The concept was introduced by Frank Yates (1948)[full citation needed] and William J. Youden (1972)[full citation needed] "as a way of avoiding bad spatial patterns of treatments in designed experiments.
The total amount of data generated per batch run will be 7 · 9 = 63 observations.
One approach to analyzing these data would be to compute the mean of all these points as well as their standard deviation and use those results as responses for each run.
Analyzing the data as suggested above is not absolutely incorrect, but doing so loses information that one might otherwise obtain.
This kind of restricted randomization always produces nested sources of variation.
Examples of nested variation or restricted randomization discussed on this page are split-plot and strip-plot designs.
Because the wafers and the sites represent unwanted sources of variation and because one of the objectives is to reduce the process sensitivity to these sources of variation, treating wafers and sites as random effects in the analysis of the data is a reasonable approach.
Split-plot designs result when a particular type of restricted randomization has occurred during the experiment.
The treatment combinations to be run (orthogonally scaled) are listed below in standard order (i.e., they have not been randomized): Consider running the experiment under the first condition listed above, with the factor solution concentration of the plating agent (S) being hard to vary.
In other words, the randomization of the treatment runs is restricted somewhat by the level of the solution concentration factor.
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).
Once one complete replicate of the experiment has been completed, a second replicate is performed with a set of four copper strips processed for a given level of solution concentration before changing the concentration and processing the remaining four strips.
The ANOVA table for this experiment would look, in part, as follows: The first three sources are from the whole-plot level, while the next 12 are from the subplot portion.
Consider running the experiment under the second condition listed above (i.e., a batch process) for which four copper strips are placed in the solution at one time.
Since there are 8 degrees of freedom for the subplot error term, this MSE can be used to test each effect that involves current.
Note that we have separate error terms for both the whole plot and the subplot effects, each based on 4 degrees of freedom.
Specifying the appropriate model for a split-plot design involves being able to identify each size of experimental unit.
The way an experimental unit is defined relative to the design structure (for example, a completely randomized design versus a randomized complete block design) and the treatment structure (for example, a full 23 factorial, a resolution V half fraction, a two-way treatment structure with a control group, etc.).
If the data from an experiment are analyzed with only one error term used in the model, misleading and invalid conclusions can be drawn from the results.
As a result of the restricted randomization that occurs in strip-plot designs, there are multiple sizes of experimental units.
The settings for a two-level factorial design for the three factors in the implant step are denoted (A, B, C), and a two-level factorial design for the three factors in the anneal step are denoted (D, E, F).
Therefore, this experiment contains three sizes of experimental units, each of which has a unique error term for estimating the significance of effects.
To put actual physical meaning to each of the experimental units in the above example, consider each combination of implant and anneal steps as an individual wafer.
This is continued until the last batch of eight wafers has been implanted with a particular combination of factors D, E, and F. Running the experiment in this way results in a strip-plot design with three sizes of experimental units.
Actually, the above description of the strip-plot design represents one block or one replicate of this experiment.
If the experiment contains no replication and the model for the implant contains only the main effects and two-factor interactions, the three-factor interaction term A*B*C (1 degree of freedom) provides the error term for the estimation of effects within the implant experimental unit.
Invoking a similar model for the anneal experimental unit produces the three-factor interaction term D*E*F for the error term (1 degree of freedom) for effects within the anneal experimental unit.
For a more detailed discussion of these designs and the appropriate analysis procedures, see: This article incorporates public domain material from the National Institute of Standards and Technology