DESIGN OF EXPERIMENTS

NESTED DESIGNS

SPLIT PLOT DESIGNS

592 Term Paper presentation

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]

3

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 for

design selection

References

4

NESTED DESIGNS

Nested Designs

Definition

Aim

Example

Split-Plot Designs:

Definition

Situations

leading to

Split-plot

Example

Initial criteria for

design selection

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

Definition

Aim

Example

Split-Plot Designs:

Definition

Situations

leading to

Split-plot

Example

Initial criteria for

design selection

References

6

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 for

design selection

References

7

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 for

design selection

References

8

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 for

design selection

References

9

Cont/ Example

5. Performing the experiment.Nested Designs

Definition

Aim

Example

Split-Plot Designs:

Definition

Situations

leading to

Split-plot

Example

Initial criteria for

design selection

References

1 2 3

1 2 3 4 1 2 3 4 1 2 3 4

x x x x x x x x x x x x

x x x x x x x x x x x x

x x x x x x x x x x x x

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SPLIT-PLOT DESIGNS

Nested Designs

Definition

Aim

Example

Split-Plot Designs:

Definition

Situations

leading to

Split-plot

Example

Initial criteria for

design selection

References

11

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 for

design selection

References

12

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 for

design selection

References

13

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 for

design selection

References

14

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 for

design selection

References

15

Cont/ Example

5. Performing the experiment.

Current Temperature Concentration

-1 -1 -1

-1 -1 1

-1 1 -1

-1 1 1

1 -1 -1

1 -1 1

1 1 -1

1 1 1

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 for

design selection

References

16

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 for

design selection

References

17

Initial criteria for design selection

(1/5)

Criteria NESTED SPLIT

Objective Screening Screening

Identical levels Not identical Identical

Sources of variation Many Min

# of experimental

units

One More than one

Randomization Partially restricted Restricted

Allow interaction Not between

nested factors

Yes

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Criteria NESTED SPLIT

sufficient distribution of

information

Goodness of fit

Provide model Yes Yes

Detect model lack of fit Yes Yes

Allow blocking Yes Yes

Allow sequential buildup

of design

Initial criteria for design selection

(2/5)

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Criteria NESTED SPLIT

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 NESTED SPLIT

Orthogonality

Balance Yes depending

on the situation

Yes depending

on the situation

Confounding ability Yes

Allow mixed model Yes Yes

Degree of model allowed Linear or

Quadratic

Linear or

Quadratic

Allow collapsing of factor

optimal process settings N/A N/A

Initial criteria for design selection

(4/5)

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Criteria NESTED SPLIT

Efficiency of design

effecting the budget of the

experiment.

Economic

estimate of pure error by

replicating only some of

the runs

Yes Yes

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 for

design selection

References

DISCUSSION

DESIGN OF EXPERIMENTS

NESTED DESIGNS

SPLIT PLOT DESIGNS