Experiments with mixtures. Designs, models, and the analysis of mixture data. 3rd ed.

*(English)*Zbl 1001.62024
Wiley Series in Probability and Statistics. Chichester: Wiley. xxii, 649 p. (2002).

This encyclopedic book, like its pioneering previous editions from 1990, see the review Zbl 0732.62069, and from 1981, see the review Zbl 0597.62087, that have become classics in the field, is an authoritative and up-to-date treatise on the design and analysis of mixture experiments. It is divided into eight chapters:

Chapter 1. Introduction; Chapter 2. The original mixture problem: Designs and models for exploring the entire simplex factor space; Chapter 3. The use of independent variables; Chapter 4. Multiple constraints on the component proportions; Chapter 5. The analysis of mixture data; Chapter 6. Other mixture model forms; Chapter 7. The inclusion of process variables in mixture experiments; Chapter 8. Additional topics; Chapter 9. Matrix algebra, least squares, and the analysis of variance; Chapter 10. Data sets from mixture experiments with partial solutions.

The main new features of this third edition, compared to the previous one, are as follows:

(a) The chronological listing of selected statistical literature on mixture experiments has been updated in Chapter 1.

(b) A new appendix on the partitioning of the sources in the analysis of variance table when fitting the Scheffe mixture models has been added to Chapter 2.

(c) Chapter 4 has received a new subsection entitled “Allowing the major component proportions to vary: Mixtures of mixtures”.

(d) Chapter 5 has been expanded with the inclusion of the currently available types of computer software outputs.

(e) A new section, entitled “Fitting a slack-variable model”, has been added to Chapter 6.

(f) A new section, entitled “Questions raised and recommendations made when fitting a combined model containing mixture components and other variables”, has been added to Chapter 7. An appendix on a generalized least squares solution with reference to a split-plot experiment has also been included in this chapter.

(g) Four new sections have been added to Chapter 8. These cover topics like (i) biplot displays for multiple response data, with illustration via a five-response example, (ii) multiple response optimization through the use of desirability functions or by the overlaying of contour plots, (iii) the modified \(L\)-pseudocomponent model, (iv) the centered and scaled intercept model, and so on.

(h) A subsection on press statistics and studentized residuals has been added to Chapter 9.

(i) The bibliography has been updated. It now runs over 15 pages.

The present edition, like the previous ones, is lucid and will form the basis of an excellent course on mixture experiments and become a most valuable reference for researchers and practitioners. The inclusion of a large number of exercises (with answers to selected ones) and numerical examples will endear the book to its readers. Chapter 9, giving the background material on matrix algebra, least squares and analysis of variance, will make the book particularly reader-friendly. In summary, the book can be thoroughly recommended to anyone who wishes to acquire a sound knowledge of this subject.

Chapter 1. Introduction; Chapter 2. The original mixture problem: Designs and models for exploring the entire simplex factor space; Chapter 3. The use of independent variables; Chapter 4. Multiple constraints on the component proportions; Chapter 5. The analysis of mixture data; Chapter 6. Other mixture model forms; Chapter 7. The inclusion of process variables in mixture experiments; Chapter 8. Additional topics; Chapter 9. Matrix algebra, least squares, and the analysis of variance; Chapter 10. Data sets from mixture experiments with partial solutions.

The main new features of this third edition, compared to the previous one, are as follows:

(a) The chronological listing of selected statistical literature on mixture experiments has been updated in Chapter 1.

(b) A new appendix on the partitioning of the sources in the analysis of variance table when fitting the Scheffe mixture models has been added to Chapter 2.

(c) Chapter 4 has received a new subsection entitled “Allowing the major component proportions to vary: Mixtures of mixtures”.

(d) Chapter 5 has been expanded with the inclusion of the currently available types of computer software outputs.

(e) A new section, entitled “Fitting a slack-variable model”, has been added to Chapter 6.

(f) A new section, entitled “Questions raised and recommendations made when fitting a combined model containing mixture components and other variables”, has been added to Chapter 7. An appendix on a generalized least squares solution with reference to a split-plot experiment has also been included in this chapter.

(g) Four new sections have been added to Chapter 8. These cover topics like (i) biplot displays for multiple response data, with illustration via a five-response example, (ii) multiple response optimization through the use of desirability functions or by the overlaying of contour plots, (iii) the modified \(L\)-pseudocomponent model, (iv) the centered and scaled intercept model, and so on.

(h) A subsection on press statistics and studentized residuals has been added to Chapter 9.

(i) The bibliography has been updated. It now runs over 15 pages.

The present edition, like the previous ones, is lucid and will form the basis of an excellent course on mixture experiments and become a most valuable reference for researchers and practitioners. The inclusion of a large number of exercises (with answers to selected ones) and numerical examples will endear the book to its readers. Chapter 9, giving the background material on matrix algebra, least squares and analysis of variance, will make the book particularly reader-friendly. In summary, the book can be thoroughly recommended to anyone who wishes to acquire a sound knowledge of this subject.

Reviewer: R.Mukerjee (Kolkata)