Functional process capability indices for nonlinear profile

A profile is a relationship between a response variable and one or more independent variables being controlled during the time. Process Capability Indices (PCI) are measured to evaluate the performance of processes in producing conforming products. Despite frequent applications of profile and a variety of available methods to monitor its different types, little researches have been carried out on determining capability indices of profile process. PCIs such as  and in profile state, are used to evaluate process capability in producing conforming profiles. This paper presents a functional approach for nonlinear profiles which usually expressed as nonlinear regression. Thus, functions such as pertaining technical specification limits, mean and natural tolerance limits are determined as nonlinear profiles and also functional limit is applied to determine Functional Capability Indices (FCI)  and  of functional nonlinear profile. Easy calculation and the ability to calculate FC in each period and at each point are from the advantages of this method over the other methods.