Single and dual reference-free CUSCORE charts for detecting unknown patterned mean shifts

Abstract

Most of the control charts in the literature focus on detecting constant mean shifts. In practice, dynamic and time-varying process mean shifts are prevalent in the monitoring of feedback-control and autocorrelated processes. The cumulative score (CUSCORE) charts have been proposed in the literature to detect dynamic and time-varying process shifts. One of such control charts is a reference-free CUSCORE (called RFCS-I) chart that may detect unknown patterned mean shifts effectively. In this paper, single and dual CUSCORE charts are developed to enable an efficient detection of unknown patterned mean shifts. The developed single CUSCORE chart, called the RFCS-II chart, is based on the control charting structure of the Crosier CUSUM (called CU-II) chart. Additionally, two RFCS-I charts are integrated with reflecting boundaries, while an integration of two RFCS-II charts is also made, to develop the dual RFCS-I (DRFCS-I) and dual RFCS-II (DRFCS-II) charts, respectively. In addition, the RFCS-I and RFCS-II charts are integrated to propose the mixed dual reference-free CUSCORE chart, called the MDRFCS chart. In essence, four CUSCORE charts, i.e. the RFCS-II, DRFCS-I, DRFCS-II and MDRFCS charts are suggested in this paper. The Monte Carlo simulation and a real application illustrate the superiority of these developed CUSCORE charts over their existing counterparts when detecting patterned mean shifts in terms of zero-state and steady-state relative mean indexes.

Keywords:

• Control chart
• CUSUM
• Monte Carlo simulation
• process mean
• run length properties
• statistical process control

Disclosure statement

No potential conflict of interest was reported by the author(s).