Effective data analysis methods for incomplete two-level factorial experiments

Designing and analysing two-level factorial or fractional factorial experiments require all experimental runs should be completed. However, in many actual industrial experiments, a portion of experimental runs cannot be completed due to either infeasibility or budget limitation, resulting in incomplete experiments. In this paper, two effective methods to estimate the factorial effects in incomplete 2 level factorial or fractional factorial experiments are developed. In the first method, each traditional factorial main effect or interaction effect is decomposed as the average of many individual elementary effects. Under this model, missing runs in factorial experiments only affect some individual elementary effects; the main effects or interactions can still be estimated by the partial average of the remaining individual elementary effects. The second method is based on estimation of missing runs by using response surface model on incomplete experimental data set. These two methods are compared with other two existing methods for incomplete factorial experiments on eight testing problems and the results show our two methods perform well.