Plotting Response Surface Contours for Three-Component Mixtures

Hare, Lynne B.; Brown, Philip L.

doi:10.1080/00224065.1977.11980797

Cited by 14 publications

(2 citation statements)

References 9 publications

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“…60 His ideas were subsequently extended by Henry Scheffe at the University of California to form the basis of simplex-lattice and simplex-centroid designs. 61 Their subsequent incorporation into modern textbooks, 62 and development of computer programs to plot the associated response surfaces, 63 has established the ternary diagram as an indispensable tool in experimental studies (often to do with industrial manufacturing processes) involving mixture-models, for example finding the optimum blend of three chemicals which maximizes the yield and/or quality of their reactionproduct.…”

Section: O N C L U S I O Nmentioning

confidence: 99%

Sources for a history of the ternary diagram

Howarth

1996

Brit. J. Hist. Sci

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Anyone reading the literature on the history of graphs will soon realize that the use of graphie displays of any type was really quite unusual until the mid-ninetenth century and that those scientists who did make use of them are often familiar to us as creative thinkers in their own fields of endeavour. A ternary diagram (also known as a triangular diagram) is a particular type of graph which consists of an equilateral triangle in which a given plotted point represents the relative proportions (a, b, c) of three end-members (A, B and C), generally expressed as percentages and constrained by a + b + c = 100%. It has long been used to portray sample composition in terms of three constituents, or an observed colour in terms of three primary colours, because it is a convenient means of representing a three-component System in a planar projection, rather than as an isometric, or similar, view of a three-dimensional space. Recent papers suggest that its use is not as familiar to some statisticians as are other commonly used forms of graph. For example, although it was cited by Peddle in 1910 and more recently by Dickinson, it is not discussed in modern texts on statistical graphies nor in the key papers on the history of graphs. However, beginning with studies of colour-mixing in the eighteenth century, it has subsequently become widely used, particularly in geology, physical chemistry and metallurgy. In this paper, I attempt to document its gradual uptake as a standard method of data display and some of the scientific advances which its use has facilitated.

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Section: O N C L U S I O Nmentioning

confidence: 99%

Sources for a history of the ternary diagram

Howarth

1996

Brit. J. Hist. Sci

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“…Those seven points in the design are necessary for the calculation of the coefficients (i.e., functions of the measured responses) in the special cubic equation derived from the Taylor series (Hare & Brown, 1977). We used a special computer program developed to plot the desired contours.…”

Section: Introductionmentioning

confidence: 99%

Grocery Store Attributes in Recovering Economies: An Empirical Investigation of Their Importance, Using Three-Component Contour Plotting

Shultz

Renko

Brčić-Stipčević

2010

Journal of International Food & Agribusiness Marketing

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The authors share results of a study conducted to measure the attributes of grocery stores that are the most important for consumers in a market recovering from war and transitioning to a market economy. Applying a trilinear coordinate plot, the authors develop a model that consists of those attributes. The findings led to conclusions that services and location, rather than the historically favored attribute of price, increasingly are key factors affecting store choice. Managerial implications are discussed and future research directions are suggested.

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Bibliography

2011

A Primer on Experiments With Mixtures

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Plotting Response Surface Contours for Three-Component Mixtures

Cited by 14 publications

References 9 publications

Sources for a history of the ternary diagram

Sources for a history of the ternary diagram

Grocery Store Attributes in Recovering Economies: An Empirical Investigation of Their Importance, Using Three-Component Contour Plotting

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