DESIGN OF EXPERIMENTS NESTED DESIGNS SPLIT PLOT DESIGNS

1. DESIGN OF EXPERIMENTSNESTED DESIGNS SPLIT 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]

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

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

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

11. Definition Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example 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: Definition Situations leading to Split-plot Example 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] Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example 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 Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example 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 Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example Initial criteria for design selection References 5. Performing the experiment. Factor solution concentration of the plating agent (S) being hard to vary

16. Cont/ Example Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example 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)

18. Initial criteria for design selection (2/5)

19. Initial criteria for design selection (3/5)

20. Initial criteria for design selection (4/5)

21. Initial criteria for design selection (5/5)

22. References Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example 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] 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

23. DISCUSSION DESIGN OF EXPERIMENTS NESTED DESIGNS SPLIT PLOT DESIGNS