Abstract
The paper illustrates a new way of using the CARSO procedure for response surfaces analyses derived from innovative experimental designs in multivariate spaces, based on Double Circulant Matrices (DCMs). We report a case study regarding a design based on a DCM for 4 variables. The final response surface model is obtained by the formerly developed CARSO method.
Highlights
Following our previous paper published on November 2012 [1], where we showed a strategy for collecting the data needed for defining a response surface on the basis of a D-optimal design, we present a further innovative strategy that requires a much lower number of experimental data, based on Double Circulant Matrices (DCMs)
The results of this first study based on collecting data on a DCM could not yet be used by the company for improving the quality of its products, the experience gained in this work will be helpful for testing what will happen with larger matrices
In particular we have clearly seen, just because we used all three sm.s, that each sm contains only one mixture giving good results, a second mixture with more or less fairly good ones, while the other two mixtures give low results. This result is not surprising: on the contrary it was somewhat expected, because each sm covers the 4D space in a regular circulant way, that creates a similar relative distance between objects, even if in different sectors of the hyperspace. If this will be proven to be true for larger matrices, as we expect, the problem of selecting the best couple might be abandoned, just because each sm to be added to the generating sequence can bring always the same type of global information
Summary
Following our previous paper published on November 2012 [1], where we showed a strategy for collecting the data needed for defining a response surface on the basis of a D-optimal design, we present a further innovative strategy that requires a much lower number of experimental data, based on Double Circulant Matrices (DCMs). The way mixtures are produced today is often based on established knowledge and tradition rather than on a scientific approach by statistical or chemometric strategies. Based on our previous experience in optimization procedures [5]-[9] we present a further innovative strategy for designing experiments in mixture analysis, by means of the DCMs, that have characteristics very similar to the requirements of Central Composite Designs (CCD), which represents the best way to gener-. (2014) Mixture Optimization by the CARSO Procedure and DCM Strategies. The final response surface model is obtained by the formerly developed CARSO method [5], where the surface equation is derived by a PLS model on the expanded matrix, containing linear, squared and bifactorial terms, and studied at extreme points by Lagrange analysis
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
