on polished silicon wafers
• 4 factors (A-D) are thought to impact the layer growth
• Experimenters wish to determine the level settings of the 4 factors so that:
• the process mean layer thickness is as close to the nominal value as possible
• the non-uniformity of the layer growth is minimized
Example - Epitaxial Layer Growth
• A 16 run 24 experiment was performed (page 97) with 6 replicates
• Notation: