Effects of missing observations on predictive capability of augmented Box-Behnken designs

Abstract

In an experiment, there are many situations when some observations are missed, ignored or unavailable due to some accidents or high cost experiments. A missing observation can make the results of a response surface model quite misleading. It can have an adverse effect on desirable properties of a design like orthogonality, rotatability and optimality. Literature exhibits that some studies have investigated the effects of missing observations on prediction capabilities of response surface designs like Central Composite designs. This work investigates the impact of a missing observation on the estimation and prediction capabilities as well as on the relative A, D and G-efficiencies of augmented Box-Behnken designs. It has been observed that precision of model parameter estimates as well as relative A, D and G-efficiencies are less affected by missing a center run, but more by missing other design points. Prediction capability is adversely affected if we try to predict the response at the same location where we have missed the design point, however, when we capture the overall situation throughout the design region, a missing observation has smaller effect on the prediction capabilities of augment Box-Behnken designs. Missing a center run has less effect than missing other design points on prediction capability of these designs.

Keywords:

• Augmented Box-Behnken designs
• missing observations
• efficiency
• predictive capability
• prediction variance