The second-order model has identified the point that predicts the highest yield. Even if the software outputs conditions with decimal precision, that point is still just a candidate point suggested by the model and the objective function.

Contours and surfaces are two views of the same fitted model.

A 3D surface plot shows the predicted height for each x·y combination. A contour plot shows the same predicted values connected by lines, as viewed from above. They are not different analyses, but rather the same model viewed from different perspectives.

If the contour lines are closed ellipses, there may be a peak or valley candidate inside. If the lines continue to improve as they approach the boundary of the design region, it is possible that the actual optimum is outside the range, but the current data does not support this. Predictions that end at the boundary are not extended by extrapolation.

The Profiler connects multiple cross-sections.

In the Prediction Profiler, moving the vertical line of one factor changes the predicted cross-section while keeping the other factor fixed at its current position. If there is an x·y interaction, the slope of x will vary depending on the y position. Do not interpret a single line in the Profiler as an independent, univariate effect.

The Profiler displays not only the prediction line, but also the confidence interval and factor range whenever possible. Observe whether the prediction uncertainty increases at the end of the range.

Desirability does not replace scientifically defining the objective.

The individual desirability, which converts the goal for each response to a value between 0 and 1, is denoted as dᵢ, and the importance weight is denoted as wᵢ. The composite desirability can then be created as a weighted geometric mean.

D = (∏ dᵢ^wᵢ)^(1/Σwᵢ)

For example, to maximize yield and minimize impurities, define the acceptable limit, target, and importance for each. The software does not scientifically justify these values. Since changing even one limit can shift the optimal candidate, the goal definition should be reported along with the results.

Confirmation experiments are new evidence not used in fitting

Independently run new experimental units at the candidate conditions and compare the predicted and observed values. Simply showing the fitted value from the same table again is not confirmation.

The confirmation plan should include the following:

• Candidate conditions and actual units
• Predicted values and prediction uncertainty
• Number of independent replicates and execution order/block
• Success criteria and acceptable prediction difference
• Rules to distinguish model, range, and process issues when failure occurs

If the observed mean differs from the prediction, do not simply conclude with "optimization failed." Check for model bias, execution condition errors, new batches, and measurement variations.

Augment adds new points to address remaining questions

If curvature at the center point was discovered in the initial factorial design, it can be expanded to a CCD by adding axial points. If the predicted optimal point is on the boundary and the information is weak, candidate points in that direction can be added. Distinguish between confirmation points and augment points for model improvement, as they have different purposes.

When selecting new points, evaluate whether the desired terms become estimable and the prediction variance is reduced when combined with the existing design. Also, record how the additional runs will be connected to the existing blocks.

In-Silico Lab: Change the objective and view new confirmation values

1. Confirm the candidate with a yield weight of 2 and an impurity weight of 1.
2. Increase the impurity weight to 4 and see if the x and y candidates move.
3. Change the seed at the same candidate and see if the 3 confirmation means fluctuate.
4. Confirm that all candidates are within −1≤x,y≤1.

The Lab compares synthetic desirability in an educational grid with 0.05 intervals. It does not reproduce continuous optimization algorithms or JMP's internal optimizer, and the confirmation values are also synthetic data.

Connect JMP expressions to result statements

Contours and Surfaces show the location of candidates, the Prediction Profiler shows factor cross-sections and targets, and Desirability shows the specified trade-offs. In the Augment evaluation, the information purpose of the additional runs is verified. Capturing the screen alone does not preserve the target, range, and confirmation plan, so the table and receipt should be saved together.

Example of Result Statement

Within the studied range, the yield maximization and impurity minimization desirability were defined with weights of 2 and 1, respectively. The candidate with the largest composite D was x=0.55, y=0.35, which is within the observed region. The mean of three new independent runs differed from the predicted yield by 0.4 units. The next augment is determined based on the target weight sensitivity and confirmation results.

Concluding the Section

• Contour, surface, and Profiler are different representations of the same model.
• The target, limit, and importance of desirability are user-defined.
• An optimal point outside the design region is not a conclusion of the current data.
• A confirmation experiment is a new, independent run not used in the fitting.
• Augment points are selected to address remaining aliases, curvature, and prediction questions.

In the next section, we will look at the output distribution and pass rate, rather than the average, when the input fluctuates around the optimal conditions.

Supplementary Materials for the Formula

• NIST/SEMATECH · Response Surface Methods
• JMP Help · Launch the Prediction Profiler Platform
• JMP Help · Augment Design Platform Options

This article and the Lab are educational synthetic materials and should not be used as evidence for actual research, process, quality, or regulatory decisions.