A methodology is developed for finding a window of operating conditions within which one should be able to produce a product having a specified set of quality characteristics. The only information that is assumed to be available is that contained within historical data on the process obtained during the production of a range of existing product grades. Multivariate statistical methods are used to build and to invert an empirical model of the existing plant operations to obtain a window of operating conditions that are capable of yielding the desired product, and that are still consistent with past operating procedures and constraints. The methods and concepts are illustrated using a simulated high pressure tubular reactor process for producing low density polyethylene.