Design criteria for model discrimination in factorial experiments with potential failing runs

Abstract

In this study, we considered the problem of design for model discrimination in factorial experiments, while there is potential to miss runs. Under such a situation, we questioned the reliability of the superior selected design based on the existing design criteria for model discrimination. In other words, any selected design may miss its efficiency in discriminating between models in the presence of failing runs. To this end, we assumed the missing probability of the runs based on some available information parameters and developed a new design criterion for model discrimination. The proposed Bayesian criterion makes allowance for counting the missing probabilities of runs. The Bayesian framework also takes into account the intercorrelation between the factorial effects. The numerical examples demonstrate the superiority of the obtained criterion to the existing ones in differentiating the rival design for model discrimination. We also considered the problem of design robustness to missing observations and suggested a ratio criterion for selecting the robust design. It was found that a robust design is not necessarily the most efficient in model discrimination and vice versa. Moreover, we also pointed to the estimation efficiency of the designs and gave a compound dual‐task design criterion.