A process capability index for simple linear profile

Abstract

In some cases, the quality of a process or a product is characterized by a linear regression model which is also called a linear profile. Process capability index is an important concept in statistical quality control and measures the ability of a process to manufacture products that meet certain specifications. There has been little attempt to study the process capability in linear profiles. In this paper, two methods are proposed for measuring the process capability in simple linear profiles. The first method uses the percentage of nonconforming parts produced at each level of the independent variable to introduce a process capability index. The second method is a multivariate process capability approach where a vector of three components is introduced. The components of the vector assess the process dispersion, its centrality, and its location within the upper and the lower specification limits. In comparison to the only existing method, numerical analysis based on simulation studies indicates that the suggested process capability measurements perform more accurately in evaluating the capability of a process generating a simple linear profile. When the error term variance is 1 and the actual percentage of nonconformities is 0.11 %, the proposed method estimates 0.11 % nonconforming percentage and a capability index of 1.06. While the existing method results in 0.27 % nonconforming percentage and a capability index of 0.9, the existing method underestimates the process capability.