design of experiments nested designs split plot designs 592 term paper presentation presented by:...
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DESIGN OF EXPERIMENTSNESTED DESIGNSSPLIT PLOT DESIGNS
592 Term Paper presentation
Presented by: Safa Khater
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Objective
Study the concept of design of experiments focusing on Nested Designs and Split Plot Designs.
“Well chosen experimental designs maximize the amount of "information" that can be obtained for a given amount of experimental effort.” [3]
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Outline
Nested Designs Definition Aim Example
Split-Plot Designs: Definition Situations leading to Split-plot Example
Initial criteria for design selection References
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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NESTED DESIGNS
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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Definition
In certain multifactor experiments, the levels of one factor are similar but not identical for different levels of another factor, (is unique to that particular factor) this is called hierarchical or nested design. [1]
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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Aim
Nested experiments are commonly used to identify the important sources of variation in a system. [4]
Such sources of variation if not well addressed, might make it impossible to guarantee some level of precision. [9]
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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Example [Ref:1]
1. Recognition of and statement of the problem
Consider a company that purchases its raw material from three different suppliers. The company wishes to determine if the purity of the raw material is the same from each supplier
2. Choice of factors, levels, and ranges.
There are 4 batches of raw material available from each of 3 suppliers
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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Cont/ Example
3. Selection of the response variable.
Three determinations of purity are to be taken from each batch
4. Choice of experimental design.
Nested design
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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Cont/ Example
5. Performing the experiment.Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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SPLIT-PLOT DESIGNS
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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Definition
In some multifactor designs involving randomized blocks, we may be unable to completely randomize the order of the runs within the block. This often results in a generalization of the randomized block design called split-plot design. [1]
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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Situations leading to Split-plot [3]
Some of the factors of interest may be 'hard to vary' while the remaining factors are easy to vary. As a result, the order in which the treatment combinations for the experiment are run is determined by the ordering of these 'hard-to-vary' factors
Experimental units are processed together as a batch for one or more of the factors in a particular treatment combination
Experimental units are processed individually, one right after the other, for the same treatment combination without resetting the factor settings for that treatment combination.
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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Example [Ref:3]
1. Recognition of and statement of the problem
Consider an experiment to examine electroplating of aluminum (non-aqueous) on copper strips (sample=16).
2. Choice of factors, levels, and ranges.
The three factors of interest are: current (A); solution temperature (T); and the solution concentration of the plating agent (S)
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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Cont/ Example
3. Selection of the response variable.
Plating rate is the measured response.
4. Choice of experimental design.
Split Plot design
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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Cont/ Example
5. Performing the experiment.
CurrentTemperatureConcentration
-1-1-1
-1-11
-11-1
-111
1-1-1
1-11
11-1
111
Factor solution concentration of the plating agent (S) being hard to vary
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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the randomization of the treatment runs is restricted somewhat by the level of the solution concentration factor.
the treatment combinations might be randomized such that those treatment runs corresponding to one level of the concentration (-1) are run first. Each copper strip is individually plated, meaning only one strip at a time is placed in the solution for a given treatment combination. Once the four runs at the low level of solution concentration have been completed, the solution is changed to the high level of concentration (1), and the remaining four runs of the experiment are performed (where again, each strip is individually plated).
Cont/ Example
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
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Initial criteria for design selection (1/5)
Criteria NESTEDSPLIT
Objective ScreeningScreening
Identical levels Not identicalIdentical
Sources of variationManyMin
# of experimental units
OneMore than one
Randomization Partially restricted Restricted
Allow interaction Not between nested factors
Yes
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Criteria NESTEDSPLIT
sufficient distribution of information
Goodness of fit
Provide model YesYes
Detect model lack of fitYesYes
Allow blockingYesYes
Allow sequential buildup of design
Initial criteria for design selection (2/5)
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Criteria NESTEDSPLIT
Provides internal estimate of error variance
Yes (more than 1error variance)
Yes (more than 1error variance)
Provide simple means of calculating estimates of coefficients
Run size economy
Design Resolution
Minimum aberration
Minimum Detectable Effect
Initial criteria for design selection (3/5)
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Criteria NESTEDSPLIT
Orthogonality
BalanceYes depending on the situation
Yes depending on the situation
Confounding abilityYes
Allow mixed modelYesYes
Degree of model allowedLinear or Quadratic
Linear or Quadratic
Allow collapsing of factor
optimal process settings N/AN/A
Initial criteria for design selection (4/5)
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Criteria NESTEDSPLIT
Efficiency of design effecting the budget of the experiment.
Economic
estimate of pure error by replicating only some of the runs
YesYes
design can handle the number of levels involved
Rotatability
Initial criteria for design selection (5/5)
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References
[1] Design and Analysis of Experiments, by Montgomery [2] Design of Experiments: A No-Name Approach by Thomas J.
Lorenzen, Virgil L. Anderson. [3] http://www.itl.nist.gov/div898/handbook/pri/section1/pri11.htm [4] Improved Quality through planned experimentation [5] Engineering Quality and Experimental Design, by D. M.
Grove and T. P. Davis [6] Experimental designs, by Cochran and Cox. [7] The Theory of the Design of Experiments, by D.R. Cox and
N. Reid [8] Design and Analysis: A Researcher’s handbook, by Geoffrey
Keppel [9] Design Your Experiments Part XIII: Other Experiment
Designs, by Kevin Kilty
Nested Designs
Definition Aim Example
Split-Plot Designs:
Definition Situations leading to Split-plot Example
Initial criteria fordesign selection
References
DISCUSSION
DESIGN OF EXPERIMENTSNESTED DESIGNSSPLIT PLOT DESIGNS