A Reference-Free Cuscore Chart for Dynamic Mean Change Detection and a Unified Framework for Charting Performance Comparison

Abstract

To detect and estimate nonconstant, time-varying mean shifts, statistical process control (SPC) tools, such as the cumulative score (Cuscore) and generalized likelihood ratio test (GLRT) charts, have recently been proposed. However, their efficiency is based on previous and exact knowledge of a reference pattern. In this article a reference-free Cuscore (RFCuscore) chart is proposed that can trace and detect dynamic mean changes quickly without knowing the reference pattern. In addition, a unified framework that contains most of the control charts is presented and applied for a theoretical comparison of the RFCuscore, Cuscore, GLRT, and CUSUM charts in detecting dynamic mean changes. Moreover, numerical simulations and a real example are used to illustrate and verify the results. Both theoretical analysis and numerical results show that the RFCuscore chart performs not only robustly, but also quickly in detecting both small and large dynamic mean changes.