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 have been called profiles. A few examples of such 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. No assumptions are made on the nature of form or the changes between the profiles other than finite squareintegrability. 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. Performance of the method is assessed