Prediction variance and G-criterion location for split-plot designs.

Wesley, Wayne R.; Simpson, James R.; Parker, Peter A.; Pignatiello Jr., Joseph J.

Prediction variance properties for completely randomized designs (CRD) are fairly well covered in the response surface literature for both spherical and cuboidal designs. This paper evaluates the impact of changes in the variance ratio on the prediction properties of second-order split-plot designs (SPD). It is shown that the variance ratio not only influences the value of the G-criterion but also its location, in contrast with the G-criterion tendencies in CRD. An analytical method, rather than a heuristic optimization algorithm, is used to compute the prediction variance properties, which include the maximum, minimum and integrated variances for second-order SPD. The analytical equations are functions of the design parameters, radius and variance ratio. As a result, the exact values for these quantities are reported along with the location of the maximum prediction variance used in the G-criterion. The two design spaces of the whole plot and the subplot are studied and as a result, relative efficiency values for these distinct spaces are suggested. Copyright © 2008 John Wiley & Sons, Ltd.

FORECASTING; ANALYSIS of variance; MATHEMATICAL statistics; RESPONSE surfaces (Statistics); GRAPHIC methods in statistics

Quality & Reliability Engineering International, 2009, Vol 25, Issue 4, p381

0748-8017

Academic Journal

10.1002/qre.975