This work has been motivated by some issues of process monitoring in casting applications. In die casting, as time passes, material is deposited on the inside wall of the die. This foreign material can cause an unacceptable level of porosity in the output of the casting process. After accumulated material reaches a certain level, some of the output of the casting process no longer meets the specifications and the process must be stopped to clean the die. Sudden changes in output quality are also common in casting processes. The degree of porosity of the output of the casting process changes suddenly if, for example, one opens the door of the production facility thereby changing the laboratory temperature, causing an immediate larger accumulation of foreign material. Also day-to-day variation in weather, changes in humidity, and other factors can be responsible for this kind of change.