DOE and Factors (or Variables)

Design of Experiments (DoE) is a structured, organized design/run matrix creation method that once run will be used to determine the relationships between the different factors/variables (Xs) affecting a process and the output of that process (Y).

Factors are system parameters that change the system performance.

Variables are system parameters that can be changed to improve the system performance. Since this chapter is part of a design study process, we will be using factors and variables interchangeably.

Reduced variables: In DOE terminology, it is standard practice to work with reduced variables that have a range of -1 to 1 for each real variable. Reduced variables are associated to real variables with the following formula:

Levels: The values taken by in the range [-1; +1]. Number of levels per variable to be considered depends on the level of non linearity in the problem; for a linear model two levels are sufficient; for a quadratic model three levels are needed.

 

Confounding (or aliasing) and Resolutions

Confounding occurs when two factors are associated with each other or “travel together” and the effect of one is confused with the effect of the other. For example, in order to improve team performance, a soccer coach asks his team to run two miles a day while the players decide to take vitamins. In this case the effects of running two miles a day and taking vitamins will be confounded since it will not be possible to identify the effect of them on team performance independently.

Confounding occurs whenever a fractional factorial design is chosen instead of a full-factorial design. The consequence of confounding in DOEs is that the values calculated for main effects will have error coming from inclusion of higher order interactions in the calculation and interaction effects will be unknown. However fractional factorials also cost a fraction of the full factorial designs and therefore in the trade-off between cost and accuracy, they are preferred.

Example:

A Full Factorial DOE for an output response that is a function of three variables is:

Table 4: Design Matrix

The effects are calculated as:

A fractional Factorial DOE for the same output response is:

Table 5: Design Matrix

As seen in this example, main effect values are not accurate since they include the interactions effects and consequently interactions are not captured. However, the results are still accurate enough for practical purposes (Full Factorial showed A, C and AC to be the most important contributors to the output response Y; Fractional Factorial showed A and C to be the most important contributors) and furthermore this DOE required half the runs of a full factorial design.

Resolution describes the degree to which estimated main effects are aliased (or confounded) with estimated 2-level interactions, 3-level interactions, and so on. The design resolution tells us how badly the design is confounded. Resolution III designs confound main effects with two-factor interactions. Resolution IV designs confound main effects with three-factor interactions (A+BCD), as well as two-factor interactions with other two-factor interactions (AB+CD). Resolution V designs confound main effects with four-factor interactions, or two-factor interactions with three-factor interactions.

Higher resolution designs have less severe confounding, but require more runs. A resolution IV design is "better" than a resolution III design because we have less-severe confounding pattern in the `IV' than in the `III' situation. However in most cases higher-order interactions are less significant than low-order interactions and therefore there is not much benefit to higher resolution designs that come at the cost of additional computational expense.

 

 

See Also

Post-Processing for DOEs