Statistical Process Monitoring of Nonlinear Profiles Using Wavelets

Many modern industrial processes are capable of generating rich and complex data records that do not readily permit the use of traditional statistical process-control techniques. For example, a "single observation" from a process might consist of n pairs of (x, y) data that can be described as y = f(x) when the process is in control. Such data structures or relationships between y and x are called profiles. Examples of profiles include calibration curves in chemical processing, oxide thickness across wafer surfaces in semiconductor manufacturing, and radar signals of military targets. In this paper, a semiparametric wavelet method is proposed for monitoring for changes in sequences of nonlinear profiles. Based on a likelihood ratio test involving a changepoint model, the method uses the spatial-adaptivity properties of wavelets to accurately detect profile changes taking nearly limitless functional forms. The method is used to differentiate between different radar profiles and its performance is assessed with Monte Carlo simulation. The results presented indicate the method can quickly detect a wide variety of changes from a given, in-control profile.