i-optimal design

**I-Optimal Design** is an **optimal experimental design that minimizes the average prediction variance across the entire design space** — focusing on the accuracy of predictions rather than parameter estimates, making it the preferred criterion when the goal is to build a predictive model. **I-Optimal vs. D-Optimal** - **I-Optimal**: Minimizes $int Var[hat{y}(x)] dx$ (integrated prediction variance over the design space). - **D-Optimal**: Minimizes parameter variance (maximizes $|X^TX|$). - **For Prediction**: I-optimal produces better predictions on average; D-optimal produces more precise parameters. - **Software**: JMP and other DOE software support I-optimal design generation. **Why It Matters** - **Surrogate Models**: When the goal is building a predictive model (virtual metrology, response surface), I-optimal is the best criterion. - **Process Optimization**: Better predictions lead to more accurate identification of the optimal operating point. - **Design Space**: I-optimal designs typically place more points at the boundaries of the factor space. **I-Optimal Design** is **designing for the best predictions** — minimizing prediction error across the entire design space for the most accurate process model.