Extended scaled prediction variance optimality for modified central composite design

Robust parameter designs (RPDs) enable the experimenter to discover how to modify the design of the product to minimize the effect due to variation from noise sources. The aim of this article is to show how this amount of work can be reduced under modified central composite design (MCCD). We propose a measure of extended scaled prediction variance (ESPV) for evaluation of RPDs on MCCD. Using these measures, we show that we can check the error or bias associated with estimating the model parameters and suggest the values of α recommended for MCCS under minimum ESPV.     

A reference prior for the analysis of a response surface

Standard response surface methodology employs a second order polynomial model to locate the stationary point ξ$\mathit{\xi }$ of the true response function. To make Bayesian analysis more direct and simpler, we refer to an alternative and equivalent parametrization, which contains ξ$\mathit{\xi }$ as parameter of interest. The marginal reference prior of ξ$\mathit{\xi }$ is derived in its general form and particular cases are also given in detail, showing the Bayesian role of rotatability.