Determination of Process Capability indices for the Slope Parameter of a Single Variable Linear Profile

In many applications the quality of a process or product is best characterized and summarized by a functional relationship between a response variable and one or more explanatory variables. Profile monitoring is used to understand and to check the stability of this relationship over time. Therefore checking the capability of a profile seems essential. Process capability indices have become very popular in assessing the capability of manufacturing processes in practice during the past decade. In this paper, a method is proposed for determining the capability of a linear profile by means of calculating the capability indices for intercept and slope, independently. The intercept measures are explanatory variables that can be treated the same as single quantities. Therefore, the problem is reduced to evaluating the process capability for slope of the profile. Since the overall slope is a linear regression on a series of subsequent observations, the mutual gradients provide a set of variables for process capability study. After checking the normality and control status of the slope variables, PCRs can be evaluated for sample data