The dual CUSUM charts with auxiliary information for process mean

Abstract

The CUSUM chart is usually designed based on a known shift size when monitoring the process mean. In practice, shift size is rarely known but it can be assumed to vary within an interval. With such a range of shift size, the dual CUSUM (DCUSUM) chart provides more sensitivity than the CUSUM chart. In this paper, auxiliary information based (AIB) DCUSUM and dual Crosier CUSUM (DCCUSUM) charts with and without fast initial response (FIR) features are proposed for efficiently monitoring the infrequent changes in the process mean, named the AIB-DCUSUM and AIB-DCCUSUM charts, respectively. Monte Carlo simulations are used to compute the run length characteristics of these control charts. The AIB-DCUSUM and AIB-DCCUSUM charts with and without FIR features are compared with the DCUSUM, DCCUSUM and AIB-CUSUM charts in terms of the integral relative average run length. It is found that the proposed charts show better performance when detecting mean shifts in different ranges. A simulated dataset is considered to illustrate the implementation of existing and proposed charts.

KEYWORDS:

• Auxiliary information
• Average run length
• Control chart
• CUSUM
• DCUSUM
• Process mean
• Statistical Process Control

Acknowledgments

The authors are thankful to the anonymous reviewer for providing useful comments that led to an improved version of the article.