Tuesday, April 26, 2011

Design and Analysis of Experiments - Chapter 4 Blocking / Latin Squares


 

Chapter 1 – Introduction To Designed Experiments

-          p 5 à see graphical representation of factorial experiment

-          randomization, replication, blocking

-          important distinction between replication and repeated measurements.

o   example -> four wafers are processed simultaneously in an oxidation furnace and then a measurement taken on oxide thickness of each wafer

§  this is repeated measurements

§  replication reflects sources of variation both between runs and (potentially) within runs.

-          Blocking

o   set of relatively homogenous experimental conditions

o   each level of nuisance factor is a block

-          recognition of and statement of problem

o   characterization or factor screening

o   optimization

o   confirmation

o   discovery

o   stability / robustness

-          design factors

o   design factors – factors selected for study

o   held constant factors

o   allowed to vary factors  à variations in experimental material à rely on randomization to balance out effects

-          nuisance factors

o   controllable  à blockable

o   uncontrollable  à analysis of covariance

o   noise

-          cause and effect diagrams – useful technique for organizing some of the information generated in pre-experimental planning.

-          Industrial era à development of response surface methodology

o   immediacy

o   sequentiality

-          robust parameter design

o   Taguchi

o   Wu

o   Kackar

 

Chapter 4: Experiments with Blocking Factors

 

-          nuisance factor

o   unknown and uncontrolled à randomization

-          known but uncontrolled

o   analysis of covariance

-          known and controllable

o   blocking

-          paired comparison problem

o   improve precision by making comparisons within matched pairs of experimental material

§  example – testing two tips

·         test each tip on same material

-          problem with completely random

o   experimental error will reflect both random error and variability between test beds

o   block – test each tip once on each test bed

o   randomized complete block

-          effects model

o   response = overall mean + treatment effect + block effect + error

o   if experiment were just completely random, variability for blocking would move into error

o   RCBD  à noise reducing technique

-          model adequacy checking

o   normality assumption

o   unequal error variance by treatment or block

o   block – treatment interaction

-          Some other aspects of randomized complete block design

o   additivity of randomized block model

o   where interactions are of interest à factorial design

o   fixed effects / random effects

 

Latin Square Design

-          is used to eliniate two nuisance sources of variability 

-          blocking in two directions

-          two restrictions on randomisation

 

 

 

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