On-line monitoring when the process yields a linear profile

Control charts monitor processes where performance is measured by one or multiple quality characteristics. Some processes, however, are characterized by a profile or a function. Here we focus on monitoring a process in semiconductor manufacturing that is characterized by a linear function. While the linear function is the simplest, it occurs frequently, for example in calibration studies. Two monitoring approaches are proposed: (1) monitor parameters, slope and intercept, with multivariate T-2 and (2) monitor average residuals between sample and reference lines with EWMA and R charts. Simulation studies indicate that both methods work well. Both methods are extendable to complex functions.