Effects of missing observations on predictive capability of central composite designs

TL;DR

This paper examines how missing observations in Central Composite Designs (CCDs) negatively impact their estimation accuracy and predictive capabilities, highlighting the importance of data completeness for reliable response surface modeling.

Contribution

It investigates the effects of missing data on CCDs' prediction and estimation, focusing on the impact of missing factorial, axial, and center points.

Findings

Missing observations reduce estimation precision and prediction accuracy.

Largest loss occurs when factorial points are missing.

Design properties like orthogonality and rotatability are compromised.

Abstract

Quite often in experimental work, many situations arise where some observations are lost or become unavailable due to some accidents or cost constraints. When there are missing observations, some desirable design properties like orthogonality, rotatability and optimality can be adversely affected. Some attention has been given, in literature, to investigating the prediction capability of response surface designs; however, little or no effort has been devoted to investigating same for such designs when some observations are missing. This work therefore investigates the impact of a single missing observation of the various design points: factorial, axial and center points, on the estimation and predictive capability of Central Composite Designs (CCDs). It was observed that for each of the designs considered, precision of model parameter estimates and the design prediction properties were adversely affected by the missing observations and that the largest loss in precision of parameters corresponds to a missing factorial point.