Control charts monitor processes where performance is measured by one or mu
ltiple quality characteristics. Some processes, however, are characterized
by a profile or a function. Here we focus on monitoring a process in semico
nductor manufacturing that is characterized by a linear function. While the
linear function is the simplest, it occurs frequently, for example in cali
bration studies. Two monitoring approaches are proposed: (1) monitor parame
ters, slope and intercept, with multivariate T-2 and (2) monitor average re
siduals between sample and reference lines with EWMA and R charts. Simulati
on studies indicate that both methods work well. Both methods are extendabl
e to complex functions.