design of experiments nested designs split plot designs 592 term paper presentation presented by:...

DESIGN OF EXPERIMENTSNESTED DESIGNSSPLIT PLOT DESIGNS

592 Term Paper presentation

Presented by: Safa Khater

2

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


Split-Plot Designs:



References

5

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


Split-Plot Designs:



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


Split-Plot Designs:



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


Split-Plot Designs:



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


Split-Plot Designs:



References

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Cont/ Example

5. Performing the experiment.Nested Designs


Split-Plot Designs:



References

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SPLIT-PLOT DESIGNS

Nested Designs


Split-Plot Designs:



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


Split-Plot Designs:



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


Split-Plot Designs:



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


Split-Plot Designs:



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


Split-Plot Designs:



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


Split-Plot Designs:



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


Split-Plot Designs:



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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sufficient distribution of information

Goodness of fit

Provide model YesYes

Detect model lack of fitYesYes

Allow blockingYesYes

Allow sequential buildup of design


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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


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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


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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


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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


Split-Plot Designs:



References

DISCUSSION

DESIGN OF EXPERIMENTSNESTED DESIGNSSPLIT PLOT DESIGNS

design of experiments nested designs split plot designs 592 term paper presentation presented by:...

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