1. DESIGN OF EXPERIMENTS NESTED DESIGNS SPLIT PLOT DESIGNS
592 Term Paper presentation
DESIGN OF EXPERIMENTS NESTED DESIGNS SPLIT PLOT DESIGNS
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]

3. Outline Nested Designs Split-Plot Designs:
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations leading to Split-plot
Initial criteria for design selection
References

4. NESTED DESIGNS Aim Example Situations leading to Split-plot
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
NESTED DESIGNS

5. Definition
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
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]

6. Aim
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
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]

7. Example [Ref:1] 1. Recognition of and statement of the problem
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
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

8. Cont/ Example 3. Selection of the response variable.
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
3. Selection of the response variable.
Three determinations of purity are to be taken from each batch
4. Choice of experimental design.
Nested design

9. Cont/ Example 5. Performing the experiment. Aim Example Situations
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
5. Performing the experiment. 1 2 3 4 x

10. SPLIT-PLOT DESIGNS Aim Example Situations leading to Split-plot
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
SPLIT-PLOT DESIGNS

11. Definition
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
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]

12. Situations leading to Split-plot [3]
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
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.

13. Example [Ref:3] 1. Recognition of and statement of the problem
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
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)

14. Cont/ Example 3. Selection of the response variable.
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
3. Selection of the response variable.
Plating rate is the measured response.
4. Choice of experimental design.
Split Plot design

15. Cont/ Example 5. Performing the experiment.
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
Current
Temperature
Concentration -1 1
Since this factor is hard to vary, the experimenter would like to randomize the treatment combinations so that the solution concentration factor has a minimal number of changes.
Factor solution concentration of the plating agent (S) being hard to vary

16. Cont/ Example
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
References
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).

17. Initial criteria for design selection (1/5)
NESTED
SPLIT
Objective
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

18. Initial criteria for design selection (2/5)
NESTED
SPLIT
sufficient distribution of information
Goodness of fit
Provide model
Yes
Detect model lack of fit
Allow blocking
Allow sequential buildup of design

19. Initial criteria for design selection (3/5)
NESTED
SPLIT
Provides internal estimate of error variance
Yes (more than 1error variance)
Provide simple means of calculating estimates of coefficients
Run size economy
Design Resolution
Minimum aberration
Minimum Detectable Effect

20. Initial criteria for design selection (4/5)
NESTED
SPLIT
Orthogonality
Balance
Yes depending on the situation
Confounding ability
Yes
Allow mixed model
Degree of model allowed
Linear or Quadratic
Allow collapsing of factor
optimal process settings
N/A

21. Initial criteria for design selection (5/5)
NESTED
SPLIT
Efficiency of design effecting the budget of the experiment.
Economic
estimate of pure error by replicating only some of the runs
Yes
design can handle the number of levels involved
Rotatability

22. References [1] Design and Analysis of Experiments, by Montgomery
Nested Designs
Definition
Aim
Example
Split-Plot Designs:
Situations
leading to
Split-plot
Initial criteria for
design selection
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]
[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

23. DESIGN OF EXPERIMENTS NESTED DESIGNS SPLIT PLOT DESIGNS
DISCUSSION