592 Term Paper presentation DESIGN OF EXPERIMENTS NESTED

592 Term Paper presentation DESIGN OF EXPERIMENTS NESTED DESIGNS SPLIT PLOT DESIGNS Presented by: Safa Khater

Objective n Study the concept of design of experiments focusing on Nested Designs and Split Plot Designs. n “Well chosen experimental designs maximize the amount of "information" that can be obtained for a given amount of experimental effort. ” [3[ 2

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

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

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

Aim Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example n Nested experiments are commonly used to identify the important sources of variation in a system. [4[ n Such sources of variation if not well addressed, might make it impossible to guarantee some level of precision. [9[ Initial criteria for design selection References 6

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 7

Cont/ Example Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot 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 Initial criteria for design selection References 8

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

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

Definition Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example Initial criteria for design selection 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 splitplot design. [1] References 11

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

Example [Ref: 3] Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example Initial criteria for design selection 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) References 13

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

Cont/ Example Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example Initial criteria for design selection 5. Performing the experiment. Current Temperature Concentration -1 -1 -1 1 -1 -1 1 1 1 -1 1 References Factor solution concentration of the plating agent (S) being hard to vary 15

Cont/ Example Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example Initial criteria for design selection References n the randomization of the treatment runs is restricted somewhat by the level of the solution concentration factor. n 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). 16

Initial criteria for design selection (1/5) Criteria 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 17

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

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

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

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

References Nested Designs Definition Aim Example Split-Plot Designs: Definition Situations leading to Split-plot Example Initial criteria for design selection References n n n n n [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/div 898/handbook/pri/section 1/pri 11. 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] 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 22

DESIGN OF EXPERIMENTS NESTED DESIGNS SPLIT PLOT DESIGNS DISCUSSION