Comparative study of the <i>C</i>_p and <i>S</i>_pmk indices for logistic regression profile using different link functions

Abstract

In some process control applications, the quality of a process or a product can be characterized by a relationship between a response variable and one or more independent variables which is typically referred to as a profile. For an in-control process, process capability indices are widely used for the characterization of the capability of a process. Although there are several studies in monitoring profiles, there are a few studies to evaluate the process capability of the profiles. In the majority of cases, the response variable in the profile follows a normal distribution, but, sometimes, this assumption is violated. In many industrial applications, the response variable is binary or binomial, as in the case of whether a product can be classified as defective or nondefective. In this article, we calculate the Cp and Spmk indices to measure the process capability when the quality of a process is characterized by a logistic regression profile with three well-known link functions, the logit, the probit and the complementary log-log.