Developing functional process capability indices for simple linear pro le

Abstract

A pro le is a relation between one response variable and one or more explanatory variables that represent the quality of a product or the performance of a process. Process Capability Indices (PCI) are measured to evaluate processes in producing conforming products. All existing methods that measure process capability indices in a simple linear pro le consider response variables at some levels of explanatory variable and ignore all ranges of x-values. In this paper, a functional approach is proposed to measure the process capability index of simple linear pro les in all ranges of explanatory variable. This new approach follows the traditional de nition of process capability indices and leads to their accurate values for a simple linear pro le. The functional approach uses a reference pro le, functional speci cation limits and functional natural tolerance limits to present a functional form of process capability indices. This functional form results in measuring the process capability at each level of the explanatory variable in a simple linear pro le, as well as the unique value of a process capability index for a simple linear pro le. A comparison study using a non-conforming proportion method shows the better performance of functional process capability indices in measuring the process capability in a simple linear pro le.