I'm an extremal and probabilistic combinatorialist. I don't know what you refer to by "profile monitoring" and "generalized least squares" but I suspect I know what it is under a different name.
My masters is in Prob & Stat from the math dept at UCSB. I think I had one course in combinatorics. My PhD dissertation uses statistical profile monitoring, which is an extension of statistical process control (SPC). Least squares relates, of course, to linear regression. Generalized least squares is looking at nonlinear regression such as logistical regression. I am looking at a response variable and using GLS to estimate the deviation from the expected value. Usually the response is a process as in SPC. My contribution will be the human response, such as a soldier response. I am trying to formulate the question I want to answer this quarter.
Does this make any sense to you at all? Did you study any mathematical statistics?