Interpreting the Analysis

No significant effects

When nothing is significant, try plotting the factors individually versus the response by using the Graph Columns node on the left side of the screen. You may pick up on some trends that are interesting, even if they are not statistically significant

Green triangles on Half Normal Plot

These triangles represent unused degrees of freedom not used to estimate an effect. The pure error differences between replicates is the most common source of green triangles. The information from the unused degrees of freedom is pooled with the natural process variation to help separate the few true effects from the effects that are just noise.

Watch out for the situation when the green triangles are higher and farther to the right than the largest effect. The estimated error is larger than the effects caused by the factor changes.

Working with Factorial Screening Designs

Screening designs are used when there are so many factors the number of runs required to estimate higher-order terms exceeds the budget.

The goal of the screening experiment is to use as few runs as possible to decide which factors will be studied in more detail during the next phase. The assumption is the factors with strong main effects are the important factors. Saturated resolution III designs are too small for this purpose unless there are in fact no interactions between the factors. Resolution III designs confound the main effects with the two-factor interactions. Fractional factorial designs that are at least resolution IV (yellow, green, or full) are necessary to correctly identify factors with strong independent effects when interactions are likely. Minimum Run Screening and Definitive Screening designs are specialized screening designs that have fewer runs, but less flexibility.

Factors that are known to effect the process outcomes should be held at some reasonable constant and not included as a variable in the experiment. Why spend the runs testing these factors when it is known they have effects and will survive the screening process?

Important factors will change the response a substantial amount. The meaning of substantial is up to the experimenter. Building a design that has at least 80% power to detect substantial effects given the expected variation helps to ensure the screening design has a reasonable chance to find the important factors. However, size of the effects is a more important metric than a significance test on the ANOVA. If no effects are significant, then force the linear terms into the model. Calculate the size of the effect by doubling the linear coefficients shown in the ANOVA. The factors with substantial effects survive to the next round. The perturbation plot is a good visual tool for showing the relative size of the effects.

Screening designs do allow for estimating the interaction effects, but do not usually have enough information to test them for significance. This means the choice of which subset of the interactions encompasses the truth is usually not clearly revealed by the data alone. Informed opinions are a necessary part of analyzing screening designs especially where interactions are involved.

Screening designs are intended to be followed by a characterization design including the previously known to be important factors and the factors that survived screening. Characterization designs concentrate on finding the important interactions and, if center points are included, detecting curvature.

Working with Mixture screening Designs

Mixture screening designs are used when there are so many components the number of runs required to estimate higher-order, blending effects, terms exceeds the budget. One must make the assumption that the linear effects will be enough to decide which components truly matter to the process.

The goal of a mixture screening experiment is to use as few runs as possible to decide which components will be studied in more detail during the latter phases of the experimentation process.

Mixture screening designs require at least 2 vertices per component to estimate the linear effects. Usually replicated center points are added to the base designs to provide a more powerful test and allow the detection of substantial blending effects. Although a mixture screening design can detect blending, there is usually not enough information to determine which components are contributing to the blending effect. The choice of which subset of the components take part in the blending requires the informed opinions of subject matter experts.

The analysis concentrates on estimating the linear gradients and effects of the individual components. These estimate are shown on the ANOVA any time a linear model is fit during the analysis of a mixture design. The Trace plot is a great visual representation of the relative effects coming from the components.

Components that have about the same gradient across all the critical responses can be treated like a family and combined into a single component for future work. This decision must be supported by subject matter expert opinion. If there is no science to justify combining components, then they shouldn’t be combined.

An example of combinable components is blending flours to make cupcakes. Three flours are used cake, bread, and all-purpose – these flours have about the same effect on taste and texture for this example. Because they are all flour, in makes sense that flour blends could be used in place of single flour. A very important part of combining factors is the similarities must carry across all critical responses.

When there are minimize and/or maximize goals for the responses, components that drive the response the wrong way can be set to the minimum possible for future work. If components have little to no beneficial effect on the response (gradient close to 0) these can also be fixed to nominal values for future work. Fixing the setting of a component removes it as a variable from future work.

Combining components into families, removing or minimizing detrimental components and fixing the levels of non-involved components accomplishes the goal of simplifying future work.