Estimation of Change Point in Two-Stage Processes Subject to Step Change and Linear Trend

Abstract

When a control chart signals, it shows the process parameters have changed due to assignable cause(s). However, control chart signal is not the real time of a change in the process. Knowing the real time of change would simplify the detection and elimination of the assignable causes of variation. In this paper, a two-stage process is considered when the mean values of quality characteristics are changed under step shift and linear drift. First, a control chart based on the discriminant analysis (DA) is utilized to monitor the process. Then, when the out-of-control signal is received, the maximum likelihood estimator (MLE) based on the DA statistics, and clustering approach based on Mahalanobis distance of residuals are developed to estimate the real time of the change. The performances of the proposed estimators under different shifts are evaluated through numerical examples and a real case. The results indicate the better performance of the clustering approach rather than the MLE in most cases under both step shift and drift.