On-Line Monitoring When the Process Yields a Linear Profile

TLDR

Control charts are used to monitor processes measured by quality characteristics, but many processes are better represented by a profile or function, with linear functions being the simplest and most common, such as in calibration studies. The study focuses on monitoring a semiconductor manufacturing process characterized by a linear function. The authors propose two monitoring approaches: multivariate T2 for slope and intercept parameters, and EWMA/R charts for average residuals between sample and reference lines. Simulation studies show that both methods perform well and can be extended to more complex functions.

Abstract

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 T2 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.