General Full Factorial Designs With k Factors
Transcript of General Full Factorial Designs With k Factors
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23-1©2008 Raj JainCSE567MWashington University in St. Louis
General Full Factorial General Full Factorial Designs With Designs With kk FactorsFactors
Raj Jain Washington University in Saint Louis
Saint Louis, MO [email protected]
These slides are available on-line at:http://www.cse.wustl.edu/~jain/cse567-08/
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23-2©2008 Raj JainCSE567MWashington University in St. Louis
OverviewOverview
! Model! Analysis of a General Design! Informal Methods
" Observation Method" Ranking Method" Range Method
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23-3©2008 Raj JainCSE567MWashington University in St. Louis
General Full Factorial Designs With k FactorsGeneral Full Factorial Designs With k Factors
! Model: k factors ⇒ 2k-1 effectsk main effects
two factor interactions,
three factor interactions,
and so on. Example: 3 factors A, B, C:
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23-4©2008 Raj JainCSE567MWashington University in St. Louis
Model ParametersModel Parameters
! Analysis: Similar to that with two factors
! The sums of squares, degrees of freedom, and F-test also extend as expected. }
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23-5©2008 Raj JainCSE567MWashington University in St. Louis
Case Study 23.1: Paging ProcessCase Study 23.1: Paging Process
! Total 81 experiments.
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23-6©2008 Raj JainCSE567MWashington University in St. Louis
Case Study 23.1 (Cont)Case Study 23.1 (Cont)! Total Number of Page Swaps
! ymax/ymin = 23134/32 = 723 ⇒ log transformation
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23-7©2008 Raj JainCSE567MWashington University in St. Louis
Case Study 23.1 (Cont)Case Study 23.1 (Cont)
! Transformed Data For the Paging Study
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23-8©2008 Raj JainCSE567MWashington University in St. Louis
Case Study 23.1 (Cont)Case Study 23.1 (Cont)! Effects:
! Also" Six two-factor interactions," Four three-factor interactions, and" One four-factor interaction.
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23-9©2008 Raj JainCSE567MWashington University in St. Louis
Case Study 23.1: ANOVA TableCase Study 23.1: ANOVA Table
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23-10©2008 Raj JainCSE567MWashington University in St. Louis
Case Study 23.1: Simplified modelCase Study 23.1: Simplified model
! Most interactions except DM are small.
Where,
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23-11©2008 Raj JainCSE567MWashington University in St. Louis
Case Study 23.1: Simplified Model (Cont)Case Study 23.1: Simplified Model (Cont)
! Interactions Between Deck Arrangement and Memory Pages
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23-12©2008 Raj JainCSE567MWashington University in St. Louis
Case Study 23.1: Error ComputationCase Study 23.1: Error Computation
!
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23-13©2008 Raj JainCSE567MWashington University in St. Louis
Case Study 23.1: Visual TestCase Study 23.1: Visual Test
! Almost a straight line.! Outlier was verified.
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23-14©2008 Raj JainCSE567MWashington University in St. Louis
Case Study 23.1: Final ModelCase Study 23.1: Final Model
Standard Error= Stdv of sample mean= Stdv of Error
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23-15©2008 Raj JainCSE567MWashington University in St. Louis
Observation MethodObservation Method
! To find the best combination.! Example: Scheduler Design! Three Classes of Jobs:
" Word processing" Interactive data processing" Background data processing
! Five Factors 25-1 design
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23-16©2008 Raj JainCSE567MWashington University in St. Louis
Example 23.1: Measured ThroughputsExample 23.1: Measured Throughputs
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23-17©2008 Raj JainCSE567MWashington University in St. Louis
Example 23.1: ConclusionsExample 23.1: Conclusions
To get high throughput for word processing jobs,:1. There should not be any preemption (A=-1)2. The time slice should be large (B=1)3. The fairness should be on (E=1)4. The settings for queue assignment and re-queueing
do not matter.
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23-18©2008 Raj JainCSE567MWashington University in St. Louis
Ranking MethodRanking Method
! Sort the experiments.
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23-19©2008 Raj JainCSE567MWashington University in St. Louis
Example 23.2: ConclusionsExample 23.2: Conclusions
1. A=-1 (no preemption) is good for word processing jobs and also that A=1 is bad.
2. B=1 (large time slice) is good for such jobs. No strong negative comment can be made about B=-1.
3. Given a choice C should be chosen at 1, that is, there should be two queues.
4. The effect of E is not clear. 5. If top rows chosen, then E=1 is a good choice.
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23-20©2008 Raj JainCSE567MWashington University in St. Louis
Range MethodRange Method! Range = Maximum-Minimum! Factors with large range are important.
! Memory size is the most influential factor.! Problem program, deck arrangement, and replacement
algorithm are next in order.
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23-21©2008 Raj JainCSE567MWashington University in St. Louis
SummarySummary
! A general k factor design can have k main effects, two factor interactions, three factor interactions, and so on.
! Information Methods:" Observation: Find the highest or lowest response" Ranking: Sort all responses" Range: Largest - smallest average response
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23-22©2008 Raj JainCSE567MWashington University in St. Louis
Exercise 23.1Exercise 23.1
Using the observation method on data of Table 23.8, find the factor levels that maximize the throughput for interactive jobs (TI). Repeat the problem for background jobs (TB).
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23-23©2008 Raj JainCSE567MWashington University in St. Louis
Exercise 23.2 Exercise 23.2
Repeat Exercise 23.1 using ranking method.
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23-24©2008 Raj JainCSE567MWashington University in St. Louis
Homework 23Homework 23
! Analyze the following results using observation and ranking methods.