5.
Process Improvement
5.3. Choosing an experimental design


Guidelines to assist the engineering judgment process of selecting process variables for a DOE 
Process variables include both inputs and outputs 
i.e., factors and responses. The selection of these
variables is best done as a team effort. The team should


Be careful when choosing the allowable range for each factor  We have to choose the range of the settings for input factors, and it is wise to give this some thought beforehand rather than just try extreme values. In some cases, extreme values will give runs that are not feasible; in other cases, extreme ranges might move one out of a smooth area of the response surface into some jagged region, or close to an asymptote.  
Twolevel designs have just a "high" and a "low" setting for each factor  The most popular experimental designs are twolevel designs. Why only two levels? There are a number of good reasons why two is the most common choice amongst engineers: one reason is that it is ideal for screening designs, simple and economical; it also gives most of the information required to go to a multilevel response surface experiment if one is needed.  
Consider adding some center points to your twolevel design  The term "twolevel design" is something of a misnomer, however, as it is recommended to include some center points during the experiment (center points are located in the middle of the design `box').  
Notation for 2Level Designs  
Matrix notation for describing an experiment 
The standard layout for a 2level design uses +1 and 1 notation to
denote the "high level" and the "low level" respectively, for each
factor. For example, the matrix below
describes an experiment in which 4 trials (or runs) were conducted with each factor set to high or low during a run according to whether the matrix had a +1 or 1 set for the factor during that trial. If the experiment had more than 2 factors, there would be an additional column in the matrix for each additional factor. Note: Some authors shorten the matrix notation for a twolevel design by just recording the plus and minus signs, leaving out the "1's". 

The use of +1 and 1 for the factor settings is called coding the data. This aids in the interpretation of the coefficients fit to any experimental model. After factor settings are coded, center points have the value "0". Coding is described in more detail in the DOE glossary.  
The Model or Analysis Matrix  
Design matrices 
If we add an "I" column and an "X1*X2" column to the matrix of 4 trials
for a twofactor experiment described
earlier, we obtain what is known as
the model or analysis matrix for this simple experiment, which
is shown below. The model matrix for a threefactor experiment is shown
later
in this section.


Model for the experiment 
The model for
this experiment is


Model in matrix notation 
In matrix notation, we can
summarize this experiment by


Orthogonal Property of Scaling in a 2Factor Experiment  
Coding produces orthogonal columns  Coding is sometime called "orthogonal coding" since all the columns of a coded 2factor design matrix (except the "I" column) are typically orthogonal. That is, the dot product for any pair of columns is zero. For example, for X_{1} and X_{2}: (1)(1) + (+1)(1) + (1)(+1) + (+1)(+1) = 0. 