A Framework for the Development of Design and Control Spaces

Abstract

We present a framework for the development of design and control spaces that simultaneously considers the raw material property space (Z), the critical to quality process variable space (X), and the critical quality attribute space (Y). The importance of jointly defining all of these spaces and simultaneously considering the eventual process feedforward–feedback control system is illustrated. It is shown that changes in any one of these spaces or in the control system will greatly affect the other spaces. Justification is provided for the use of multivariate principal component analysis and projection to latent structures methods to define more meaningful raw material design spaces and the use of statistical process control concepts to redefine control spaces.

Appendix

This appendix provides details of the simulation model necessary for the reader to reproduce the results presented in this article. The true simulation model takes the form:

$$y = \beta _0 + \beta _1 x_1^2 + \beta _2 x_1 x_2 + \beta _3 x_2^2 + \beta _4 x_1 + \beta _5 x_2 + \beta _6 x_2 z_1 + \beta _7 x_2 z_2 + \beta _8 z_1 + \beta _9 z_2 $$

(1)

The specific parameter values in Eq. 1 are listed in Table 1.

Table 1 Specific parameter values for Eq. 1

Furthermore, the specific principal property values for the raw materials (z ₁, z ₂) that were used in the case study are listed in Table 2.

Table 2 Specific principal property (z ₁, z ₂) combinations for the raw materials that were used in the simulated case study