Residual Analysis in Generalized Function-on-Scalar Regression for an HVOF Spraying Process

The coating of materials plays an important role in various fields of engineering. Essential properties such as wear protection can be improved by a suitable coating technique. One of these techniques is high‐velocity oxygen‐fuel spraying. A drawback of high‐velocity oxygen‐fuel spraying is that it lacks reproducibility due to effects which are hard to measure directly. However, coating powder particles are observable over time during their flight towards the material and contain valuable information about the state of the process. Because of their smooth nature, measures of temperature and velocity can be assumed as target variables in generalized function‐on‐scalar regression. We propose methods to perform residual analysis in this framework aiming at the detection of individual residual functions which deviate from the majority of residuals. These methods help to detect anomalies in the process and hence improve the estimators. Functional target variables result in functional residuals whose analysis is barely explored. One reason might be that ordinary residual plots should be inspected at each observed point in time. We circumvent this infeasible procedure by the use of functional depths that help to identify unusual residuals and thereby gain deeper insight of the data‐generating process. In a simulation study, we find that a good depth for detecting trend outliers is the h‐modal depth as long as the link function is chosen correctly. In case of shape outliers rFUNTA pseudo‐depth performs well.