Providing comprehensive control chart for monitoring of linear and nonlinear profiles using functional data analysis.

Abstract

Considering profiles as functional variables, two control charts are proposed for their monitoring in phase II. Due to its conformity with the nature of real-world profiles, applying functional model leads to proposed control charts obtained through functional data analysis techniques with desired features. These include simplicity in calculation and possibility of using them for different profiles such as linear and non-linear (even in the presence of complex within-profile Autocorrelation forms). These features distinguish the functional model from the regression models common in profile monitoring. Simulated computer simulations show that, in different states, the proposed control charts have a lower average run length than other methods, which indicates the desired performance of the proposed functional approach. Morevere, in some non-linear cases with complex autocorrelation, other methods completely fail, and only the proposed control charts are able to detect the occurring deviation, and even in these cases, the average run length of these control charts is highly desirable.