Statistical Adjustments to Engineering Models

Statistical models are commonly used in quality-improvement studies. However, such models tend to perform poorly when predictions are made away from the observed data points. On the other hand, engineering models derived using the underlying physics of the process do not always match satisfactorily with reality. This article proposes engineering—statistical models that overcome the disadvantages of engineering models and statistical models. The engineering—statistical model is obtained through some adjustments to the engineering model using experimental data. The adjustments are done in a sequential way and are based on empirical Bayes methods. We also develop approximate frequentist procedures for adjustments that are computationally much easier to implement. The usefulness of the methodology is illustrated using a problem of predicting surface roughness in a microcutting process and the optimization of a spot-welding process.