lecture 7
Download
Skip this Video
Download Presentation
Lecture 7

Loading in 2 Seconds...

play fullscreen
1 / 18

Lecture 7 - PowerPoint PPT Presentation


  • 303 Views
  • Uploaded on

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

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

PowerPoint Slideshow about 'Lecture 7' - jayden


An Image/Link below is provided (as is) to download presentation

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
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
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
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
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
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
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
Analysis of a BIBD
  • Model I:
  • Model II:
  • Hypothesis:
  • F-test:
comments
Comments
  • Similar to other cases, can do parameter estimation using the typical constraints
  • Can also do multiple comparisons
example 2 3111
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?
slide15
Model I:
  • Model II:
  • Hypothesis:
  • F-test:
chapter 3 full factorial experiments at 2 levels
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
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 growth18
Example - Epitaxial Layer Growth
  • A 16 run 24 experiment was performed (page 97) with 6 replicates
  • Notation:
ad