Step-Change and Drift in the Parameters of Logistic Regression Profiles Using Robust Estimators: Examination and Analysis

It has been established in the literature that the most sought-after usual method for estimating the parameters of linear profiles is the least squares method, while the maximum likelihood estimation (MLE) is used for most non-linear profiles. Various robust-based methods have been presented to estimate the parameters of the model. The authors propose a novel method for estimating the parameters of simple linear profiles and three methods for logistic profiles. As such, Phase II profile monitoring was considered for regression profiles with contaminated data. That is, both basic assumptions considered in most studies and researches in the field of monitoring profiles are simultaneously violated here. The methods examined for logistic regression profiles are the maximum weighted likelihood estimation (MWLE) method, the ridge M-estimator method, and the weighted ridge M-estimator method, which is a combination of the first two methods. The results indicate that in the presence of outlier data, the type I error rate is highly inflated. Furthermore, the proposed calculation methods and their results were tested on step changes and drifts. Also, a test power diagram was plotted for each of the proposed methods. The findings indicated that the robust-based methods significantly outperformed the classical methods in terms of step-change and drift. Among the proposed robust methods, the weighted ridge M-estimate combined method exhibited the best performance, while the MLE method performed the worst among the four proposed methods.