An intuitive design pattern for sequentially estimating parameters of a 2k factorial experiment with active confounding avoidance and least treatment combinations

• Propose the concept of active confounding avoidance.
• Formalize the concepts of least treatment combinations and forward compatibility.
• Propose new concepts of 2k,i reduced model and 2k,i reduced design.
• Propose a simple pattern for generating 2k,i designs and sequential expansion.
• All 2k,i and intermediate designs have the aforementioned desirable properties.

2k Full factorial designs may be prohibitively expensive when the number of factors k is large. The most popular technique developed to reduce the number of treatment combinations is the fractional factorial design; confounding in estimating the model parameters naturally results in various resolution and aberration levels. While very useful, these resolution levels may not satisfy experimenters’ requirements for estimatibility and cost reduction. For example, while Resolution V ensures a common requirement that no two-factor interactions are confounded, it also imposes an often undesired restriction that a main effect cannot be confounded with a three-factor interaction, which may very well be non-existent or negligible. We propose a new concept of “active confounding avoidance” whose goal is to identify, for any given set of parameters, a set of treatment combinations such that estimates of the parameters are not confounded with one another. We show that the “least-treatment-combinations” methods developed for identifying a minimal set of m treatment combinations for a 2k model with only m non-zero parameters achieve this goal. We then propose a simple design pattern that achieves active confounding avoidance for parameters spanning from all main effects up to all i-factor interactions, for all i = 1, 2, … , k, all with the least number of treatment combinations. The pattern also specifies how treatment combinations should be sequenced for experimentation according to a parameter sequence of decreasing magnitude possibly specified by the experimenter based on prior knowledge. The former sequence is optimal in that the experimentation can stop whenever the current model is deemed adequate and experiments already conducted could be considered necessary.