Analysis Methods for Two‐Level Non‐Regular Fractional Factorial Designs With 9–14 Factors in 16 Runs

Regular two‐level fractional factorial designs are widely used for factor screening experiments, where the objective is to efficiently identify the set of active factors from a larger initial group of factors. The 16‐run designs are very popular for screening because they can accommodate a reasonably large number of factors, and for 6–8 factors, they are Resolution IV, while for larger numbers of factors they are Resolution III. Assuming that 3‐factor and higher‐order interactions are negligible, the Resolution IV designs provide a clear estimate of the main effects while aliasing all 2‐factor interactions with each other, and the Resolution III designs alias main effects and 2‐factor interactions. Because of the aliasing, follow‐up experiments are often required to obtain complete information about main effects and 2‐factor interactions. However, there are many situations where follow‐up experimentation isn't possible. Nonregular fractional designs that do not have complete aliasing involving main effects and 2‐factor interactions can be a good alternative for these situations. However, analysis methods for these designs are an ongoing area of research. We investigate analysis methods for a class of non‐regular 2‐level fractional factorials for 9–14 factors in 16 runs. In these designs, there is no complete aliasing between the main factors and the two‐factor interactions, so these designs are useful alternatives to the regular Resolution III fractions. The analysis methods we consider are forward stepwise regression, the least absolute shrinkage and selection operator (LASSO), and the Dantzig selector method. We show that in most cases, for large and medium underlying model regression coefficients, stepwise regression and the LASSO outperform the Dantzig selector in correctly identifying the set of active factors for situations where the number of active factors does not exceed approximately half of the number of degrees of freedom for the design.