The sum of all mixture factor values in a mixture experiment is a constant, usually, and henceforth assumed to be 1. Each individual factor’s value can range between 0 and 1, and three are represented on the axes of the ternary plot.
For a three factor mixture experiment in which the factors sum to 1, the plot axes run from a vertex (where a factor’s value is 1 and the other two are 0) perpendicular to the other side (where that factor is 0 and the sum of the other two factors is 1). See Explanation of p1 Axis.
For example, in Explanation of p1 Axis, the proportion of p1 is 1 at the top vertex and 0 along the bottom edge. The tick mark labels are read along the left side of the plot. Similar explanations hold for p2 and p3.
Explanation of p1 Axis
The ternary plot can only show three factors at a time. If there are more than three factors in the model that you are profiling, the total of the three on-axis (displayed) factors is 1 minus the total of the off-axis (non-displayed) factors. Also, the plot axes are scaled such that the maximum value a factor can attain is 1 minus the total for the off-axis factors.
For example Scaled Axes to Account for Off-Axis Factors Total shows the Mixture Profiler for an experiment with 5 factors. The Five Factor Mixture.jmp data table is being used, with the Y1 Predicted column as the formula. The on-axis factors are x1, x2 and x3, while x4 and x5 are off-axis. The value for x4 is 0.1 and the value for x5 is 0.2, for a total of 0.3. This means the sum of x1, x2 and x3 has to equal 1 – 0.3 = 0.7. In fact, their Current X values add to 0.7. Also, note that the maximum value for a plot axis is now 0.7, not 1.
If you change the value for either x4 or x5, then the values for x1, x2 and x3 change, keeping their relative proportions, to accommodate the constraint that factor values sum to 1.