Fit, Diagnose Model and Center Points

Fitting and diagnosing a model is one of the most critical steps in designed experiments. While the experimental structure determines what you can learn, the model fit determines how well you can trust what you’ve learned. In the Improve phase, where DOE results directly inform improvement decisions, you need a model that accurately reflects the process and provides reliable predictions. Fitting the model, diagnosing its assumptions, and using center points to detect curvature ensure that your conclusions are both statistically sound and practically meaningful. 

The first step is fitting the model. For a 2ᵏ factorial design, this typically involves estimating main effects and two‑way interactions. The model is built by regressing the response on coded factor levels, which simplifies interpretation and ensures orthogonality. The resulting coefficients tell you how each factor and interaction influences the response. Main effects show the independent influence of each factor; interactions reveal whether the effect of one factor depends on the level of another. 

Once the model is fit, the next step is diagnosing its adequacy. This involves examining residuals to ensure that the model meets key assumptions: linearity, independence, normality, and constant variance. Residuals should appear as random noise. Patterns in residuals—such as curvature, funnel shapes, or time‑based drift—signal that the model is missing important structure. These diagnostics protect you from drawing incorrect conclusions or making misguided improvement decisions. 

Center points play a crucial role in diagnosing curvature. A 2ᵏ factorial design uses only high and low levels for each factor, which means it cannot detect non‑linear relationships. Center points—runs conducted at the midpoint of all factor levels—provide a way to test for curvature. If the average response at the center points differs significantly from the average of the factorial points, curvature is present. This indicates that a linear model is insufficient and that a quadratic model or response surface design may be needed. 

Center points also help estimate pure error, which strengthens the reliability of significance tests. Pure error reflects natural process variation and provides a baseline for evaluating whether observed effects are meaningful. 

In the Improve phase, fitting and diagnosing the model ensures that your DOE results are trustworthy. Center points add depth to your understanding by revealing curvature and strengthening error estimates. Together, these steps ensure that your improvement decisions are grounded in a model that accurately reflects the process.