Seven-Factor Central Composite Design Robust to A Pair of Missing Observations.

Abstract:

Seven-factor central composite design has been studied with respect to a pair of missing observations. The central composite designs comprise of factorial, axial and center parts. All possible combinations of the missing points are considered. The study is based on the criterion of minimizing the maximum loss, which depends mainly on the number of factors involved in the experiment, the distance of the axial point from the design centre (  ) and position of the missing points. The work considered the case of minimizing the maximum loss when two observations are missing in a Central Composite Design (CCD) with k =7. The loss of every possible combination of two missing observations was calculated using minimax loss criterion, and groups of two missing observations producing same losses formed. The process was repeated for a range of  values to locate the  for which the maximum loss is minimum. It was discovered that the loss effect of missing a pair of factorial points is a decreasing function of increasing , while the loss effect of a pair of axial points is a decreasing and increasing function of increasing . The loss effect of missing a factorial and axial point has no specific direction of increase or decrease on increasing  values. It was also discovered that irrespective of the value of k, when a couple of a pair of observations is missing the design will breakdown.