Copyright© 2008 Stephen Smith & Associates Inc. All rights reserved
A standard industrial strategy starts with a screening design to understand which process factors have the biggest effect. If necessary, there is a follow up with an optimization design that let’s us model the process response surface as a function of the most important process factors.
For some processes, this standard approach takes too long. In this case, orthogonal array designs combine screening and response surface exploration into a single step.
An experimental design is orthogonal when each level of every experimental factor is found in combination with each level of all the other experimental factors. In practice, in more complex situations - when we lose data, or there are other constraints (like expense) we may use a design whose columns are not completely orthogonal. The general rule is, the more orthogonal the columns are, the better the design and the more independent information that can be extracted from the design.
The amount of uncertainty in the prediction of a dependent variable depends on the variability of the experimental points and on how independent each main factor is from the other main factors. We want an experimental design that extracts the most information and leaves the least amount of uncertainty for the prediction of future values. Designs that best meet these criteria are called “rotatable”.
Orthogonality and rotatability depend upon the number of points in the centre of a design, and upon axial distance. The axial distance is the distance of the maximum and minimum factor levels from the centre of the design. The axial distance that will improve rotatability can be calculated for many experimental designs.
For a specific experimental design, there is a relationship between sample size and the probability of achieving statistical significance. For a fixed error rate and a set of population descriptors, power calculations will tell you the correct sample size to achieve a specific power of statistical test; or tell you the power of a test that is achievable from a specific sample size.
Experimental Strategy
Design Fundamentals
