Process Capability Analysis for NonLinear Profiles Using Depth Functions

There are practical situations in which the quality of a process or product can be better characterized by a functional relationship between a response variable and one or more explanatory variables, which is called profile. Such profiles frequently can be represented adequately using linear or nonlinear models. While there are several studies in monitoring profiles, there are few studies to evaluate the capability of a process with profile quality characteristic , specifically, there is no method in the literature to analyze process capability characterized by nonlinear profiles. In this paper, we propose two methods to measure the capability of these processes, based on the concept of functional depth. These methods do not have distributional assumptions and extend to functional data the PCIs proposed by Clements 1 to measure the capability of a process characterized by a random variable. Performance of the proposed methods is evaluated through simulation studies. An example illustrates the applicability of these methods.