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Montgomery

Choice of Factors and Levels

As noted in Table 1, this step and the next one are often done in the reverse order, or they may be done simultaneously. In any event, the experimenter must choose the factors to be varied in the experiment, the ranges over which these factors will be varied, and the specific levels at which runs will be madę. Thought must also be given to how these factors are to be controlled at the desired values and how they are to be measured. The experimenter will also have to decide on a region of interest for each variable (that is, on the rangę over which each factor will be varied) and on how many levels of each variable to use. Process knowledge is reąuired to do this. This process knowledge is usually a combination of practical experience and theoretical understanding.

It is important to investigate all factors that may be of importance, and to not be overly-influenced by past experience; particularly when we are in the early stages of experimentation or when the process is not very maturę. When the objective is factor screening or process characterization it is usually best to keep the number of factor levels Iow (most often two levels should be used). Specifically, the 2^k fractorial or 2^{k p} fractional factorial design augmented with center points should be the basie building błock of nearly all experimental programs.

When evaluating the design variables, it is also important to identify potential nuisance factors and factors that may be held constant during the experiment. If nuisance factors can be controlled, then they are candidates for blocking the design, while if they cannot be controlled (but they can be measured), then the analysis of covariance needs to be considered as the possible statistical methodology for data analysis. One must treat held-constant factors very carefully. If a held-constant factor interacts with other factors, then very misleading conclusions about the system can result.

Selection of the Response Variable

This section should be titled "Selection of the Response Variables", sińce all (or nearly all) real-world experiments have multiple responses. The classical single-response case only occurs in textbooks and joumal articles. Coleman and Montgomery (1993) argue for continuous responses measured on appropriate units that reflect the appropriate features of interest in the experimental unit. It is desirable for the response variable to not be near a natural boundary. It is also important to determine an appropriate performance measure for each response. Most often, the performance measure will be either