How do you update and improve a Box-Behnken design based on feedback and new data?

1 Evaluate your model

The first step is to evaluate how well your BBD model fits the data and meets the assumptions. You can use various statistical tools, such as analysis of variance (ANOVA), residual plots, normal probability plots, and lack-of-fit tests, to check the significance, adequacy, and validity of your model. You should also compare the predicted and observed responses, and calculate the coefficient of determination (R-squared) and the root mean square error (RMSE). These measures can help you assess the accuracy and precision of your model.

2 Identify potential problems

The second step is to identify any potential problems or limitations with your BBD model. These could include nonlinear or complex relationships between the factors and the response, outliers or influential points that distort the model, multicollinearity or high correlation among the factors, constraints or restrictions on the factor levels or the response, and noise or variability in the data. All of these can reduce the robustness, stability, and reliability of the results.

3 Modify your design

The third step is to modify your BBD design based on the problems you identified and the feedback you received. Depending on the situation and the objective, there are various ways to do this. For example, you can add or remove factors or levels to modify the scope or complexity of the experiment, or add or remove axial or central points to adjust the precision or resolution of the model. Additionally, adding or removing replicates or blocks can increase or decrease the power or robustness of the test. You can also add or remove center or corner points to adjust the rotatability or orthogonality of the design, transform or scale the factors or response to improve linearity or normality, and apply or relax constraints and restrictions to expand or narrow the feasible region.

4 Re-analyze your data

The fourth step is to re-analyze your data using the modified BBD design. You should repeat the same steps as in the first step, but with the new data and design. You should also compare the results of the original and modified models, and see if there are any significant changes or improvements in the fit, significance, adequacy, validity, accuracy, precision, reliability, or reproducibility of the model.

5 Validate your model

The fifth step is to validate your model using independent or external data. This can be done by conducting a confirmation experiment, where you test the optimal settings suggested by your model and measure the actual response. You can then compare the predicted and observed responses, and calculate the prediction error or the confidence interval. This can help you verify the validity and generalizability of your model.

6 Communicate your results

The final step is to communicate your results and recommendations based on your BBD model. You should present your findings in a clear and concise way, using tables, graphs, equations, or summaries. You should also highlight the main effects, interactions, and optimal settings of the factors, and explain how they affect the response. You should also discuss the limitations, assumptions, and uncertainties of your model, and suggest any further steps or improvements that can be done.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?