Empirical likelihood ratio charts for profiles with attribute data and random predictors in the presence of within‐profile correlation

Abstract

AbstractProfile monitoring has been an increasingly popular statistical process control (SPC) problem recently. In many applications, quality characteristics of interest are attribute data, which can be adequately characterized by generalized linear models. Most existing control charts for monitoring such profiles in the literature assume that observations within each profile are independent, which is often violated in practice. This paper aims to provide a unified framework for Phase II monitoring of profiles with attribute data and random predictors in the presence of within‐profile correlation. To this end, a working correlation matrix is introduced to take the dependency into account. Then, a new control scheme is designed based on the empirical likelihood ratio test. The advantages of the proposed method are that both changes in the mean and the correlation can be detected, and the correlation structure is assumption‐free. Simulation studies show that the proposed method outperforms the existing schemes in nearly all cases, and it is more effective and robust. A real example of automobile warranty claims is demonstrated to illustrate the implementation of the proposed control chart.